Matrix Theory Reloaded: A BPS Road to Holography

TL;DR

This paper explores BPS decoupling limits in matrix theories on D-branes, revealing their role in generating holographic dualities, including novel non-Lorentzian geometries, and connecting these limits to deformations like $T\bar{T}$ in field theories.

Contribution

It systematically studies BPS decoupling limits and their relation to holography, introducing a unified framework involving DLCQ and deformations of matrix theories.

Findings

BPS limits induce near-horizon AdS/CFT geometries.

Multiple BPS limits generate new holographic examples with non-Lorentzian bulk geometries.

Deformations of matrix theories relate to $T\bar{T}$-like flows in field theories.

Abstract

We revisit the decoupling limits that lead to matrix theories on D-branes. We highlight the BPS nature of these limits, in which the target space geometry becomes non-Lorentzian and wrapped D-branes experience instantaneous gravitational forces. Applied to curved D-brane geometries, we show that a single BPS decoupling limit induces the bulk near-horizon limit leading to AdS/CFT. By consecutively applying two such limits, we systematically generate further examples of holography, including novel versions with non-Lorentzian bulk geometry. Uplifted to M-theory, we are led to a unified framework where each BPS decoupling limit corresponds to a Discrete Light Cone Quantisation (DLCQ). We conjecture that a DLCQ${}^n$/DLCQ${}^{m}$ correspondence, with $m>n$, captures the notion of holography in string theory. In particular, AdS${}_5$/CFT${}_4$ can be viewed as an example of DLCQ${}^0$/DLCQ${}^{1}$, with the extra DLCQ on the field theory side corresponding to the near-horizon limit in the bulk geometry. We further show that undoing these BPS decoupling limits can be viewed as deformations of matrix theories. We explain how these deformations are related to the $T\bar{T}$ deformation in two dimensions. In the context of holography, this allows us to view the ten-dimensional near-horizon brane geometry as an intrinsic deformation of the flat non-Lorentzian geometry that arises asymptotically. In field theoretic terms, these generalisations lead to $T\bar{T}$-like flow equations for the D$p$-brane DBI action.