The Quantum Structure of Space and Time (293 pages)

Singularities 77

3.6 Discussion

T. Banks Generically, in your models you seem to have few initial states and many

final states. What does unitarity mean in a context like that?

E. Silverstein Which model are you referring to specifically?

T. Banks The model where you use the Hartle-Hawking initial state.

E. Silverstein In that model, we merely determine what that state looks like in

the bulk.
T. Banks I was under the impression that you were endorsing the fact that a
Hartle-Hawking prescription picks out one initial state.

E. Silverstein I am not claiming that consistency picks out this one state, merely

that perturbative time-dependent string theory with this initial state is well-

defined.

T. Banks So there might be an infinite Hilbert space of consistent initial states?

E. Silverstein That is what I discussed in another part of my talk. There might

only be a subset allowed by consistency.

3.7 Prepared Comments

3.7.1

Near spacelike singularity limit and a SUGRA/[Elo/K(Elo)] correspon-

dence

The consideration of the near horizon limit (Maldacena) of certain black D-

branes has greatly enriched our comprehension of string theory. In this limit, there

emerges a correspondence between two seemingly different theories: 10-dimensional

string theory in ADS spacetime on one side, and a lower-dimensional CFT on the

other side. It is believed that this correspondence maps two different descriptions

of the (continuation of the) same physics.

In recent years, the consideration of the near spacelike singularity limit of generic

(classical) solutions of 10-dimensional string theories, or 11-dimensional supergrav-

ity, has suggested the existence of a correspondence between (say) 11-dimensional

supergravity and a one-dimensional Elo/K(Elo) nonlinear (T model [l]. If this cor-

respondence were confirmed, it might provide both the basis of a new definition

of M-theory, and a description of the ‘de-emergence’ of space near a cosmological

singularity (where the 10-dimensional spatial extension would be replaced by the

infinite number of coordinates of the Elo/K(Elo) coset space).

Thibault Damour: Cosmological Singularities and El0

Cosmological billiards

The first hint of a correspondence SUGRA/[Elo/K(Elo)] (or, for short,

SUGRAIElo) emerged through the study, B la Belinskii-Khalatnikov-Lifshitz

(BKL), of the structure of cosmological singularities in string theory and SUGRAll

[a]. Belinskii, Khalatnikov and Lifshitz [3] introduced an approximate way of dis-