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**AdS solutions through transgression.**
*(English)*
Zbl 1245.83060

Summary: We present new classes of explicit supersymmetric \(AdS_{3}\) solutions of type IIB supergravity with non-vanishing five-form flux and \(AdS_{2}\) solutions of \(D = 11\) supergravity with electric four-form flux. The former are dual to two-dimensional SCFTs with (0,2) supersymmetry and the latter to supersymmetric quantum mechanics with two supercharges. We also investigate more general classes of \(AdS_{3}\) solutions of type IIB supergravity and \(AdS_{2}\) solutions of \(D = 11\) supergravity which in addition have non-vanishing three-form flux and magnetic four-form flux, respectively. The construction of these more general solutions makes essential use of the Chern-Simons or “transgression” terms in the Bianchi identity or the equation of motion of the field strengths in the supergravity theories. We construct infinite new classes of explicit examples and for some of the type IIB solutions determine the central charge of the dual SCFTs. The type IIB solutions with non-vanishing three-form flux that we construct include a two-torus, and after two T-dualities and an S-duality, we obtain new \(AdS_{3}\) solutions with only the NS fields being non-trivial.

### MSC:

83E30 | String and superstring theories in gravitational theory |

83E50 | Supergravity |

81T30 | String and superstring theories; other extended objects (e.g., branes) in quantum field theory |