Abstract
We propose a holographic duality between a 2 dimensional (2d) chiral superconformal field theory and a certain theory of supergravity in 3d with flatspace boundary conditions that is obtained as a double scaling limit of a parity breaking theory of supergravity. We show how the asymptotic symmetries of the bulk theory reduce from the "despotic" Super Bondi-Metzner-Sachs algebra (or equivalently the Inhomogeneous Super Galilean Conformal Algebra) to a single copy of the Super-Virasoro algebra in this limit and also reproduce the same reduction from a study of null vectors in the putative 2d dual field theory.
Highlights
The holographic principle offers us a path to a quantum theory of gravity through a nongravitational field theory in one lower dimension
Using the notion of asymptotic symmetries at the null boundary of spacetime characterized by the BondiMetzner-Sachs (BMS) group [10,11,12], holography for asymptotically flat spacetimes [13,14] has recently met with a certain number of successes, though the discussion has often been confined to three dimensions and with theories without supersymmetry
Through an analysis on null vectors in the field theory with SGCAI symmetry, we show that the scaling limit that we proposed in the bulk corresponds to a consistent truncation from an inhomogeneous Galilean conformal field theory (SGCFTI) to a chiral half of a superconformal field theory in 2d
Summary
The holographic principle offers us a path to a quantum theory of gravity through a nongravitational field theory in one lower dimension. We perform a scaling limit on the field theory with super-BMS symmetries and, through an analysis of null vectors, show that there is a consistent truncation to a single copy of a super-Virasoro algebra. The calculation of charges on the bulk side yields results consistent with this, with the charges that correspond to the other generators of the super-BMS3 algebra identically vanishing in the scaling limit from the initial parity breaking theory. In Einstein gravity, the central charges take the values cL 1⁄4 0 and cM 1⁄4 3=G [12] These symmetries can be looked upon as the symmetries of a putative dual 2d field theory living on the null boundary of flat space. There are three appendixes supplementing the calculations performed on the bulk theory and one with some details of the boundary theory
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