Symmetric backgrounds of type IIB supergravity

Abstract

A. In this paper we study homogeneous backgrounds of type IIB supergravity where the underlying geometry is that of a symmetric space. We determine which ten-dimensional lorentzian symmetric spaces (up to local isometry) admit such backgrounds and in about two thirds of the cases we determine fully their moduli space.

Classifying integrable symmetric space strings via factorized scattering

“…This agrees with the analysis in[3] where it was shown, when the B-field is on S 2 -factors, that a sufficient condition for a Lax connection to exist is that H abe H cde ∝ R ab cd , leading to the same condition on the fi's 6. This would not be true away from the low-energy limit.…”

“…We will focus here on type II supergravity which is the most interesting case. It is not hard to show that there are only two types of symmetric space solution possible [6]: pp-waves (or Cahen-Wallach spaces) or AdS n × M 10−n with M 10−n a Riemannian symmetric space. For the first class the Green-Schwarz string action becomes quadratic in light-cone gauge and hence trivially integrable.…”

“…We are therefore left with the problem of analyzing the integrability of strings in symmetric AdS n × M 10−n backgrounds. Such backgrounds were classified, for n > 2, in [7] following [6] which analyzed the type IIB case. Out of these some are known to be integrable, namely all the supersymmetric solutions plus two non-supersymmetric ones.…”

Trivial solutions of generalized supergravity vs non-abelian T-duality anomaly

“…The analysis is very similar to the one performed in [25] for the standard type IIB case. Any invariant form consists of three pieces: the volume form on CW d wedged with some number of dx i (i = d − 1, ..., 8) from Ê 10−d , a sum of other invariant forms on CW d wedged with invariant forms on Ê 10−d i.e.…”

All superalgebras for warped AdS 2 and black hole near horizon geometries

“…. , k are linearly independent Killing spinors on the spatial horizon section S. In addition the horizon conjecture implies that 30) and that the matrix ( φ r + , φ s + ) is non-degenerate because of (2.8). In what follows without loss of generality we shall take ( φ r + , φ s + ) to be proportional to the identity matrix though we shall leave φ r + , φ s + in the formulae below as this illustrates better the origin and the meaning of some of the terms.…”