Collisions of Cosmic F- and D- Strings

Field Theory Cosmic StringInteractionsCosmic Strings from vortices formed at some phasetransition (e.g. some hybrid inflation models).Inter-vortex reconnection probability is essentially 1(numerically; Matzner).Collisions of Cosmic F- and D- Strings – p.2

¢ £¥¤§¦¢ £¨¡¢£¥ ¨ ©£¥¡¡¢String Pair Interactions and theNetworkNaively, cosmic string network density scales like.Radiation: ; Dust: . . .Collisions of Cosmic F- and D- Strings – p.3

¢ £¥¤§¦¢ £¨¡¢£¥ ¨ ©£¥¡¡¢String Pair Interactions and theNetworkNaively, cosmic string network density scales like.Radiation: ; Dust: . . .String interactions force network to lock onto scaling ofdominant species.Collisions of Cosmic F- and D- Strings – p.3

¢ £¥¤§¦¢ £¨¡¢£¥ ¨ ©£¥¡ ¡¢String Pair Interactions and theNetworkNaively, cosmic string network density scales like.Radiation: ; Dust: . . .String interactions force network to lock onto scaling ofdominant species.For a probability of interactionnetwork density scales likelosses to loop formation)., the interacting(simulations;Collisions of Cosmic F- and D- Strings – p.3

The End of Brane InflationString theory inflationary models involving movementof branes and anti-branes (& variants).Collisions of Cosmic F- and D- Strings – p.4

The End of Brane InflationString theory inflationary models involving movementof 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.4

The End of Brane InflationString theory inflationary models involving movementof 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.Collisions of Cosmic F- and D- Strings – p.4

The End of Brane InflationString theory inflationary models involving movementof 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.4

String Types and StabilityDifferent string types are (meta)-stable in differentmodels (Copeland, Myers, Polchinski).Collisions of Cosmic F- and D- Strings – p.5

String Types and StabilityDifferent string types are (meta)-stable in differentmodels (Copeland, Myers, Polchinski).Possibility of having F-, D- and-strings.Collisions of Cosmic F- and D- Strings – p.5

String Types and StabilityDifferent string types are (meta)-stable in differentmodels (Copeland, Myers, Polchinski).Possibility of having F-, D- and-strings.-strings stable in KKLMMT when no branes are inthe inflationary throat ( relatively prime, ).Collisions of Cosmic F- and D- Strings – p.5

String Types and StabilityDifferent string types are (meta)-stable in differentmodels (Copeland, Myers, Polchinski).Possibility of having F-, D- and-strings.-strings stable in KKLMMT when no branes are inthe inflationary throat ( relatively prime, ).General brane inflation (non-stabilised) models canhave long-lived F-, D- and -strings.Collisions of Cosmic F- and D- Strings – p.5

Field Theory vs String Theory Stringsdistinguishes string theory from field theorycosmic strings.Collisions of Cosmic F- and D- Strings – p.6

Field Theory vs String Theory Stringsdistinguishes string theory from field theorycosmic strings.-string networks distinguish (simple) F.T. fromstring theory cosmic strings.Collisions of Cosmic F- and D- Strings – p.6

Field Theory vs String Theory Stringsdistinguishes string theory from field theorycosmic 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.6

Field Theory vs String Theory Stringsdistinguishes string theory from field theorycosmic 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 estimatesand network simulations; detectable differences.Collisions of Cosmic F- and D- Strings – p.6

¡ ¢!" # # !%$" Field Theory vs String Theory Stringsdistinguishes string theory from field theorycosmic 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 estimatesand network simulations; detectable differences.Results:;.Collisions of Cosmic F- and D- Strings – p.6

&String Interaction TypesF+F or D+D reconnection.Collisions of Cosmic F- and D- Strings – p.7

' ©&'String Interaction Typesconnection.Collisions of Cosmic F- and D- Strings – p.7

' ©&'String Interaction Typesdisconnection.Collisions of Cosmic F- and D- Strings – p.7

Flat-Space Cosmic StringInteractionsPerform calculations in flat 10D spacetime on torii.Collisions of Cosmic F- and D- Strings – p.8

Flat-Space Cosmic StringInteractionsPerform calculations in flat 10D spacetime on torii.Account for warping by effective confining potential.Collisions of Cosmic F- and D- Strings – p.8

Flat-Space Cosmic StringInteractionsPerform 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.8

Flat-Space Cosmic StringInteractionsPerform 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

F-F InteractionCompactify 2D of 4D spacetime directions on torus anduse wound closed strings (Polchinski, 1988).Collisions of Cosmic F- and D- Strings – p.9

F-F InteractionUse unitarity to sum over all final states and macroscopicstring limit (Polchinksi 1988).Collisions of Cosmic F- and D- Strings – p.9

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WYX>Z[ \F-InteractionInteraction 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.11

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D-D Interaction:Pair ProductionAdd a second boundary for interaction of two D-strings.Collisions of Cosmic F- and D- Strings – p.13

¦‡ ¢ †§9 '10 SD-D Interaction:Pair ProductionAdd a second boundary for interaction of two D-strings.Open string spectrum for branes at an angle; Tachyon(), 4 massless fermions, . . .(at 0 impact parameter; Berkooz, Douglas, Leigh).Collisions of Cosmic F- and D- Strings – p.13

¦‡ ¢ †§9 '10 S ' ' D-D Interaction:Pair ProductionAdd a second boundary for interaction of two D-strings.Open string spectrum for branes at an angle; Tachyon(), 4 massless fermions, . . .(at 0 impact parameter; Berkooz, Douglas, Leigh).Similar for-interaction.Collisions of Cosmic F- and D- Strings – p.13

‰/¡S¨@Kˆ¨Ž§ ˆ ¦//0+S¨/KJ! ‘—‘ ˆ¨ K ¢– § – ¡ –•––0¢hD-D Interaction:Pair ProductionJ”“ ¨ ‘’‘ ˆ¨ K‘’‘ ˆ¨Jˆ“ ¨ ‘—‘ ˆ¨ K $J‘—‘ ˆ¨JˆCollisions of Cosmic F- and D- Strings – p.146„¢‚?Š ¡ ƒŒ‹¨ £¨

§¦§˜š¢¡lŸ £, ›œž§¤¡ £¡l £,¥©¥§¦ Š¡¢? @§¦6„©¨ $D-D Interaction:Pair ProductionTotal inelastic probability (Schwinger; Bachas), or theprobability of producing at least one pair of F-strings isImCollisions of Cosmic F- and D- Strings – p.15

§¦§˜š¢¡lŸ £, ›œžM N¦§¤¡ £¡l £,¥©¥§¦ Š¡¢? @§¦6„©¨ $D-D Interaction:Pair ProductionTotal inelastic probability (Schwinger; Bachas), or theprobability of producing at least one pair of F-strings isImSince, a single pair of F-strings will notcause connection. #Collisions of Cosmic F- and D- Strings – p.15

D-D Interaction:ConnectionIf few F pairs are produced, the D-strings continue butkink, stretching the F’s. F’s eventually annihilate.Collisions of Cosmic F- and D- Strings – p.16

D-D Interaction:ConnectionIf few F pairs are produced, the D-strings continue butkink, 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 rollsand D’s reconnect (Hashimoto, Taylor; Hashimoto,Nagaoka).Collisions of Cosmic F- and D- Strings – p.16

¦“/ «‚¬ R4¢ªUBV­ 0 “ D-D Interaction:ConnectionPrecise condition for reconnection(¢®°¯V­¡)./ LCollisions of Cosmic F- and D- Strings – p.17

¦“/ «‚¬ R4¢ª MN±UBV­ 0 “ D-D Interaction:ConnectionPrecise condition for reconnection(¢®°¯V­¡)./ LImpact parameter is generally small,.Collisions of Cosmic F- and D- Strings – p.17

¦“/ «‚¬ R4¢ª MN±UBV­ 0 “ D-D Interaction:ConnectionPrecise condition for reconnection(¢®°¯V­¡)./ LImpact parameter is generally small,.At most cosmic velocities, only tachyon and masslessfermions are important.Collisions of Cosmic F- and D- Strings – p.17

¦“UV«³¬ R / ²­§´ H/ «‚¬ R4¢ª MN±UBV­ 0 “ D-D Interaction:ConnectionPrecise condition for reconnection(¢®°¯V­¡)./ LImpact parameter is generally small,.At most cosmic velocities, only tachyon and masslessfermions are important.Then, 4 fermionic strings always are produced, soneed at leasttachyonic strings. 0 “ Collisions of Cosmic F- and D- Strings – p.17

¦“š˜UV«³¬ R / ²­²HUBVM N R §§´ H­ 0 “ ´ Š/ «‚¬ R4¢ª MN±¡µUBV­ 0 “ D-D Interaction:ConnectionPrecise condition for reconnection(¢®°¯V­¡)./ LImpact parameter is generally small,.At most cosmic velocities, only tachyon and masslessfermions are important.Then, 4 fermionic strings always are produced, soneed at leasttachyonic strings.Probability is 0 “ „©¨ $Collisions of Cosmic F- and D- Strings – p.17

¦¢ £¥¤D6 Ž¹¸º£»¸£»º©D·6 M¥¥£Compactification EffectsMetric and dilaton depend on compact coords,·¡ £ :.Collisions of Cosmic F- and D- Strings – p.18

D¥£D¢· 6©6¦¦$D·6Compactification Effects:Metric and dilaton depend on compact coords,. £ M¥£»¸£»º Ž¹¸º·¡£¥¤:Defines a worldsheet potential for A,¼809 'Collisions of Cosmic F- and D- Strings – p.18

D¥£D¢· 6©6¦¦$D·6'9©¦D$·6Compactification Effects:Metric and dilaton depend on compact coords,. £ M¥£»¸£»º Ž¹¸º·¡£¥¤:Defines a worldsheet potential for A,¼809 'Fluctuations of position about a minimum are! A,¼ ¾½¿V109 ' ¢!!! 8 , A,¼Collisions of Cosmic F- and D- Strings – p.18

D¡©D·O6/Fluctuations: F-StringsF-F wavefunction overlap:6 $! A,¼¿V 8!! 8 , 109 ' ¢ hCollisions of Cosmic F- and D- Strings – p.19

Fluctuations: F- & D-StringsF-D can have separated minima if dilaton depends on.Collisions of Cosmic F- and D- Strings – p.20

&# O 8ÀO•˜š9´² $$$ ¿V ' ## $Fluctuations: F- & D-StringsF-D can have separated minima if dilaton depends on.supression of wavefunction overlap volume: 8§ Collisions of Cosmic F- and D- Strings – p.20

¢Â Á M NFluctuations: D-StringsLocalised to first order.Collisions of Cosmic F- and D- Strings – p.21

09 '¢ ¢¢Â Á 9'M N¿V ² $$$´ $ ! A,¼Fluctuations: D-StringsLocalised to first order.Fluctuations induce effective impact parameter; openstring masses increase by:Collisions of Cosmic F- and D- Strings – p.21

˜š09 '¢ §¢10 A,¼¢Â Á A,¼9 !'M N¿V ² $$$´ $ “ !¿¥V ² $$$´ $Fluctuations: D-StringsLocalised to first order.Fluctuations induce effective impact parameter; openstring masses increase by:Reconnection probability supressed byCollisions of Cosmic F- and D- Strings – p.21

à M N„¢ Fluctuations in KKLMMT ModelVol.Collisions of Cosmic F- and D- Strings – p.22

·¡±D6Fluctuations in KKLMMT ModelAssume CY curvature has effectgeometry.on the throatCollisions of Cosmic F- and D- Strings – p.22

¾½¿VH M NÄÃ! 9 ' $·Fluctuations in KKLMMT ModelTwo cases:Fluctuations are localised on:Collisions of Cosmic F- and D- Strings – p.23

¾½Ã ¾½¿VH M NÄM NÃ! 9 ' $·' $ 9Fluctuations in KKLMMT ModelTwo cases:Fluctuations are localised on:Fluctuations fill the:Collisions of Cosmic F- and D- Strings – p.23

!!M$ ¿¥VResults: KKLMMT„¢ N„¢©M N„¢¿VCollisions of Cosmic F- and D- Strings – p.24 $ÅM ¢ N„¢©M NFF reconnection: ¦ Max

¦ Maxª !¿¥V„¢©M N $ÅM ¢ N„¢¿VM / „¢ N!!„¢©M N$ Results: KKLMMTFF reconnection:RequireG.U.T. value,.M N canrange between 1 and theCollisions of Cosmic F- and D- Strings – p.24

!!M $ÅM ¢ N$ ¿¥VªM N canÅ!Æ!!ÆResults: KKLMMT„¢ N„¢©M N„¢¿Vrange between 1 and theCollisions of Cosmic F- and D- Strings – p.24„¢©M N.,.FF reconnection: ¦ Max,RequireG.U.T. value ! !%$, !!$,

!!M$ ªÅ!Æ!!ÆResults: KKLMMTFF reconnection:„¢ N $ÅM ¢ N ¦ Max„¢©M N„¢¿V„¢©M N¿¥Vrange between 1 and the,M N can.RequireG.U.T. value !, !%$,. !!$,F- connection probability increased bylocalised at same ). M N (if Collisions of Cosmic F- and D- Strings – p.24

µ # # Ƙ¡­UVR N M §š¢ ÅM N´²ÅM N! $¦ MinResults: KKLMMT@¨ „©¨ …Ç 6„¢?Collisions of Cosmic F- and D- Strings – p.25 0 “ ŠDD reconnection:09 '“

µ # # Ƙ¡§š¢ 'S9Results: KKLMMTDD reconnection:@¨ „©¨ …Ç 6„¢? 0 “ Š­UVR N M ÅM N´²ÅM N! $¦ Min09 '“Supression is angle dependent; tachyon production islimited when.¢10 Collisions of Cosmic F- and D- Strings – p.25

µ # # Ƙ¡§š¢ 'S9" # # !%$Results: KKLMMTDD reconnection:@¨ „©¨ …Ç 6„¢? 0 “ Š­UVR N M ÅM N´²ÅM N! $¦ Min09 '“Supression is angle dependent; tachyon production islimited when.¢10 .Collisions of Cosmic F- and D- Strings – p.25

¡ +/!¡ //!É!É!¡¡ÊÈDetection and Bounds:&Model Tensions:(KKLMMT).(General Brane Inflation).Collisions of Cosmic F- and D- Strings – p.26

¡ +/!¡ //!ÉË¡ Ì!•É!É!¡¡Ê¢ÈDetection and Bounds:&Model Tensions:(KKLMMT).(General Brane Inflation).Cosmic Microwave Background: sensitive to..Collisions of Cosmic F- and D- Strings – p.26

¡ +/!¡ //!ÉËÉ !¡ Ì!•É!É!É !¡¡¡¡Ê///ÈDetection and Bounds:&Model Tensions:(KKLMMT).(General Brane Inflation).Cosmic Microwave Background: sensitive to..¢Gravitational wave bursts: sensitive only tofrequency sensitive to .LIGO II:.LISA:.. BurstCollisions of Cosmic F- and D- Strings – p.26

¡ +/!¡ //!ÉËÉ !É !¡ Ì!•¡É!É!É !¡¡¡¡Ê///ÈDetection and Bounds:&Model Tensions:(KKLMMT).(General Brane Inflation).Cosmic Microwave Background: sensitive to..¢Gravitational wave bursts: sensitive only tofrequency sensitive to .LIGO II:.LISA:.. BurstPulsar timing (stocastic GW background,.&):Collisions of Cosmic F- and D- Strings – p.26

¡ +/!¡ //!ÉËÉ !É !¡ Ì!•¡É!É!É !¡¡¡¡Ê///ÈDetection and Bounds:&Model Tensions:(KKLMMT).(General Brane Inflation).Cosmic Microwave Background: sensitive to..¢Gravitational wave bursts: sensitive only tofrequency sensitive to .LIGO II:.LISA:.. BurstPulsar timing (stocastic GW background,.&):Lensing: sensitive to.Collisions of Cosmic F- and D- Strings – p.26

# # !%$¡ ¢!" "Summary..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.27

Observation: Gravitational Waves-21-21.5-22-22.5-23-23.5-24-24.5-25-12 -10 -8 -6 -4-18-18.5-19-19.5-20-20.5-21-21.5-22-12 -10 -8 -6 -4GW burst sensitive to(Damour, Vilenkin [gr-qc/0104026])only, to first order.Burst frequency sensitive to network density &therefore .Collisions of Cosmic F- and D- Strings – p.28

Observation: CMB(Winstein)Collisions of Cosmic F- and D- Strings – p.29