Gauge/Gravity Duality 2

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Gauge/Gravity Duality 2
AdS/CFT Correspondence TODAY Quarks
Deforming AdS Confinement Chiral Symmetry
Breaking LATER Other brane games
Holographic effective field theory
Prof Nick Evans
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AdS/CFT Summary
N4 SYM U(Nc) l 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/a 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
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2
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Glueballs
The N4 theory is conformal and so doesnt have
bound states
A simple cure is to compactify the 3d space in
which the N4 theory lives to introduce a scale
and break conformal invariance.. Lets just do
the case where the 31d space becomes a 3-torus
with all radii equal Tr F is the dilaton
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AdS/CFT Summary
So far we are at large N
(1/90?) have adjoint matter fields not
in QCD have N4 supersymmetry
have a conformal symmetry no running coupling
do not have quarks
We have our work cut out to approach QCD!
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An N2 theory with
SO(2) on A8,A9 now acts on quarks too the quark
mass term breaks it
SO(6) broken to SO(4) on A4-A7 plus.
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(No) Confinement
Maldacena
D7
The strings representing two quarks like to tie
together an interaction energy between them
forms.. Its Coulombic V 1/r As it must be in
a conformal theory.
D3
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Weve produced a theory of quarks and strongly
coupled glue but it is governed by
b 0 conformal dynamics
1/r potentials no confinement
lt q q gt 0
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Deformation
Since N4 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
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AdS-Schwarzschild
Compact time direction
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
H
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Screening
The string between the quarks breaks and they are
screened by the plasma
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Quasi-normal modes meson melting
Linearized 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
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We now have many examples of deformed N4 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
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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
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Example N2
Pilch Warner, Polchinski, Peet, Buchel
N4 SYM mass for 2 gauginos equal mass for 4
scalars
lightest 2 scalars can have vev
scalar mass and vev cf multi-centre solutions
c is fermion mass
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Example N2
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.
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Example N1
Pilch Warner, Polchinski Strassler
N4 SYM mass for 3 gauginos equal mass for 6
scalars
GPPZ 5d equations
PS discuss arrangements of D3 in centre etc
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Example YangMills
Babington, Crooks, NE
N4 SYM mass for 4 gauginos equal mass for 6
scalars
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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
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QCD-like Quark Summary
D3-D7 system introduces quarks
Deforming AdS typically generates a hard wall
Inducing confinement chiral symmetry breaking