Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1999-03-25
Phys.Rev. D60 (1999) 064012
Physics
High Energy Physics
High Energy Physics - Theory
14 pages, RevTeX, typos corrected, to appear in Phys. Rev. D
Scientific paper
10.1103/PhysRevD.60.064012
We study the modular transformation properties of Euclidean solutions of 3D gravity whose asymptotic geometry has the topology of a torus. These solutions represent saddle points of the grand canonical partition function with an important example being the BTZ black hole, and their properties under modular transformations are inherited from the boundary conformal field theory encoding the asymptotic dynamics. Within the Chern Simons formulation, classical solutions are characterised by specific holonomies describing the wrapping of the gauge field around cycles of the torus. We find that provided these holonomies transform in an appropriate manner, there exists an associated modular invariant grand canonical partition function and that the spectrum of saddle points naturally includes a thermal bath in $AdS_3$ as discussed by Maldacena and Strominger. Indeed, certain modular transformations can naturally be described within classical bulk dynamics as mapping between different foliations with a "time" coordinate along different cycles of the asymptotic torus.
Brotz Thorsten
Ortiz Mauricio
Ritz Adam
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