1. 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

2. AdS/CFT Summary N=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 s 22

3. 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

5. 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!

6. 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…

10. (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

11. We’ve produced a theory of quarks and strongly coupled glue but it is governed by  = 0 – conformal dynamics 1/r potentials – no confinement = 0

12. 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…

14. 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

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

17. 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…

18. 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…

19. 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…

20. 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

21. 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….

22. 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

23. Example: YangMills* N=4 SYM + mass for 4 gauginos + equal mass for 6 scalars Babington, Crooks, NE

24. 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

26. QCD-like Quark Summary D3-D7 system introduces quarks Deforming AdS typically generates a hard wall Inducing confinement & chiral symmetry breaking