Topics in 2 + 1 gravity and conformal field theory

Johnson, Richard Gunn (2009) Topics in 2 + 1 gravity and conformal field theory. PhD thesis, University of Nottingham.



We study the Hamiltonian dynamics for a system of two colliding point particles coupled to (2+1)-dimensional gravity with a negative cosmological constant by anchoring the dynamics of the system to its spatial infinity. We reduce the Chern-Simons formulation of the gravitational action, finding the reduced Hamiltonian for three special cases of the particle masses, in a phase space chart coordinatised by the geodesic distance between the two particles and its conjugate momentum. The dimension of the reduced phase space is two. At the threshold of black hole formation, the black hole mass depends linearly on the momentum, in agreement with previous analysis in a holonomy-based phase space chart. We use the reduced action to compute the semiclassical probability amplitude of two particles to tunnel out of the black hole, finding that the imaginary part of the action is equal to the Bekenstein-Hawking entropy of the hole.

We also study the form that conformal field theory (CFT) correlation functions take in coset spaces of (2, C). We realise the (2, C) twistor space T in two distinct but equivalent ways, deriving some important facts about this space, and we also give one representation of another coset space B. We examine the form of CFT correlation functions in T, B and two other related spaces using techniques from representation theory and make a number of comments on the twistor transform for T.

Item Type:Thesis (PhD)
Supervisors:Krasnov, K.
Louko, J.M.T.
Faculties/Schools:UK Campuses > Faculty of Science > School of Mathematical Sciences
ID Code:675
Deposited By:Dr Richard Johnson
Deposited On:22 Sep 2010 18:29
Last Modified:22 Sep 2010 18:29

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