We provide a non conformal generalization of the Compère-Song-Strominger (CSS) boundary conditions for AdS3 gravity that breaks the \hat{u}(1) Kac-Moody-Virasoro symmetry to two u(1)s. The holographic dual specified by the new boundary conditions can be understood as an irrelevant deformation of a warped conformal field theory (WCFT). Upon consistent reduction to two dimensions, AdS3 gravity results in a deformed Jackiw-Teitelboim dilaton gravity model coupled to a Maxwell field. We show that near extremality the boundary conditions inherited from generalized CSS boundary conditions in three dimensions give rise to an effective action exhibiting the same symmetry breaking pattern as the complex Sachdev-Ye-Kitaev models. Besides the Schwarzian term reflecting the breaking of conformal symmetry, the effective action contains an additional term that captures the breaking of the \hat{u}(1) Kac-Moody symmetry.

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This paper is devoted to the study of orthogonality and disjointness preserving linear maps between Fourier and FourierStieltjes algebras of locally compact groups. We show that a linear bijection : A (G 1) A (G 2)(resp. : B (G 1) B (G 2)) between two Fourier algebras (resp. FourierStieltjes algebras) of locally compact groups will induce a topological group isomorphism between G 1 and G 2, provided that preserves both disjointness and some kind of orthogonality. This improves earlier results of JJ Font and MS Monfared, where amenability of the groups or continuity of the linear maps are assumed. We also study the structure of bounded and unbounded disjointness preserving linear functionals of Fourier algebras. In the development, general results about disjointness and orthogonality preserving linear maps between C-algebras, W-algebras and their preduals are obtained.

We prove that all monomials of κ-classes and ψ-classes are independent in $R^k(\ocM_{g,n})/R^k(\partial\ocM_{g,n})$ for all k≤[g/3]. We also give a simple argument for κ_l≠0 in $R^l(\ocM_g)$ for l≤g−2.

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