TIFR Annual Report 2003-04 THEORETICAL PHYSICS String Theory and Mathematical Physics

Research in String Theory was carried out on a very broad front, encompassing mirror symmetry, matrix models, duality, compactifications, the study of string theory in a curved background and its relation to gauge theories, and the interaction of string theory with cosmology. Some progress was made towards quantizing string theory in AdS5 × S in the limit of zero curvature, which is dual to the free limit of N = 4 Super Yang-Mills in four dimensions. A topological matrix model that encodes the scattering amplitudes of noncritical string theory was reformulated as a model with a matrix Liouville potential and open-string tachyon effective actions were investigated. The rolling tachyon of 2-dim. string theory was discussed as a non-commutative soliton in the c=1 matrix model. The solution is non-perturbative in the string coupling and leads to a finite calculation of D0 brane decay. Closed string tachyon condensation was studied in the C/ZN orbifold. An exact supergravity solution describing the decay was found, and the orbifold at large N was shown to be dual to a supergravity system. An Inflationary Model in String Theory was constructed. Mirror symmetry was extended to the heterotic string. A possible generalisation of the Fay trisecant identity to vector bundles was identified.