Dual Non-Lorentzian Backgrounds for Matrix Theories

TL;DR

This paper investigates non-Lorentzian geometries from string theory decoupling limits, exploring duality transformations and their asymmetric properties, and connects these findings to non-commutative gauge theories and holography.

Contribution

It reveals novel asymmetric duality properties of non-Lorentzian backgrounds and integrates these insights into the holographic framework involving non-commutative Yang-Mills theories.

Findings

Duality transformations can change the foliation codimension of backgrounds.

Asymmetry in T- and S-duality affects non-commutative structures.

New holographic examples with non-Lorentzian geometries are constructed.

Abstract

We study properties of non-Lorentzian geometries arising from BPS decoupling limits of string theory that are central to matrix theory and the AdS/CFT correspondence. We focus on duality transformations between ten-dimensional non-Lorentzian geometries coupled to matrix theory on D-branes. We demonstrate that T- and S-duality transformations exhibit novel asymmetric properties: depending not only on the choice of transformation but also on the value of the background fields, the codimension of the foliation structure of the dual non-Lorentzian background may be different or the same. This duality asymmetry underlies features observed in the study of non-commutativity and Morita equivalence in matrix and gauge theory. Finally, we show how the holographic correspondence involving non-commutative Yang-Mills fits into our framework, from which we further obtain novel holographic examples with non-Lorentzian bulk geometries.