Towards Gravity solutions of AdS/CMT

TL;DR

In this work the authors construct gravity duals with two scaling exponents $a$ and $b$ to model 2+1 dimensional CMT systems. They derive the generalized scaling metric and study the field theory side via the operator dimension relation $\Delta(\Delta-a-2b)=m^2L^2$ and the BF bound, highlighting how the two exponents control the spectrum and stability. For generic $a,b$ the two point function is difficult to compute, but in the solvable case $a/b=2$ they obtain an analytic bulk-to-boundary propagator and a closed form massless correlator, illustrating how nonrelativistic scaling affects correlators. The results broaden the class of gravity duals with independent temporal and spatial scaling and provide explicit methods to compute boundary observables in these backgrounds.

Abstract

In this short note, we have generalized and constructed gravity solutions with two "exponents" {\it a la} Kachru, Liu and Mulligan. The coordinate system that is used to construct the gravity solution is useful when $b$ vanishes. It means we can describe the theory having only the temporal scale invariance apart from the combination of both temporal and spatial scale invariance. The two point correlation function of the scalar field in the mass less limit is computed in a special case that is $a/b=2$.