Gauge/Gravity Duality 2

Prof Nick Evans

AdS/CFT Correspondence

TODAY

Quarks

Deforming AdS

Confinement

Chiral Symmetry Breaking

LATER

Other brane games

Holographic effective field theory

AdS/CFT SummaryN=4 SYM

U(Nc)

= g N

SO(2,4) superconformal group

SO(6) flavour (R) symmetry

RG scale

Sources and operators

Glueballs

Type IIB strings in AdS5xS5

Only gauge invariant operators

R’ = 4 pi g N

SO(2,4) metric isometries

SO(6) S5 isometries

Radial coordinate

Constants of integration in sugra field solutions

Regular linearized fluctuations of dilaton

s2 2

Glueballs The N=4 theory is conformal and so doesn’t have bound states…

A simple cure is to compactify the 3d space in which the N=4 theory lives to introduce a scale and break conformal invariance..

Lets just do the case where the 3+1d space becomes a 3-torus with all radii equal – Tr F is the dilaton…2

AdS/CFT Summary

So far we

are at large N (1/9=0?)

have adjoint matter fields not in QCD

have N=4 supersymmetry

have a conformal symmetry – no running coupling

do not have quarks

We have our work cut out to approach QCD!

An N=2 theory with

SO(6) broken to SO(4) on A4-A7 plus….

SO(2) on A8,A9 now acts on quarks too… the quark mass term breaks it…

(No) Confinement

D3

D7 The strings representing two quarks like to tie together – an interaction energy between them forms..

It’s Coulombic

V ~ 1/r

As it must be in a conformal theory….

Maldacena

We’ve produced a theory of quarks and strongly coupled glue but it is governed by

= 0 – conformal dynamics

1/r potentials – no confinement

< q q > = 0

Deformation

Since N=4 SYM and AdS5 x S5 are dual it must be true that any perturbation of one side must match a perturbation on the other…

So one can look for solutions of the supergravity Einstein equations which look like AdS in some limit…

Then try to interpret them on the field theory side…

AdS-Schwarzschild

Asymptotically AdS, SO(6) invariant at all scales… but has a horizon that swallows information at r …. Witten interpreted this as the gauge theory at finite temperature… black hole has right thermodynamic properties…

Compact time direction

H

The string between the quarks breaks and they are screened by the plasma

Screening

Quasi-normal modes & meson meltingLinearized fluctuations in eg the scalars on the D7 brane must now enter the black hole horizon…

Quasi-normal modes are those modes that near the horizon have only in-falling pieces…

The mass of the bound states become complex – they decay into the thermal bath…

We now have many examples of deformed N=4 SYM – the UV is the susy theory.. the IR has eg masses for particles breaking supersymmetry and conformality…

Confining theories develop a wall – a block to small RG scales…

A linear potential grows between the quarks…

Glueballs with a hard wall

If we impose the presence of a block on the IR radial direction we must impose a boundary condition on functions of radius… one can pick…

In pure AdS continuum of states with f(r) taking all gradients..

Now only very particular M allowed by that boundary condition

Discrete mass states with mass gap…

Example: N=2*

N=4 SYM + mass for 2 gauginos + equal mass for 4 scalars

+ lightest 2 scalars can have vev

Pilch & Warner, Polchinski, Peet, Buchel

scalar mass and vev – cf multi-centre solutions

is fermion mass

Example: N=2* Pilch & Warner, Polchinski, Peet, Buchel

Numerical solutions have a blow up in the dilaton (enhancon) that can be matched onto solutions for gauge theory coupling….

Example: N=1*

N=4 SYM + mass for 3 gauginos + equal mass for 6 scalars

GPPZ 5d equations

PS discuss arrangements of D3 in centre etc…

Pilch & Warner, Polchinski & Strassler

Example: YangMills*

N=4 SYM + mass for 4 gauginos + equal mass for 6 scalars

Babington, Crooks, NE

Example: an insightful toy

Note – in the above we never decouple superpartners…

- the physics is really in the running coupling…

- lets simplify to allow computation & insight…

Give the dilaton a profile of your choice….

hard wall

soft wall

QCD-like Quark SummaryD3-D7 system introduces quarks

Deforming AdS typically generates a hard wall

Inducing confinement & chiral symmetry breaking