ICTP After 45 Nov. 6-8, 2010

AdS charged black hole

N. Iqbal

AdS charged black hole + Dirac equation

N. Iqbal

AdS charged black hole + Dirac equation = strange metal

N. Iqbal

Strange metal (non-Fermi liquid): conducting phase found in high-Tc, heavy-fermion, and other materials, which does not fit the Landau-Fermi `Standard Model.’

Faulkner, Iqbal, Liu, McGreevy, Vegh 1003.1728

cf. Sachdev 1006.3794: AdS2 IR throat is `locally critical.’

This connection is a special case of

gauge theory =

• A connection that was unknown, and largely unsuspected, before 1997.

• The same theory, expressed in different variables

• Different classical limits of a single quantum theory (e.g. waves vs. particles).

Information flows in both directions:

gauge theory

• `Harmonic oscillator’ for gauge theory plasmas (e.g. LHC, ca. Nov. 8, 2010). η/s, etc.

• Modeling transport at a quantum critical point

Information flows in both directions:

gauge theory

• `Emergent gravity.’

• Our most complete construction of a theory of quantum gravity.

• When gravity emerges, it seems that strings, extra dimensions, branes, etc. come along as well.

Thought experiment Lesson

Gravitational scattering

.

Replace points with strings

Strings in a small box D-branes!

Black hole entropy S = A/4G

D-brane/ black brane connection

Black hole information Gauge/gravity duality!

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Emergent gravity must be holographic (‘t Hooft, Susskind): the fundamental degrees of freedom of quantum gravity in any region live on the surface, not the interior

• The Weinberg-Witten theorem.

• Black hole entropy, SBH = A/4lPlanck.

• Black hole information, which requires a radical breakdown of spacetime locality.

G. ‘t Hooft

2

The gauge theory on the boundary encodes a lot of the physics of quantum gravity. Thought experiments in an AdS box:

Black hole formation and evaporation

Hyper-Planckian scattering

Spacetime topology change

Resolution of some spacetime singularities

AdS

Conceptual questions for quantum gravity. One has a construction of gravity in AdS space in which:

1. Black hole information is preserved: Hawking radiation is pure.

2. The Bekenstein-Hawking entropy counts all the states of the black hole.

3. Lorentz invariance is preserved.

4. Instantonic wormholes do not contribute to the path integral (Arkani-Hamed, Orgera, JP, 0705.2768).

Open questions: 1.  Derive the duality! What are we missing? 2.  Extend to the large set of `landscape’ AdS vacua. So

far, AdS x X for rather special X.

3.  Find Hawking’s mistake! How, in the bulk description, does the Hawking radiation remain pure? Related: how to see discreteness of BH spectrum.

4.  Extend to local observations, not just those of boundary observer.

5.  Get out of the box! Extend the holographic principle to cosmological spacetimes:

Attempts, I

Necessary conditions for a CFT to have an effective gravitational dual: 1) Many fields → LAdS >> LPlanck; 2) Strong coupling (more precisely, large anomalous dimensions for most fields) → LAdS >> Lstring

Conjecture (Heemskerk, Penedones, JP, Sully 0907.0151): these conditions are actually sufficient. Partial result: can solve crossing conditions

in simple model, solutions 1-1 with local bulk actions.

Attempts, II

Develop the connection between evolution in the AdS radial coor- dinate z and the Wilson RG flow (Heemskerk, JP 1010.1264).

A few surprises: • Wilson flow is in full space of multi-trace operators. • Locality of the Wilson action requires isochronous gauge-fixed path integral, not Wheeler-DeWitt.

Is there any precise cutoff in the field theory that maps to the radial cutoff in the bulk? • Possible answer in terms of alternate quantization of the field theory.

Conclusions

• Gauge/gravity duality implies unexpected connections among the diverse parts of physics, which are still being unraveled.

• String theory is not such a new thing, it was hidden all along inside gauge theory; but is it not the final theory, only a stepping-stone towards it.

• The final form of the theory of quantum gravity is still mysterious, but it seems that it must be `holographic,’ nonlocal in a fundamental way.