# Teh: Philosophical Perspectives on the Gauge-Gravity Duality

2013-09-28 17:31:22: Nic is about to kick off, with a
reassuring 13 slides.

The title is: Philosophical Perspectives on
Holographic Duality

2013-09-28 17:34:08: 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).

2013-09-28 17:36:25: 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.

2013-09-28 17:38:57: 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)

2013-09-28 17:42:24: 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.

2013-09-28 17:45:09: 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.

2013-09-28 17:49:18:
$T_1$ 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.

2013-09-28
17:51:24
: 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)

2013-09-28 17:53:59: 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 $SO(2,1) \times SO(2,1)$ Cherns-Simons theory.

2013-09-28 17:58:10: 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.

2013-09-28 17:57:46

2013-09-28 18:02:06: 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.

2013-09-28 18:05:52: Made it to the questions, phew.

Dave Baker: Is Witten saying that this is essentially a notational difference?

Nic: We just don’t know what dynamics is in 3D gravity.  The dynamics of the CFT, which we know more about, allows us to map initial to final states which have their gravitational correspondents.

Eleanor Knox: Puzzled by the maps we have between boundary and bulk.  Why are the co-ords. the same?

Nic: This is highly schematic.  Let me explain how the correspondence works in more detail. …

2013-09-28 18:16:41: Daniele Orti: What about dynamics?  No matter. Pure gravity there is not much to calculate.

Nic: Well the correct CFT dual would have matter states.  But we’re not sure how to get there.

[From the back]

We can look at asymptotic behavior, which we can specify, and that leads to AdS results.

Chris Wuthrich: I don’t quite understand the correspondence we have.  Are you saying that the notions of equivalence we have are not applicable?

Nic: It may be that we’re not at a sufficiently advanced level.  The categorical equivalence fails in other cases.

Another question?

CW: No, I was just saying I didn’t understand. Would you like to comment? [laughter]

Nic: Categorical tools have been applied to holography.

Sam Fletcher: But we can weaken categorical equivalence.  We don’t even know in this case what the categories are in this case to relate.  Would need to be sure of what the categories are.

Jeremy Butterfield: An old man question: long ago, the syntactic view said two theories were equivalent if they were (mtually) definitionally extensible. Halvorson would reject this, since allows labels to stick to structures [poor paraphrase].  But can model isomorphism not be improved so that having the same models i.e. having each other as one’s definitional equivalent?

[Interjection] Clark Glymour has recently responded to Halvorson somewhere along these lines.

Nic: I agree with JNB. But would be hard to write out syntactically.  Category of models is useful as it is native to modern math.  This is a good thing.

Exits, for taxi awaiting outside.  [Applause]