Probing Out of Equilibrium Physics

Nick Evans University of Southampton

• D3/D7 and time dependent solutions• Thermalization• Finite T phase transitions• Quenches• Inflation

Can also apply to D3/D5 defect theory…

Orthonormal, complete set of wave functions

Add Confinement & Chiral Symmetry Breaking

Dilaton Flow Geometry: Gubser, Sfetsos

BEEGK, Ghoroku..

B field enters the DBI action as a dilaton profile – causes chiral symmetry breaking but not confinement.

Thermalizing N=2 Meson CloudsTime dependent problems for the probe are simple and the ODEs solvable in eg Mathematica

In linearized approx.. We can fill space with a cloud of non-interacting mesons…

UV

IR

Das, Nishioka , Takayanagi

For small amplitude interacting solution.. at early times we see classic perturbation theory mixing between states

Leave for long enough and presumably, time averaged, the energy per mode will look Boltzman exp(-m/kT)….

Mesons thermalize but do they dissolve into quark plasma?

Is the formation of a world-sheet zero in g_tt an horizon and hence thermalization?

A full solution at large amplitude:

Horizons come, horizons go…

Could the initial condition have contained overlap with a thermal state at line one?

To form a static or growing horizon we must have back-reaction….

Phase Transitions in Gapped SystemsEg B+T D3/D7 system

Horizon grows and eats D7 - first order phase transition…

To watch this transition in real time we use Janik’s time dependent solution for a cooling/warming fireball…

Johnson, Filev

Expectations of First Order Transition

Transition proceeds by bubble nucleation….

NE, Kalaydzhyan, Kim, Kirsch 10.11.2519

Quenches in Gapped SystemsWe can also change B at fixed T…

Rolls and over shoots

At finite T the additional physics emerges when the D7 hits the horizon… the mesonic spectrum becomes quasi-normal and there is energy loss

NE, French, Kim 1009.5678 ,

Cf Bhaseen, Gauntlett , Simons, Julian Sonner, Wiseman

Oscillation away from black hole

We have identified five behaviours

Oscillation onto black hole either on

a) first pass onto black holeb) After multiple passes over black hole

Oscillation onto black hole, loosing energy and ending in oscillatory phase just above horizon…

No change after quench…

Currently mapping out phase diagram (with Jon Shock, Keun-Young Kim)

Composite InflatonsThe simple quench from B=0 to B none zero is an inflation roll…

How can we extend this roll?

This would replace the unnatural scalar in inflation models with a strongly coupled gauge theory… ie a composite inflaton…

We need…

NE, French, Kim 1009.5678 ,1208.3060

Walking DynamicsSuch theories probably exist …

Cf Banks Zak Seiberg N=1 SUSY duality

Such theories have enhanced UV quark condensate

Constructing gravity duals of such theories is hard work.. (cf Kiritsis, Jarvinen.. Nunez, Piai… )…

What does a probe D7 see in a deformed AdS background?

The mass is just a statement of the running of the dimension of qq

The instability is due to a violation of the BF bound

Effective Probe Dynamics Alvares, NE, Kim 1204.2474

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The roll from false vacuum to true…

The meson masses of the unstable vacuum.. There is a single inflaton… whose mass falls to zero as one approaches the transition…

You can also time the roll in an explicit time dependent computation and show it increases in time as one approaches the CW transition…

If you’re willing to fine tune to the transition you can get an arbitrarily flat potential/ long roll time…

Summary

• Probe branes provide a computational simple way to study non-equilibrium problems

• Meson thermalization is present but not breakdown into a quark plasma

• Real time computations through gap-no gap phase transitions are possible

• Expected features of a quench are present - oscillations damped by energy loss to quasi-normal modes

• Can compute when strongly coupled physics contributes to cosmology now - walking dynamics seems linked to inflation…