Maths HEP Lunchtime Seminars: A gravity/spin-model correspondence
25 November 2010 13:00 in CM101 (note: non-standard day!)
We propose a general correspondence between gravity and spin models, inspired by the well-known IR equivalence between lattice gauge theories and the spin models. This suggests a connection between continuous type Hawking-phase transitions in gravity and the continuous order-disorder transitions in
ferromagnets. The black-hole phase corresponds to the ordered and the graviton gas corresponds to the disordered phases respectively. A
simple set-up based on Einstein-dilaton gravity indicates that the
vicinity of the phase transition is governed by a linear-dilaton CFT.
Employing this CFT we calculate scaling of observables near T_c, and obtain mean-field scaling in a semi-classical approximation. In case of the XY model the Goldstone mode is identified with the zero mode of the NS-NS two-form. One can show that the second speed of sound vanishes at the transition also with the mean field exponent.