Triangle Seminars
Tuesday, 18 Mar 2008
Infinite-dimensional diffusions and integrable equations
Pierre van Moerbeke
(Brandeis, USA)
Abstract:
It is shown that non-intersecting Brownian particles, leaving
from one point on the real line and forced to return to one or two points lead to some infinite-dimensional diffusions, which are described by non-linear PDE's. These equations have their origin in the theory of multicomponent KP equations.
It is shown that non-intersecting Brownian particles, leaving
from one point on the real line and forced to return to one or two points lead to some infinite-dimensional diffusions, which are described by non-linear PDE's. These equations have their origin in the theory of multicomponent KP equations.
Posted by: brunel
Wednesday, 19 Mar 2008
Braneworld black holes
Simon Ross
(Durham)
Abstract:
I will review the problem of constructing black holes on a braneworld with AdS bulk, and the arguments that a full classical 5D solution will correspond to a quantum corrected 4D black hole. I will show that for negative brane cosmological constant, a Schwarzschild-AdS black string in the bulk can be consistently interpreted as a quantum-corrected black hole on the brane, but the form of the quantum corrections is unlike what we would expect.
I will review the problem of constructing black holes on a braneworld with AdS bulk, and the arguments that a full classical 5D solution will correspond to a quantum corrected 4D black hole. I will show that for negative brane cosmological constant, a Schwarzschild-AdS black string in the bulk can be consistently interpreted as a quantum-corrected black hole on the brane, but the form of the quantum corrections is unlike what we would expect.
Posted by: KCL
Eikonal Methods in AdS/CFT: graviton exchange and the pomeron
Miguel Costa
(University of Porto)
Abstract:
We derive the eikonal approximation to high energy interactions in Anti-de Sitter spacetime, resuming in terms of a generalized phase shift, ladder and cross ladder graphs associated to the exchange of a spin j field, to all orders in the coupling constant. Using the AdS/CFT correspondence, the resulting amplitude determines the behavior of the dual CFT four point function for small values of cross ratios, in a Lorentzian regime. We explore the consequences of this result to the dual CFT. In the planar limit this Lorentzian amplitude is dominated by a Regge pole whose nature varies as a function of the 't Hooft coupling. At large coupling, the pole corresponds to graviton exchange in AdS, whereas at weak coupling, the pole is that of the hard perturbative BFKL pomeron. The conformal symmetry of the transverse space E2 is trivially realized on the dual holographic space H3, allowing for a unified description of both weak and strong 't Hooft coupling regimes. The analysis suggests a possible AdS eikonal resummation of multi-pomeron exchanges implementing AdS unitarity, which differs from the usual 4-dimensional eikonal exponentiation.
We derive the eikonal approximation to high energy interactions in Anti-de Sitter spacetime, resuming in terms of a generalized phase shift, ladder and cross ladder graphs associated to the exchange of a spin j field, to all orders in the coupling constant. Using the AdS/CFT correspondence, the resulting amplitude determines the behavior of the dual CFT four point function for small values of cross ratios, in a Lorentzian regime. We explore the consequences of this result to the dual CFT. In the planar limit this Lorentzian amplitude is dominated by a Regge pole whose nature varies as a function of the 't Hooft coupling. At large coupling, the pole corresponds to graviton exchange in AdS, whereas at weak coupling, the pole is that of the hard perturbative BFKL pomeron. The conformal symmetry of the transverse space E2 is trivially realized on the dual holographic space H3, allowing for a unified description of both weak and strong 't Hooft coupling regimes. The analysis suggests a possible AdS eikonal resummation of multi-pomeron exchanges implementing AdS unitarity, which differs from the usual 4-dimensional eikonal exponentiation.
Posted by: KCL