TIFR Annual Report 2005-06 THEORETICAL PHYSICS String Theory and Mathematical Physics

Highlights Work was continued on exact counting of black hole states and comparison with the quantum corrected macroscopic entropy. A method was developed to exactly bosonize a system of finite number of non-relativistic fermions in one dimension, with applications to many problems in field theory, string theory and condensed matter physics including the classic Tomonaga problem of bosonization of non-relativistic fermions on a circle. Gauge theoretic description of black holes was studied via the AdS/CFT correspondence, focussing on Yang Mills description of localized black holes, phase transitions between black holes and black strings, and the precise counting of supersymmetric states of N=4 super Yang Mills theory on a three-sphere in order to understand supersymmetric black holes. Noncritical string theories were reexamined in a modern context in the light of D-branes and holography, and new results were obtained for their matrix descriptions, correlators and dualities. A new class of orientifolded, supersymmetry-preserving geometries in critical string theory was found. Work was done on closed string tachyons and stringy small black rings. A vector bundle generalization of Fay's trisecant identity was proposed. The attractor phenomenon was found for non-supersymmetric extremal black holes under suitable conditions. Explicit examples in string theory were constructed including rotating geometries and a C-theorem applicable to the non-supersymmetric case was formulated. Time dependent cosmologies were studied in string theory by constructing time dependent supergravity backgrounds which have Super-Yang Mills duals in the presence of time dependent sources. The black hole-string transition of the ten dimensional small Schwarzschild black hole in anti de Sitter space times a five-sphere was described using the dual SU(N) gauge theory in the large N limit. 1 TEXT Black hole entropy The entropy of a black hole is of fundamental significance in a quantum theory of gravity because it involves all three fundamental constants of nature and offers very precise quantitative information about the quantum structure of gravity. Comparison of subleading corrections offers a nontrivial and precise test of string theory as a consistent quantum theory of gravity. In a series of papers quantum corrections to the entropy of a class of black holes in string theory were investigated. It was shown that the entropy of these black holes can be explained in terms of the microscopic statistical counting to all orders in an asymptotic expansion. The macroscopic entropy itself arises as follows. The classical spacetime geometry of these states contains a null singularity and …