A handlebody calculus for topology change

We calculate transition probabilities for various processes involving giant gravitons and small gravitons in AdS space, using the dual N = 4 SYM theory. The normalization factors for these probabilities involve, in general, correlators for manifolds of non-trivial topology which are obtained by gluing simpler four-manifolds. This follows from the factorization properties which relate CFT correlators for different topologies. These points are illustrated, in the first instance, in the simpler example of a two dimensional Matrix CFT. We give the bulk five dimensional interpretation, involving neighborhoods of Witten graphs, of these gluing properties of the four dimensional boundary CFT. As a corollary we give a simple description, based on Witten graphs, of a multiplicity of bulk topologies corresponding to a fixed boundary topology. We also propose to interpret the correlators as topology-changing transition amplitudes between LLM geometries.

show abstract

“…We will start with a brief review of handlebody decompositions. For a physics discussion of these see [52,53].…”

mentioning

confidence: 99%

Correlators, probabilities and topologies in Script N = 4 SYM

Brown

Ramgoolam

Koch

et al. 2007

J. High Energy Phys.

View full text Add to dashboard Cite

show abstract

“…See [55]. In a past-finite causet the level of an element x is the number of links in the longest chain a < b < ... < c < x.…”

Section: Topology Changementioning

confidence: 99%

Causal Sets: Discrete Gravity

Sorkin

Lectures on Quantum Gravity

150

229

View full text Add to dashboard Cite

“…Trivial examples of topology change with CTCs are known (Borde 1997, Dowker & Garcia 1997; in which either the initial or final surface is empty -(see for example figure 3). There are also examples with no timelike curve from the initial to final surface, because they are all confined to the interior of M. In this case Σ 2 cannot be considered to be in the future of Σ 1 .…”

Section: Spacetimes With Closed Timelike Curvesmentioning

confidence: 99%

“…Some authors consider the causal structure to be more fundamental and have examined spacetimes with singularities in order to allow topology change (Dowker & Garcia 1997, Sorkin 1997). This paper does not consider singularities, it retains the framework of classical general relativityincluding a continuous spacetime manifold with a continuous metric.…”

Section: Introductionmentioning

confidence: 99%

Untitled

Hadley¹

1999

International Journal of Theoretical Physics

View full text Add to dashboard Cite

The non-classical features of quantum mechanics are reproduced using models constructed with a classical theory -general relativity. The inability to define complete initial data consistently and independently of future measurements, non-locality, and the non-Boolean logical structure are reproduced by these examples. The key feature of the models is the role of topology change. It is the breakdown of causal structure associated with topology change that leads to the apparently non-classical behaviour. For geons, topology change is required to describe the interaction of particles. It is therefore natural to regard topology change as an essential part of the measurement process. This leads to models in which the measurement imposes additional non-redundant boundary conditions. The initial state cannot be described independently of the measurement and there is a causal connection between the measurement and the initial state.

show abstract

A handlebody calculus for topology change

Cited by 29 publications

References 31 publications

Correlators, probabilities and topologies in Script N = 4 SYM

Correlators, probabilities and topologies in Script N = 4 SYM

Causal Sets: Discrete Gravity

Untitled

Contact Info

Product

Resources

About