DeWitt-Virasoro construction

We study a particular approach for analyzing worldsheet conformal invariance for bosonic string propagating in a curved background using hamiltonian formalism. We work in the Schrodinger picture of a single particle description of the problem where the particle moves in an infinite-dimensional space. Background independence is maintained in this approach by adopting DeWitt's (Phys.Rev.85:653-661,1952) coordinate independent formulation of quantum mechanics. This enables us to construct certain background independent notion of Virasoro generators, called DeWitt-Virasoro (DWV) generators, and invariant matrix elements of an arbitrary operator constructed out of them in spin-zero representation. We show that the DWV algebra is given by the Witt algebra with additional anomalous terms that vanish for Ricci-flat backgrounds. The actual quantum Virasoro generators should be obtained by first introducing the vacuum state and then normal ordering the DWV generators with respect to that. We demonstrate the procedure in the simple cases of flat and pp-wave backgrounds. This is a shorter version of arXiv:0912.3987 [hep-th] with many technical derivations omitted.Comment: 18 pages, shorter version of arXiv:0912.3987 [hep-th] accepted for publication in Pramana - Journal of Physic

Type IIB supergravity solutions with AdS5 from Abelian and non-Abelian T dualities

We present a large class of new backgrounds that are solutions of type IIB supergravity with a warped AdS${}_5$ factor, non-trivial axion-dilaton, $B$-field and three-form Ramond-Ramond flux but yet have no five-form flux. We obtain these solutions and many of their variations by judiciously applying non-Abelian and Abelian T-dualities, as well as coordinate shifts to AdS${}_5\times X_5$ IIB supergravity solutions with $X_5=S^5, T^{1,1}, Y^{p,q}$. We address a number of issues pertaining to charge quantization in the context of non-Abelian T-duality. We comment on some properties of the expected dual super conformal field theories by studying their CFT central charge holographically. We also use the structure of the supergravity Page charges, central charges and some probe branes to infer aspects of the dual super conformal field theories.Comment: 71 pages, one table. v2: References added, some normalizations corrected, results unchange