What is the arena in which physical reality unfolds? (From Albert)  That is what is at stake.

But EK will be questioning this approach.

1. Which is more fundamental?

Do they have different domains? Cope better with closely related cases?

2. Which objects represent space-time role?

EK: this is to be functionally determined (one of those controversial claims).

Contrast `functional kind’ with `compositional kind.’  We specify functional role and then look for what instantiates that role in the theory.

Take it for granted that AdS/CFT correspondence holds.  What are the realist interpretational options?

1. Bulk theory is reality.

2. Boundary theory is reality

3. Both represent the same reality?

How do we make sense of 3?

Intends to say many controversial things about spacetime. So leave objections til the end.

The debate we will be looking at:  holonomies (Belot, Healey) vs. fibre bundle substantivalism (Arntzenius, Nounou).

Aharonov-Bohm effect used to argue that holonomies about closed paths to be the fundamental physical quantities.

Arntzenius: Fibre bundles *really exist* and their parts.

Obviously dimensionality will be distinct here.

AdS/CFT is a generic name for the class of conjectures about dualities linking higher and lower dimensional theories.

Can we make sense of the idea that these two descriptions are of the *same* reality? Is there not a fact of the matter about how many dimensions there are?

But there questions are not so weird for philosophy, really.  Think of gauge theory arguments; configuration space realists in quantum theory.

Reassures us that this will *really* be non-technical.

Compares self to opinionated weekender in the land of String Theory (along lines of Nick’s earlier metaphor). [Laughter]

We will address a slightly more familiar case: gauge theories on fibre bundles.

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]

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. …

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.