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.

Nic further reassures us that the talk will be mostly non-technical.

1. What is the philosophical interest of holographic duality?

2. What relevance does it have to the philosophy of quantum gravity?

Nic will connect (1) to other issues in philosophy of physics, and hope to illustrate (2).

Nic is about to kick off, with a reassuring 13 slides.

The title is: Philosophical Perspectives on Holographic Duality

Having to move much more quickly now, Huggett briefly goes over how ST implies General Relativity, first in empty space and then adding in some matter.  Question 6:  What is the significance of these results?

Huggett claims that one possible answer is: String theory is actually background independent.

Assume (i) that ST is an adequate TOE, in sense that the string spectrum includes quanta for all the background fields you like; and (ii) that the terms in the action accurately capture the effective behavior of those coherent states.  Then by (i) the G_mu_nu field is composed of stringy excitations, and by (ii) it satises the Einstein Field Equations (making it the gravitational field, and the excitations gravitons). In other words, in the most literal sense the general relativistic theory of spacetime is a low energy effective theory of strings.

Which ought to get philosophers excited!

No time for questions 😦

Huggett offers 2 alternative interpretations of T-duality, in connection with the 3rd question.   Two interpretive decisions need to be made:

•  First interpretive decision: either the T-duals agree on the physical world, or they do not. If they do . . .
• Second interpretive decision: do both say that strings literally live in a space of radius R (but represent that fact dierently); or do they represent facts the same way, and so say nothing beyond their shared consequences  (so that the radius is indeterminate between R and 1=R.)

Either way, both interpretations agree that the target space’s radius (i.e., the phenomenal space we live in) is very very big.  Whew!