The interesting point: both dual theories are required to reach an interpretation.  Witten goes back and forth between them to fix certain parameters, and constrain the form of the CFT.

In AdS/CFT the GKPW formula tells us how to relate observables of coupling fields in the bulk to fields at the boundary.

We understand the concepts of the theories (in part) through understanding their relation to their dual.  Also a heuristic tool for theory construction.

We are interested in BTZ black hole solution, the aysmpototic symmetries of which form algebras and have a central charge.

Cherns-Simons theory on a manifold with boundary induces a boundary CFT which is dual.

The central charge acquires a physical interpretation through this duality. The boundary CFT is part of the way we understand the gravitational phenomena.

Witten: This is like the S-matrix.

For holography we need a negative cosmological constant.

To reach the realm of (quantum) Cherns-Simon theory we add a topological interaction term to the Einstein–Hilbert action.

Recast as the action for two gauge fields for an $SO(2,1)\timesSO(2,1)$ Cherns-Simons theory.

Review of 3D gravity/CFT duality

the metric $ds^2$ can be written in terms of the vielbein $ds^2=\overline{g}_{ab}e^i^ae^b_j dx^idx^j$.

Set $\overline{g} to \eta$ and then we have a SU(2) [?] symmetry …. (slide sadly now departed)

$T_1$ and $T_2$ are our dual theories.

Naive account of equivalence: $\exists$ map between theories that relate respective physical quantities.

Categorical equivalence is a somewhat meta-level version of isomorphism.  Only real way we have to talk about inter (mathematical) theory relations.

Sometimes the maps are the result of a happy coincidence.  Sometimes e.g. Legendre transformation we have a more meaningful example.  Links together two theoretical structures (in distinct theories) with a similar role.

When are two theories equivalent?

An under-explored question in phil.phys.  Recent example of conflict: North and Curiel on primacy of Hamiltonian vs. Lagrangian forms of Classical Mechanics.

Halvorson attacks isomorphism as a criterion for equivalence. Suggests categorical equivalence as a remedy.

Holographic duality provides an additional, and distinct, way of thinking about equivalence.

What is the physical significance of gauge symmetries?

Many discussions in the philosophy of physics.  Dis-analogy of gauge symmetries to global symmetries via Galilean ship constructions.  Greaves and Wallace object. They claim there can be physical symmetries in terms of asymptotic symmetries, i.e. there can be Galilean ship constructions.

Notes that asymptotic symmetries play an important role in holographic duality.

Rovelli’s (very) recent paper claims gauge d.o.f. contain information about possible couplings between physical symmetries.

Some conceptual problems:

3D gravity <==> Cherns-Simons theory (quantization thereof).  Not quite clear.

(3D gravity is 2+1 space + time dimensions)

Unclear which CFT to choose as the dual, of whether they even exist.

Sources are Carlip (2005) and Witten (2007)

First, the dualities under question are conjectures.

The specific duality we’re looking at is: 3D GR with negative cosmological constant is equivalent to an appropriate conformal field theory on the boundary of AdST

Apparently none of the terms in this phrase have widespread agreement as to their precise meaning.