Non-relativistic AdS/CFT and the GCA

6th International Symposium on Quantum Theory and Symmetries

Bagchi, Arjun^1 ; Gopakumar, Rajesh^1

Harish-Chandra Research Institute, Chhatnag Road, Jhusi 211019, India^1

关键词: Einstein's equations;    Geometric structure;    Infinite dimensional;    On potentials;    Radial direction;    Real-life systems;    Schrodinger;    Spacetime;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/462/1/012017/pdf
DOI  :  10.1088/1742-6596/462/1/012017

来源: IOP

【 摘 要 】

We construct a non-relativistic limit of the AdS/CFT conjecture by taking, on the boundary side, a parametric group contraction of the relativistic conformal group. This leads to an algebra with the same number of generators called the Galilean Conformal Algebra (GCA). The GCA is to be contrasted with the more widely studied Schrodinger algebra which has fewer generators. The GCA, interestingly, can be given an infinite dimensional lift for any dimension of spacetime and this infinite algebra contains a Virasoro Kac-Moody sub-algebra. We comment briefly on potential realizations of this algebra in real-life systems. We also propose a somewhat unusual geometric structure for the bulk gravity dual to the GCA. This involves taking a Newton-Cartan like limit of Einstein's equations in anti de Sitter space which singles out an AdS2comprising of the time and radial direction. The infinite dimensional GCA arises out of the contraction of the bulk Killing vectors and is identified with the (asymptotic) isometries of this Newton-Cartan structure.