Gauge/Gravity Duality 2 Prof Nick Evans AdS/CFT Correspondence TODAY Quarks Deforming AdS...
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Transcript of Gauge/Gravity Duality 2 Prof Nick Evans AdS/CFT Correspondence TODAY Quarks Deforming AdS...
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