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8/3/2019 Nicholas Jones- Collisions of Cosmic F- and D- Strings
http://slidepdf.com/reader/full/nicholas-jones-collisions-of-cosmic-f-and-d-strings 1/74
Collisions of Cosmic F- and D- Strings Nicholas Jones
Cornell University
with Jackson & Polchinski [th/0405229]
(NJ, Stoica, Tye [th/0203163], [th/0303269] )
Collisions of Cosmic F- and D- Strings – p.
8/3/2019 Nicholas Jones- Collisions of Cosmic F- and D- Strings
http://slidepdf.com/reader/full/nicholas-jones-collisions-of-cosmic-f-and-d-strings 2/74
Field Theory Cosmic Strin
Interaction
Cosmic Strings from vortices formed at some phase
transition (e.g. some hybrid inflation models).
Collisions of Cosmic F- and D- Strings – p.
8/3/2019 Nicholas Jones- Collisions of Cosmic F- and D- Strings
http://slidepdf.com/reader/full/nicholas-jones-collisions-of-cosmic-f-and-d-strings 3/74
Field Theory Cosmic Strin
Interaction
Cosmic Strings from vortices formed at some phase
transition (e.g. some hybrid inflation models).Inter-vortex reconnection probability is essentially 1(numerically; Matzner).
Collisions of Cosmic F- and D- Strings – p.
8/3/2019 Nicholas Jones- Collisions of Cosmic F- and D- Strings
http://slidepdf.com/reader/full/nicholas-jones-collisions-of-cosmic-f-and-d-strings 4/74
String Pair Interactions and the
Networ
Naively, cosmic string network density scales like
¡
¢
£
¤
¢
¦
§
£
̈
¢
©
̈
¢
£
£
.Radiation:
¡
; Dust:
¡
. . .
Collisions of Cosmic F- and D- Strings – p.
8/3/2019 Nicholas Jones- Collisions of Cosmic F- and D- Strings
http://slidepdf.com/reader/full/nicholas-jones-collisions-of-cosmic-f-and-d-strings 5/74
String Pair Interactions and the
Networ
Naively, cosmic string network density scales like
¡
¢
£
¤
¢
¦
§
£
̈
¢
©
̈
¢
£
£
.Radiation:
¡
; Dust:
¡
. . .
String interactions force network to lock onto scaling of
dominant species.
Collisions of Cosmic F- and D- Strings – p.
8/3/2019 Nicholas Jones- Collisions of Cosmic F- and D- Strings
http://slidepdf.com/reader/full/nicholas-jones-collisions-of-cosmic-f-and-d-strings 6/74
String Pair Interactions and the
Networ
Naively, cosmic string network density scales like
¡
¢
£
¤
¢
¦
§
£
̈
¢
©
̈
¢
£
£
.Radiation:
¡
; Dust:
¡
. . .
String interactions force network to lock onto scaling of
dominant species.For a probability of interaction
, the interactingnetwork density scales like
!
(simulations;
losses to loop formation).
Collisions of Cosmic F- and D- Strings – p.
8/3/2019 Nicholas Jones- Collisions of Cosmic F- and D- Strings
http://slidepdf.com/reader/full/nicholas-jones-collisions-of-cosmic-f-and-d-strings 7/74
String Pair Interactions and the
Networ
Naively, cosmic string network density scales like
¡
¢
£
¤
¢
¦
§
£
̈
¢
©
̈
¢
£
£
.Radiation:
¡
; Dust:
¡
. . .
String interactions force network to lock onto scaling of
dominant species.For a probability of interaction
, the interactingnetwork density scales like
!
(simulations;
losses to loop formation).
"
#
, enhancement of cosmic string effects &observables.
Collisions of Cosmic F- and D- Strings – p.
8/3/2019 Nicholas Jones- Collisions of Cosmic F- and D- Strings
http://slidepdf.com/reader/full/nicholas-jones-collisions-of-cosmic-f-and-d-strings 8/74
The End of Brane Inflation
String theory inflationary models involving movement
of branes and anti-branes (& variants).
Collisions of Cosmic F- and D- Strings – p.
8/3/2019 Nicholas Jones- Collisions of Cosmic F- and D- Strings
http://slidepdf.com/reader/full/nicholas-jones-collisions-of-cosmic-f-and-d-strings 9/74
The End of Brane Inflation
String theory inflationary models involving movement
of branes and anti-branes (& variants).Irrespective of details (warping, compactification ...),the brane collision ending inflation is hybrid inflation.
Collisions of Cosmic F- and D- Strings – p.
8/3/2019 Nicholas Jones- Collisions of Cosmic F- and D- Strings
http://slidepdf.com/reader/full/nicholas-jones-collisions-of-cosmic-f-and-d-strings 10/74
8/3/2019 Nicholas Jones- Collisions of Cosmic F- and D- Strings
http://slidepdf.com/reader/full/nicholas-jones-collisions-of-cosmic-f-and-d-strings 11/74
The End of Brane Inflation
String theory inflationary models involving movement
of branes and anti-branes (& variants).Irrespective of details (warping, compactification ...),the brane collision ending inflation is hybrid inflation.
Inflation ends when the complex tachyon rolls.
Post inflation, string-like defects (only) are formed; nomonopoles or domain walls (NJ, Stoica, Tye; Sarangi,
Tye).
Collisions of Cosmic F- and D- Strings – p.
8/3/2019 Nicholas Jones- Collisions of Cosmic F- and D- Strings
http://slidepdf.com/reader/full/nicholas-jones-collisions-of-cosmic-f-and-d-strings 12/74
String Types and Stabilit
Different string types are (meta)-stable in different
models (Copeland, Myers, Polchinski).
Collisions of Cosmic F- and D- Strings – p.
8/3/2019 Nicholas Jones- Collisions of Cosmic F- and D- Strings
http://slidepdf.com/reader/full/nicholas-jones-collisions-of-cosmic-f-and-d-strings 13/74
String Types and Stabilit
Different string types are (meta)-stable in different
models (Copeland, Myers, Polchinski).Possibility of having F-, D- and
$
&
(
-strings.
Collisions of Cosmic F- and D- Strings – p.
8/3/2019 Nicholas Jones- Collisions of Cosmic F- and D- Strings
http://slidepdf.com/reader/full/nicholas-jones-collisions-of-cosmic-f-and-d-strings 14/74
String Types and Stabilit
Different string types are (meta)-stable in different
models (Copeland, Myers, Polchinski).Possibility of having F-, D- and
$
&
(
-strings.
$
&
(
-strings stable in KKLMMT when no branes are in
the inflationary throat ( $
&
(
relatively prime,)
$
)
"
!
0
).
Collisions of Cosmic F- and D- Strings – p.
8/3/2019 Nicholas Jones- Collisions of Cosmic F- and D- Strings
http://slidepdf.com/reader/full/nicholas-jones-collisions-of-cosmic-f-and-d-strings 15/74
String Types and Stabilit
Different string types are (meta)-stable in different
models (Copeland, Myers, Polchinski).Possibility of having F-, D- and
$
&
(
-strings.
$
&
(
-strings stable in KKLMMT when no branes are in
the inflationary throat ( $
&
(
relatively prime,)
$
)
"
!
0
).
General brane inflation (non-stabilised) models canhave long-lived F-, D- and
$
&
(
-strings.
Collisions of Cosmic F- and D- Strings – p.
8/3/2019 Nicholas Jones- Collisions of Cosmic F- and D- Strings
http://slidepdf.com/reader/full/nicholas-jones-collisions-of-cosmic-f-and-d-strings 16/74
Field Theory vs String Theory Strings
"
#
distinguishes string theory from field theory
cosmic strings.
Collisions of Cosmic F- and D- Strings – p.
8/3/2019 Nicholas Jones- Collisions of Cosmic F- and D- Strings
http://slidepdf.com/reader/full/nicholas-jones-collisions-of-cosmic-f-and-d-strings 17/74
Field Theory vs String Theory Strings
"
#
distinguishes string theory from field theory
cosmic strings.
$
&
(
-string networks distinguish (simple) F.T. fromstring theory cosmic strings.
Collisions of Cosmic F- and D- Strings – p.
8/3/2019 Nicholas Jones- Collisions of Cosmic F- and D- Strings
http://slidepdf.com/reader/full/nicholas-jones-collisions-of-cosmic-f-and-d-strings 18/74
Field Theory vs String Theory Strings
"
#
distinguishes string theory from field theory
cosmic strings.
$
&
(
-string networks distinguish (simple) F.T. fromstring theory cosmic strings.
Spectrum of tensions distinguish F.T. from string theorycosmic strings.
Collisions of Cosmic F- and D- Strings – p.
8/3/2019 Nicholas Jones- Collisions of Cosmic F- and D- Strings
http://slidepdf.com/reader/full/nicholas-jones-collisions-of-cosmic-f-and-d-strings 19/74
Field Theory vs String Theory Strings
"
#
distinguishes string theory from field theory
cosmic strings.
$
&
(
-string networks distinguish (simple) F.T. fromstring theory cosmic strings.
Spectrum of tensions distinguish F.T. from string theorycosmic strings.
Calculate
&
$
&
(
interactions for scaling estimates
and network simulations; detectable differences.
Collisions of Cosmic F- and D- Strings – p.
8/3/2019 Nicholas Jones- Collisions of Cosmic F- and D- Strings
http://slidepdf.com/reader/full/nicholas-jones-collisions-of-cosmic-f-and-d-strings 20/74
Field Theory vs String Theory Strings
"
#
distinguishes string theory from field theory
cosmic strings.
$
&
(
-string networks distinguish (simple) F.T. fromstring theory cosmic strings.
Spectrum of tensions distinguish F.T. from string theorycosmic strings.
Calculate
&
$
&
(
interactions for scaling estimates
and network simulations; detectable differences.
Results:
1 1
# 3
¡
¢
4
#
;
5 5
3
6
#
4
#
.
Collisions of Cosmic F- and D- Strings – p.
8/3/2019 Nicholas Jones- Collisions of Cosmic F- and D- Strings
http://slidepdf.com/reader/full/nicholas-jones-collisions-of-cosmic-f-and-d-strings 21/74
String Interaction Types
8
F+F or D+D reconnection.
Collisions of Cosmic F- and D- Strings – p.
8/3/2019 Nicholas Jones- Collisions of Cosmic F- and D- Strings
http://slidepdf.com/reader/full/nicholas-jones-collisions-of-cosmic-f-and-d-strings 22/74
String Interaction Types
8
$
&
(
©
$
9
&
(
9
connection.
Collisions of Cosmic F- and D- Strings – p.
8/3/2019 Nicholas Jones- Collisions of Cosmic F- and D- Strings
http://slidepdf.com/reader/full/nicholas-jones-collisions-of-cosmic-f-and-d-strings 23/74
String Interaction Types
8
$
&
(
©
$
9
&
(
9
disconnection.
Collisions of Cosmic F- and D- Strings – p.
Flat-Space Cosmic Strin
8/3/2019 Nicholas Jones- Collisions of Cosmic F- and D- Strings
http://slidepdf.com/reader/full/nicholas-jones-collisions-of-cosmic-f-and-d-strings 24/74
Flat Space Cosmic Strin
Interaction
Perform calculations in flat 10D spacetime on torii.
Collisions of Cosmic F- and D- Strings – p.
Flat-Space Cosmic Strin
8/3/2019 Nicholas Jones- Collisions of Cosmic F- and D- Strings
http://slidepdf.com/reader/full/nicholas-jones-collisions-of-cosmic-f-and-d-strings 25/74
Flat Space Cosmic Strin
Interaction
Perform calculations in flat 10D spacetime on torii.
Account for warping by effective confining potential.
Collisions of Cosmic F- and D- Strings – p.
Flat-Space Cosmic Strin
8/3/2019 Nicholas Jones- Collisions of Cosmic F- and D- Strings
http://slidepdf.com/reader/full/nicholas-jones-collisions-of-cosmic-f-and-d-strings 26/74
Flat Space Cosmic Strin
Interaction
Perform calculations in flat 10D spacetime on torii.
Account for warping by effective confining potential.Quantum fluctuations of string position give aneffective volume of compactification.
Collisions of Cosmic F- and D- Strings – p.
Flat-Space Cosmic Strin
8/3/2019 Nicholas Jones- Collisions of Cosmic F- and D- Strings
http://slidepdf.com/reader/full/nicholas-jones-collisions-of-cosmic-f-and-d-strings 27/74
at Space Cos c St
Interaction
Perform calculations in flat 10D spacetime on torii.
Account for warping by effective confining potential.Quantum fluctuations of string position give aneffective volume of compactification.
Valid if geometry varying slowly on string scale.
Collisions of Cosmic F- and D- Strings – p.
8/3/2019 Nicholas Jones- Collisions of Cosmic F- and D- Strings
http://slidepdf.com/reader/full/nicholas-jones-collisions-of-cosmic-f-and-d-strings 28/74
F-F Interaction
Compactify 2D of 4D spacetime directions on torus anduse wound closed strings (Polchinski, 1988).
Collisions of Cosmic F- and D- Strings – p.
8/3/2019 Nicholas Jones- Collisions of Cosmic F- and D- Strings
http://slidepdf.com/reader/full/nicholas-jones-collisions-of-cosmic-f-and-d-strings 29/74
F-F Interaction
Use unitarity to sum over all final states and macroscopicstring limit (Polchinksi 1988).
Collisions of Cosmic F- and D- Strings – p.
8/3/2019 Nicholas Jones- Collisions of Cosmic F- and D- Strings
http://slidepdf.com/reader/full/nicholas-jones-collisions-of-cosmic-f-and-d-strings 30/74
F-F Interaction
@
¦
A
B
C
D
C
F
G
A
B
C
D
C
F
¢
A
B
¡
G
D
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G
F
A
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¡
G
D
¡
G
F
¦
0
H
¢
P
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¢
F
$
R
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9
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9
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c
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9
t
#
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6
Collisions of Cosmic F- and D- Strings – p.1
8/3/2019 Nicholas Jones- Collisions of Cosmic F- and D- Strings
http://slidepdf.com/reader/full/nicholas-jones-collisions-of-cosmic-f-and-d-strings 31/74
F-
Interaction
Interaction of a wound closed string with a boundary; addDirichlet boundary conditions, Chan-Paton factors &
constant electric flux.
Collisions of Cosmic F- and D- Strings – p.1
8/3/2019 Nicholas Jones- Collisions of Cosmic F- and D- Strings
http://slidepdf.com/reader/full/nicholas-jones-collisions-of-cosmic-f-and-d-strings 32/74
F-
Interaction
Unitarity etc...
B
h
F
B
T
F
¡
c
d
¢
j
k
l
B
h
¡
T
F
D
n
B
h
F
n
B
T
F
j
h
¡
T
D
j
o
¡
h
h
¡
T
h
C
T
h
h
h
C
C C
¡
z
z
z
{
|
(Callan, Lovelace, Nappi, Yost; Seiberg, Witten; . . . )Collisions of Cosmic F- and D- Strings – p.1
8/3/2019 Nicholas Jones- Collisions of Cosmic F- and D- Strings
http://slidepdf.com/reader/full/nicholas-jones-collisions-of-cosmic-f-and-d-strings 33/74
D-D Interaction
8/3/2019 Nicholas Jones- Collisions of Cosmic F- and D- Strings
http://slidepdf.com/reader/full/nicholas-jones-collisions-of-cosmic-f-and-d-strings 34/74
Pair Production
Add a second boundary for interaction of two D-strings.
Collisions of Cosmic F- and D- Strings – p.1
D-D Interaction
8/3/2019 Nicholas Jones- Collisions of Cosmic F- and D- Strings
http://slidepdf.com/reader/full/nicholas-jones-collisions-of-cosmic-f-and-d-strings 35/74
Pair Production
Add a second boundary for interaction of two D-strings.
Open string spectrum for branes at an angle; Tachyon(
¢
¦
§
!
0
H
W
9
), 4 massless fermions, . . .(at 0 impact parameter; Berkooz, Douglas, Leigh).
Collisions of Cosmic F- and D- Strings – p.1
D-D Interaction
8/3/2019 Nicholas Jones- Collisions of Cosmic F- and D- Strings
http://slidepdf.com/reader/full/nicholas-jones-collisions-of-cosmic-f-and-d-strings 36/74
Pair Production
Add a second boundary for interaction of two D-strings.
Open string spectrum for branes at an angle; Tachyon(
¢
¦
§
!
0
H
W
9
), 4 massless fermions, . . .(at 0 impact parameter; Berkooz, Douglas, Leigh).
Similar for
$
&
(
-
$
9
&
(
9
interaction.
Collisions of Cosmic F- and D- Strings – p.1
D-D Interaction
8/3/2019 Nicholas Jones- Collisions of Cosmic F- and D- Strings
http://slidepdf.com/reader/full/nicholas-jones-collisions-of-cosmic-f-and-d-strings 37/74
Pair Production
¦
§
0
C
£
̈
̈
¡
T
¢
c
d
̈
G
t
̈
H
̈
u
G
t
̈
̈
u
¡
¢
§
#
¡
G
t
3
̈
u
¢
t
̈
H
̈
u
t
̈
̈
u
6
Collisions of Cosmic F- and D- Strings – p.1
8/3/2019 Nicholas Jones- Collisions of Cosmic F- and D- Strings
http://slidepdf.com/reader/full/nicholas-jones-collisions-of-cosmic-f-and-d-strings 38/74
D-D Interaction
8/3/2019 Nicholas Jones- Collisions of Cosmic F- and D- Strings
http://slidepdf.com/reader/full/nicholas-jones-collisions-of-cosmic-f-and-d-strings 39/74
Pair Production
Total inelastic probability (Schwinger; Bachas), or theprobability of producing at least one pair of F-strings is
#
§
§
0
Im
¦
#
§
l
D
#
§
l
D
#
©
&
¦
¡
¢
c
d
T
6
Since
1
!
5
¦
w
x
, a single pair of F-strings will notcause connection.
Collisions of Cosmic F- and D- Strings – p.1
D-D Interaction
8/3/2019 Nicholas Jones- Collisions of Cosmic F- and D- Strings
http://slidepdf.com/reader/full/nicholas-jones-collisions-of-cosmic-f-and-d-strings 40/74
Connection
If few F pairs are produced, the D-strings continue but
kink, stretching the F’s. F’s eventually annihilate.
Collisions of Cosmic F- and D- Strings – p.1
D-D Interaction
8/3/2019 Nicholas Jones- Collisions of Cosmic F- and D- Strings
http://slidepdf.com/reader/full/nicholas-jones-collisions-of-cosmic-f-and-d-strings 41/74
Connection
If few F pairs are produced, the D-strings continue but
kink, stretching the F’s. F’s eventually annihilate.
If many F pairs are produced, their total tension issufficient to stick the D-strings together; tachyon rolls
and D’s reconnect (Hashimoto, Taylor; Hashimoto,Nagaoka).
Collisions of Cosmic F- and D- Strings – p.1
D-D Interaction
C i
8/3/2019 Nicholas Jones- Collisions of Cosmic F- and D- Strings
http://slidepdf.com/reader/full/nicholas-jones-collisions-of-cosmic-f-and-d-strings 42/74
Connection
Precise condition for reconnectionR
ª
G
«
¬
-
H
!
0
(
¦
¢
®
̄
-
¡
G
v
).
Collisions of Cosmic F- and D- Strings – p.1
D-D Interaction
C ti
8/3/2019 Nicholas Jones- Collisions of Cosmic F- and D- Strings
http://slidepdf.com/reader/full/nicholas-jones-collisions-of-cosmic-f-and-d-strings 43/74
Connection
Precise condition for reconnectionR
ª
G
«
¬
-
H
!
0
(
¦
¢
®
̄
-
¡
G
v
).
Impact parameter is generally small,±
w
x
.
Collisions of Cosmic F- and D- Strings – p.1
D-D Interaction
C ti
8/3/2019 Nicholas Jones- Collisions of Cosmic F- and D- Strings
http://slidepdf.com/reader/full/nicholas-jones-collisions-of-cosmic-f-and-d-strings 44/74
Connection
Precise condition for reconnectionR
ª
G
«
¬
-
H
!
0
(
¦
¢
®
̄
-
¡
G
v
).Impact parameter is generally small,
±
w
x
.
At most cosmic velocities, only tachyon and masslessfermions are important.
Collisions of Cosmic F- and D- Strings – p.1
D-D Interaction
C ti
8/3/2019 Nicholas Jones- Collisions of Cosmic F- and D- Strings
http://slidepdf.com/reader/full/nicholas-jones-collisions-of-cosmic-f-and-d-strings 45/74
Connection
Precise condition for reconnectionR
ª
G
«
¬
-
H
!
0
(
¦
¢
®
̄
-
¡
G
v
).Impact parameter is generally small,
±
w
x
.
At most cosmic velocities, only tachyon and masslessfermions are important.
Then, 4 fermionic strings always are produced, so
need at least²
G
«
¬
-
H
!
0
§
r
´
tachyonic strings.
Collisions of Cosmic F- and D- Strings – p.1
D-D Interaction
Connection
8/3/2019 Nicholas Jones- Collisions of Cosmic F- and D- Strings
http://slidepdf.com/reader/full/nicholas-jones-collisions-of-cosmic-f-and-d-strings 46/74
Connection
Precise condition for reconnectionR
ª
G
«
¬
-
H
!
0
(
¦
¢
®
̄
-
¡
G
v
).Impact parameter is generally small,
±
w
x
.
At most cosmic velocities, only tachyon and masslessfermions are important.
Then, 4 fermionic strings always are produced, so
need at least²
G
«
¬
-
H
!
0
§
r
´
tachyonic strings.
Probability is
²
r
§
#
w
x
-
H
!
0
´
¡
µ
6
Collisions of Cosmic F- and D- Strings – p.1
Compactification Effect
8/3/2019 Nicholas Jones- Collisions of Cosmic F- and D- Strings
http://slidepdf.com/reader/full/nicholas-jones-collisions-of-cosmic-f-and-d-strings 47/74
Compactification Effect
Metric and dilaton depend on compact coords,¶
:£
¤
¢
¦
·
¡
h
T
¶
̧ º
£ »
̧
£ »
º
©
·
h
T
¶
w
¶
£¶
£¶
.
Collisions of Cosmic F- and D- Strings – p.1
Compactification Effect
8/3/2019 Nicholas Jones- Collisions of Cosmic F- and D- Strings
http://slidepdf.com/reader/full/nicholas-jones-collisions-of-cosmic-f-and-d-strings 48/74
Compactification Effect
Metric and dilaton depend on compact coords,¶
:£
¤
¢
¦
·
¡
h
T
¶
̧ º
£ »
̧
£ »
º
©
·
h
T
¶
w
¶
£¶
£¶
.Defines a worldsheet potential for
¶
:
V
¶
¦
e
D
¼
¶
0
H
W
9
·
h
T
¶
6
Collisions of Cosmic F- and D- Strings – p.1
Compactification Effect
8/3/2019 Nicholas Jones- Collisions of Cosmic F- and D- Strings
http://slidepdf.com/reader/full/nicholas-jones-collisions-of-cosmic-f-and-d-strings 49/74
Compactification Effect
Metric and dilaton depend on compact coords,¶
:£
¤
¢
¦
·
¡
h
T
¶
̧ º
£ »
̧
£ »
º
©
·
h
T
¶
w
¶
£¶
£¶
.Defines a worldsheet potential for
¶
:
V
¶
¦
e
D
¼
¶
0
H
W
9
·
h
T
¶
6
Fluctuations of position about a minimum are
½
¶
¶
¾
¦
W
9
0
e
D
¼
3
¿
#
©
e
D
¼
3
0
H
W
9
¢
·
h
T
3
V
D
3
6
Collisions of Cosmic F- and D- Strings – p.1
Fluctuations: F-Strings
8/3/2019 Nicholas Jones- Collisions of Cosmic F- and D- Strings
http://slidepdf.com/reader/full/nicholas-jones-collisions-of-cosmic-f-and-d-strings 50/74
Fluctuations: F Strings
F-F wavefunction overlap:
#
V
y
1 1
G
¿
#
©
e
D
¼
3
0
H
W
9
¢
·
h
T
3
V
D
3
¡
h
T
6
Collisions of Cosmic F- and D- Strings – p.1
Fluctuations: F- & D-Strings
8/3/2019 Nicholas Jones- Collisions of Cosmic F- and D- Strings
http://slidepdf.com/reader/full/nicholas-jones-collisions-of-cosmic-f-and-d-strings 51/74
Fluctuations: F & D Strings
F-D can have separated minima if dilaton depends on¶
.
Collisions of Cosmic F- and D- Strings – p.2
Fluctuations: F- & D-Strings
8/3/2019 Nicholas Jones- Collisions of Cosmic F- and D- Strings
http://slidepdf.com/reader/full/nicholas-jones-collisions-of-cosmic-f-and-d-strings 52/74
Fluctuations: F & D Strings
F-D can have separated minima if dilaton depends on¶
.8
supression of wavefunction overlap volume:
#
V
y
1 5
À
#
V
y
1 1
§
¶
5
¶
5
W
9
¿
²
6 6 6
´
6
Collisions of Cosmic F- and D- Strings – p.2
Fluctuations: D-Strings
8/3/2019 Nicholas Jones- Collisions of Cosmic F- and D- Strings
http://slidepdf.com/reader/full/nicholas-jones-collisions-of-cosmic-f-and-d-strings 53/74
g
Localised to first orderÁ
¶
¢
Â
w
x .
Collisions of Cosmic F- and D- Strings – p.2
Fluctuations: D-Strings
8/3/2019 Nicholas Jones- Collisions of Cosmic F- and D- Strings
http://slidepdf.com/reader/full/nicholas-jones-collisions-of-cosmic-f-and-d-strings 54/74
g
Localised to first orderÁ
¶
¢
Â
w
x .
Fluctuations induce effective impact parameter; openstring masses increase by:
¶
¢
0
H
W
9
¢
W
9
e
D
¼
3
¿
²
6 6 6
´
6
Collisions of Cosmic F- and D- Strings – p.2
Fluctuations: D-Strings
8/3/2019 Nicholas Jones- Collisions of Cosmic F- and D- Strings
http://slidepdf.com/reader/full/nicholas-jones-collisions-of-cosmic-f-and-d-strings 55/74
g
Localised to first orderÁ
¶
¢
Â
w
x .
Fluctuations induce effective impact parameter; openstring masses increase by:
¶
¢
0
H
W
9
¢
W
9
e
D
¼
3
¿
²
6 6 6
´
6
Reconnection probability supressed by
§
#
0
H
e
D
¼
3
¿
²
6 6 6
´
6
Collisions of Cosmic F- and D- Strings – p.2
Fluctuations in KKLMMT Mode
8/3/2019 Nicholas Jones- Collisions of Cosmic F- and D- Strings
http://slidepdf.com/reader/full/nicholas-jones-collisions-of-cosmic-f-and-d-strings 56/74
Fluctuations in KKLMMT Mode
Vol
Ã
w
x
¢
.Collisions of Cosmic F- and D- Strings – p.2
Fluctuations in KKLMMT Mode
8/3/2019 Nicholas Jones- Collisions of Cosmic F- and D- Strings
http://slidepdf.com/reader/full/nicholas-jones-collisions-of-cosmic-f-and-d-strings 57/74
Assume CY curvature has effect
±
·
¡
h
T
on the throatgeometry.Collisions of Cosmic F- and D- Strings – p.2
Fluctuations in KKLMMT Mode
8/3/2019 Nicholas Jones- Collisions of Cosmic F- and D- Strings
http://slidepdf.com/reader/full/nicholas-jones-collisions-of-cosmic-f-and-d-strings 58/74
Two cases:
Fluctuations are localised on Ã
:
½
¶
¶
¾
Ä
r
w
x
¿
·
3
W
9
6
Collisions of Cosmic F- and D- Strings – p.2
Fluctuations in KKLMMT Mode
8/3/2019 Nicholas Jones- Collisions of Cosmic F- and D- Strings
http://slidepdf.com/reader/full/nicholas-jones-collisions-of-cosmic-f-and-d-strings 59/74
Two cases:
Fluctuations are localised on Ã
:
½
¶
¶
¾
Ä
r
w
x
¿
·
3
W
9
6
Fluctuations fill the Ã
:½
¶
¶
¾
w
x
W
9
6
Collisions of Cosmic F- and D- Strings – p.2
Results: KKLMM
8/3/2019 Nicholas Jones- Collisions of Cosmic F- and D- Strings
http://slidepdf.com/reader/full/nicholas-jones-collisions-of-cosmic-f-and-d-strings 60/74
FF reconnection:
1 1
¦ Max
#
6
Å
w
¢
x
¿
¢
#
©
w
x
&
# 3 3
w
G
¢
x
¢
¿
¢
#
©
w
x
6
Collisions of Cosmic F- and D- Strings – p.2
Results: KKLMM
8/3/2019 Nicholas Jones- Collisions of Cosmic F- and D- Strings
http://slidepdf.com/reader/full/nicholas-jones-collisions-of-cosmic-f-and-d-strings 61/74
FF reconnection:
1 1
¦ Max
#
6
Å
w
¢
x
¿
¢
#
©
w
x
&
# 3 3
w
G
¢
x
¢
¿
¢
#
©
w
x
6
Require ª
# 0
,w
x
can range between 1 and theG.U.T. value
#
!
0 3
.
Collisions of Cosmic F- and D- Strings – p.2
Results: KKLMM
8/3/2019 Nicholas Jones- Collisions of Cosmic F- and D- Strings
http://slidepdf.com/reader/full/nicholas-jones-collisions-of-cosmic-f-and-d-strings 62/74
FF reconnection:
1 1
¦ Max
#
6
Å
w
¢
x
¿
¢
#
©
w
x
&
# 3 3
w
G
¢
x
¢
¿
¢
#
©
w
x
6
Require ª
# 0
,w
x
can range between 1 and theG.U.T. value
#
!
0 3
.
Æ
0 3
,
1 1
3
6
0 Å
,Æ
# 3 3
,
1 1
3
6
3 #
.
Collisions of Cosmic F- and D- Strings – p.2
Results: KKLMM
8/3/2019 Nicholas Jones- Collisions of Cosmic F- and D- Strings
http://slidepdf.com/reader/full/nicholas-jones-collisions-of-cosmic-f-and-d-strings 63/74
FF reconnection:
1 1
¦ Max
#
6
Å
w
¢
x
¿
¢
#
©
w
x
&
# 3 3
w
G
¢
x
¢
¿
¢
#
©
w
x
6
Require ª
# 0
,w
x
can range between 1 and theG.U.T. value
#
!
0 3
.
Æ
0 3
,
1 1
3
6
0 Å
,Æ
# 3 3
,
1 1
3
6
3 #
.
F-
$
&
(
connection probability increased by#
!
w
x (if
localised at same¶
).
Collisions of Cosmic F- and D- Strings – p.2
Results: KKLMM
8/3/2019 Nicholas Jones- Collisions of Cosmic F- and D- Strings
http://slidepdf.com/reader/full/nicholas-jones-collisions-of-cosmic-f-and-d-strings 64/74
DD reconnection:
5 5
Æ
§
#
w
x
-
H
!
0
¡
µ
Ç
T
¢
c
d
&
¶
¢
0
H
W
9
¦ Min²
# Å
w
x
&
3
6
Å
w
x
´
Collisions of Cosmic F- and D- Strings – p.2
Results: KKLMM
8/3/2019 Nicholas Jones- Collisions of Cosmic F- and D- Strings
http://slidepdf.com/reader/full/nicholas-jones-collisions-of-cosmic-f-and-d-strings 65/74
DD reconnection:
5 5
Æ
§
#
w
x
-
H
!
0
¡
µ
Ç
T
¢
c
d
&
¶
¢
0
H
W
9
¦ Min²
# Å
w
x
&
3
6
Å
w
x
´
Supression is angle dependent; tachyon production is
limited when
"
¶
¢
!
0
H
W
9
.
Collisions of Cosmic F- and D- Strings – p.2
Results: KKLMM
8/3/2019 Nicholas Jones- Collisions of Cosmic F- and D- Strings
http://slidepdf.com/reader/full/nicholas-jones-collisions-of-cosmic-f-and-d-strings 66/74
DD reconnection:
5 5
Æ
§
#
w
x
-
H
!
0
¡
µ
Ç
T
¢
c
d
&
¶
¢
0
H
W
9
¦ Min²
# Å
w
x
&
3
6
Å
w
x
´
Supression is angle dependent; tachyon production is
limited when
"
¶
¢
!
0
H
W
9
.
5 5
3
6
#
4
#
.
Collisions of Cosmic F- and D- Strings – p.2
Detection and Bounds: & È
8/3/2019 Nicholas Jones- Collisions of Cosmic F- and D- Strings
http://slidepdf.com/reader/full/nicholas-jones-collisions-of-cosmic-f-and-d-strings 67/74
Model Tensions:# 3
¡
GC
É
# 3
¡
Ê
(KKLMMT).# 3
¡
G G
É
# 3
¡
(General Brane Inflation).
Collisions of Cosmic F- and D- Strings – p.2
Detection and Bounds: & È
8/3/2019 Nicholas Jones- Collisions of Cosmic F- and D- Strings
http://slidepdf.com/reader/full/nicholas-jones-collisions-of-cosmic-f-and-d-strings 68/74
Model Tensions:# 3
¡
GC
É
# 3
¡
Ê
(KKLMMT).# 3
¡
G G
É
# 3
¡
(General Brane Inflation).
Cosmic Microwave Background: sensitive to
¢
!
.É
Ë
# 3
¡
Ì
.
Collisions of Cosmic F- and D- Strings – p.2
Detection and Bounds: & È
8/3/2019 Nicholas Jones- Collisions of Cosmic F- and D- Strings
http://slidepdf.com/reader/full/nicholas-jones-collisions-of-cosmic-f-and-d-strings 69/74
Model Tensions:# 3
¡
GC
É
# 3
¡
Ê
(KKLMMT).# 3
¡
G G
É
# 3
¡
(General Brane Inflation).
Cosmic Microwave Background: sensitive to
¢
!
.É
Ë
# 3
¡
Ì
.
Gravitational wave bursts: sensitive only to . Burstfrequency sensitive to
.LIGO II:
É
# 3
¡
G G
.
LISA:É
# 3
¡
G
.
Collisions of Cosmic F- and D- Strings – p.2
Detection and Bounds: & È
8/3/2019 Nicholas Jones- Collisions of Cosmic F- and D- Strings
http://slidepdf.com/reader/full/nicholas-jones-collisions-of-cosmic-f-and-d-strings 70/74
Model Tensions:# 3
¡
GC
É
# 3
¡
Ê
(KKLMMT).# 3
¡
G G
É
# 3
¡
(General Brane Inflation).
Cosmic Microwave Background: sensitive to
¢
!
.É
Ë
# 3
¡
Ì
.
Gravitational wave bursts: sensitive only to . Burstfrequency sensitive to
.LIGO II:
É
# 3
¡
G G
.
LISA:É
# 3
¡
G
.
Pulsar timing (stocastic GW background, &
):É
"
# 3
¡
.
Collisions of Cosmic F- and D- Strings – p.2
Detection and Bounds: & È
8/3/2019 Nicholas Jones- Collisions of Cosmic F- and D- Strings
http://slidepdf.com/reader/full/nicholas-jones-collisions-of-cosmic-f-and-d-strings 71/74
Model Tensions:# 3
¡
GC
É
# 3
¡
Ê
(KKLMMT).# 3
¡
G G
É
# 3
¡
(General Brane Inflation).
Cosmic Microwave Background: sensitive to
¢
!
.É
Ë
# 3
¡
Ì
.
Gravitational wave bursts: sensitive only to . Burstfrequency sensitive to
.LIGO II:
É
# 3
¡
G G
.
LISA:É
# 3
¡
G
.
Pulsar timing (stocastic GW background, &
):É
"
# 3
¡
.
Lensing: sensitive to .Collisions of Cosmic F- and D- Strings – p.2
Summar
8/3/2019 Nicholas Jones- Collisions of Cosmic F- and D- Strings
http://slidepdf.com/reader/full/nicholas-jones-collisions-of-cosmic-f-and-d-strings 72/74
1 1
# 3
¡
¢
4
#
.
5 5
3
6
#
4
#
.In most cases distinguishable from gauge theorystrings; enhanced densities at a given tension.
$
&
(
-string networks can be very different from scalingsolutions; interesting or disasterous?
Collisions of Cosmic F- and D- Strings – p.2
Observation: Gravitational Waves
8/3/2019 Nicholas Jones- Collisions of Cosmic F- and D- Strings
http://slidepdf.com/reader/full/nicholas-jones-collisions-of-cosmic-f-and-d-strings 73/74
-12 -10 -8 -6 -4
-25
-24.5
-24
-23.5
-23
-22.
5
-22
-21.5
-21
-12 -10 -8 -6 -4
-22
-21.5
-21
-20.5
-20
-19.5
-19
-18.5
-18
(Damour, Vilenkin [gr-qc/0104026])
GW burst sensitive to only, to first order.
Burst frequency sensitive to network density &therefore
.
Collisions of Cosmic F- and D- Strings – p.2
Observation: CMB
Recommended