Nicholas Jones- Collisions of Cosmic F- and 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 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.



Field Theory Cosmic Strin

Interaction

Cosmic Strings from vortices formed at some phase

transition (e.g. some hybrid inflation models).




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).




String Pair Interactions and the

Networ

Naively, cosmic string network density scales like

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.Radiation:

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; Dust:

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. . .





Networ


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.Radiation:

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; Dust:

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. . .

String interactions force network to lock onto scaling of

dominant species.





Networ


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̈

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.Radiation:

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; Dust:

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. . .


dominant species.For a probability of interaction

, the interactingnetwork density scales like

!

(simulations;

losses to loop formation).





Networ


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̈

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.Radiation:

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; Dust:

¡

. . .


dominant species.For a probability of interaction

, the interactingnetwork density scales like

!

(simulations;

losses to loop formation).

"

#

, enhancement of cosmic string effects &observables.




The End of Brane Inflation

String theory inflationary models involving movement

of branes and anti-branes (& variants).






of branes and anti-branes (& variants).Irrespective of details (warping, compactification ...),the brane collision ending inflation is hybrid inflation.








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).




String Types and Stabilit

Different string types are (meta)-stable in different

models (Copeland, Myers, Polchinski).






models (Copeland, Myers, Polchinski).Possibility of having F-, D- and

$

&

(

-strings.







$

&

(

-strings.

$

&

(

-strings stable in KKLMMT when no branes are in

the inflationary throat ( $

&

(

relatively prime,)

$

)

"

!

0

).







$

&

(

-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.




Field Theory vs String Theory Strings

"

#

distinguishes string theory from field theory

cosmic strings.





"

#


cosmic strings.

$

&

(

-string networks distinguish (simple) F.T. fromstring theory cosmic strings.





"

#


cosmic strings.

$

&

(


Spectrum of tensions distinguish F.T. from string theorycosmic strings.





"

#


cosmic strings.

$

&

(



Calculate

&

$

&

(

interactions for scaling estimates

and network simulations; detectable differences.





"

#


cosmic strings.

$

&

(



Calculate

&

$

&

(

interactions for scaling estimates

and network simulations; detectable differences.

Results:

1 1

# 3

¡

¢

4

#

;

5 5

3

6

#

4

#

.




String Interaction Types

8

F+F or D+D reconnection.





8

$

&

(

©

$

9

&

(

9

connection.





8

$

&

(

©

$

9

&

(

9

disconnection.


Flat-Space Cosmic Strin



Flat Space Cosmic Strin

Interaction

Perform calculations in flat 10D spacetime on torii.






Interaction


Account for warping by effective confining potential.






Interaction


Account for warping by effective confining potential.Quantum fluctuations of string position give aneffective volume of compactification.





at Space Cos c St

Interaction


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.




F-F Interaction

Compactify 2D of 4D spacetime directions on torus anduse wound closed strings (Polchinski, 1988).




F-F Interaction

Use unitarity to sum over all final states and macroscopicstring limit (Polchinksi 1988).




F-F Interaction

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B

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6

Collisions of Cosmic F- and D- Strings – p.1



F-

Interaction

Interaction of a wound closed string with a boundary; addDirichlet boundary conditions, Chan-Paton factors &

constant electric flux.




F-

Interaction

Unitarity etc...

B

h

F

B

T

F

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h

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(Callan, Lovelace, Nappi, Yost; Seiberg, Witten; . . . )Collisions of Cosmic F- and D- Strings – p.1



D-D Interaction



Pair Production

Add a second boundary for interaction of two D-strings.


D-D Interaction



Pair Production


Open string spectrum for branes at an angle; Tachyon(

¢

¦

§

!

0

H

W

9

), 4 massless fermions, . . .(at 0 impact parameter; Berkooz, Douglas, Leigh).


D-D Interaction



Pair Production


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.


D-D Interaction



Pair Production

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§

0

C

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t

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§

#

¡

G

t

3

̈

u

¢

t

̈

H

̈

u

t

̈

̈

u

6




D-D Interaction



Pair Production

Total inelastic probability (Schwinger; Bachas), or theprobability of producing at least one pair of F-strings is

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§

§

0

Im

¦

#

§

l

D

#

§

l

D

#

©

&

¦

¡

¢

c

d

T

6

Since

1

!

5

¦

w

x

, a single pair of F-strings will notcause connection.


D-D Interaction



Connection

If few F pairs are produced, the D-strings continue but

kink, stretching the F’s. F’s eventually annihilate.


D-D Interaction



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).


D-D Interaction

C i



Connection

Precise condition for reconnectionR

ª

G

«

¬

-

H

!

0

(

¦

¢

®

̄

-

¡

G

v

).


D-D Interaction

C ti



Connection


ª

G

«

¬

-

H

!

0

(

¦

¢

®

̄

-

¡

G

v

).

Impact parameter is generally small,±

w

x

.


D-D Interaction

C ti



Connection


ª

G

«

¬

-

H

!

0

(

¦

¢

®

̄

-

¡

G

v

).Impact parameter is generally small,

±

w

x

.

At most cosmic velocities, only tachyon and masslessfermions are important.


D-D Interaction

C ti



Connection


ª

G

«

¬

-

H

!

0

(

¦

¢

®

̄

-

¡

G

v


±

w

x

.


Then, 4 fermionic strings always are produced, so

need at least²

G

«

¬

-

H

!

0

§

r

´

tachyonic strings.


D-D Interaction

Connection



Connection


ª

G

«

¬

-

H

!

0

(

¦

¢

®

̄

-

¡

G

v


±

w

x

.


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


Compactification Effect




Metric and dilaton depend on compact coords,¶

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¡

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T

¶

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£ »

̧

£ »

º

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·

h

T

¶

w

¶

£¶

£¶

.







:£

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h

T

¶

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£ »

̧

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º

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·

h

T

¶

w

¶

£¶

£¶

.Defines a worldsheet potential for

¶

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D

¼

¶

0

H

W

9

·

h

T

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6







:£

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£ »

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·

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.Defines a worldsheet potential for

¶

:

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¶

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e

D

¼

¶

0

H

W

9

·

h

T

¶

6

Fluctuations of position about a minimum are

½

¶

¶

¾

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W

9

0

e

D

¼

3

¿

#

©

e

D

¼

3

0

H

W

9

¢

·

h

T

3

V

D

3

6


Fluctuations: F-Strings



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


Fluctuations: F- & D-Strings



Fluctuations: F & D Strings

F-D can have separated minima if dilaton depends on¶

.


Fluctuations: F- & D-Strings



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


Fluctuations: D-Strings



g

Localised to first orderÁ

¶

¢

Â

w

x .





g


¶

¢

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





g


¶

¢

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


Fluctuations in KKLMMT Mode




Vol

Ã

w

x

¢

.Collisions of Cosmic F- and D- Strings – p.2




Assume CY curvature has effect

±

·

¡

h

T

on the throatgeometry.Collisions of Cosmic F- and D- Strings – p.2




Two cases:

Fluctuations are localised on Ã

:

½

¶

¶

¾

Ä

r

w

x

¿

·

3

W

9

6





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


Results: KKLMM



FF reconnection:

1 1

¦ Max

#

6

Å

w

¢

x

¿

¢

#

©

w

x

&

# 3 3

w

G

¢

x

¢

¿

¢

#

©

w

x

6


Results: KKLMM



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

.


Results: KKLMM



FF reconnection:

1 1

¦ Max

#

6

Å

w

¢

x

¿

¢

#

©

w

x

&

# 3 3

w

G

¢

x

¢

¿

¢

#

©

w

x

6

Require ª

# 0

,w

x


#

!

0 3

.

Æ

0 3

,

1 1

3

6

0 Å

,Æ

# 3 3

,

1 1

3

6

3 #

.


Results: KKLMM



FF reconnection:

1 1

¦ Max

#

6

Å

w

¢

x

¿

¢

#

©

w

x

&

# 3 3

w

G

¢

x

¢

¿

¢

#

©

w

x

6

Require ª

# 0

,w

x


#

!

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¶

).


Results: KKLMM



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

´


Results: KKLMM



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

.


Results: KKLMM



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

#

.


Detection and Bounds: & È



Model Tensions:# 3

¡

GC

É

# 3

¡

Ê

(KKLMMT).# 3

¡

G G

É

# 3

¡

(General Brane Inflation).





Model Tensions:# 3

¡

GC

É

# 3

¡

Ê

(KKLMMT).# 3

¡

G G

É

# 3

¡


Cosmic Microwave Background: sensitive to

¢

!

.É

Ë

# 3

¡

Ì

.





Model Tensions:# 3

¡

GC

É

# 3

¡

Ê

(KKLMMT).# 3

¡

G G

É

# 3

¡



¢

!

.É

Ë

# 3

¡

Ì

.

Gravitational wave bursts: sensitive only to . Burstfrequency sensitive to

.LIGO II:

É

# 3

¡

G G

.

LISA:É

# 3

¡

G

.





Model Tensions:# 3

¡

GC

É

# 3

¡

Ê

(KKLMMT).# 3

¡

G G

É

# 3

¡



¢

!

.É

Ë

# 3

¡

Ì

.


.LIGO II:

É

# 3

¡

G G

.

LISA:É

# 3

¡

G

.

Pulsar timing (stocastic GW background, &

):É

"

# 3

¡

.





Model Tensions:# 3

¡

GC

É

# 3

¡

Ê

(KKLMMT).# 3

¡

G G

É

# 3

¡



¢

!

.É

Ë

# 3

¡

Ì

.


.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



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?


Observation: Gravitational Waves



-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

.


Observation: CMB



(Winstein)Collisions of Cosmic F- and D- Strings – p.2

Documents

Nicholas Jones- Collisions of Cosmic F- and D- Strings