### DFPD-11/TH/1 Constructing Lifshitz solutions from AdS

"... cassani, faedo @ pd.infn.it Under general assumptions, we show that a gravitational theory in d + 1 dimensions admitting an AdS solution can be reduced to a d-dimensional theory containing a Lifshitz solution with dynamical exponent z = 2. Working in a d = 4, N = 2 supergravity setup, we prove that ..."

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cassani, faedo @ pd.infn.it Under general assumptions, we show that a gravitational theory in d + 1 dimensions admitting an AdS solution can be reduced to a d-dimensional theory containing a Lifshitz solution with dynamical exponent z = 2. Working in a d = 4, N = 2 supergravity setup, we prove that if the AdS background is N = 2 supersymmetric, then the Lifshitz geometry preserves 1/4 of the supercharges, and we construct the corresponding Killing spinors. We illustrate these results in examples from supersymmetric consistent truncations of type IIB supergravity, enhancing the class of known 4-dimensional Lifshitz solutions of string theory. As a byproduct, we find a new AdS4 × S1 × T 1,1 solution of type IIB. ar X iv

### Classical Integrability of the Squashed Three-sphere, Warped AdS3 and Schroedinger Spacetime via T–Duality

"... We discuss the integrability of 2d non-linear sigma models with target space being the squashed three-sphere, warped anti–de Sitter space and the Schroedinger spacetime. These models can be obtained via T–duality from integrable models. We construct an infinite family of non-local conserved charges ..."

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We discuss the integrability of 2d non-linear sigma models with target space being the squashed three-sphere, warped anti–de Sitter space and the Schroedinger spacetime. These models can be obtained via T–duality from integrable models. We construct an infinite family of non-local conserved charges from the T–dual Lax currents, enhancing the symmetry of warped anti–de Sitter space and the Schroedinger spacetime to ŝl2(R) ⊕ ŝl2(R). ar X iv