Matrix Theory, AdS/CFT and Higgs-Coulomb Equivalence

TL;DR

This paper explores the relationship between Matrix theory and AdS/CFT descriptions, revealing a natural mapping between Coulomb and Higgs branches and demonstrating non-commutative space-time in certain brane configurations.

Contribution

It provides an explicit mapping between states in Matrix theory and AdS/CFT, extending to the (2,0) theory and showing non-commutative geometry effects.

Findings

Mapping between Coulomb and Higgs branches via variable change

Explicit correspondence for M5-brane states in AdS7×S4

Evidence of non-commutative space-time in D0-brane scenarios

Abstract

We discuss the relation between the Matrix theory definitions of a class of decoupled theories and their AdS/CFT description in terms of the corresponding near-horizon geometry. The near horizon geometry, naively part of the Coulomb branch, is embedded in the Higgs branch via a natural change of variables. The principles of the map apply to all DLCQ descriptions in terms of hyper-K\"ahler quotients, such as the ADHM quantum mechanics for the D1-D5 system. We then focus the (2,0) field theory, and obtain an explicit mapping from all states in the $N_0=1$ momentum sector of $N_4$ M5-branes to states in (a DLCQ version of) $AdS_7\times S^4$. We show that, even for a single D0-brane, the space-time coordinates become non-commuting variables, suggesting an inherent non-commutativity of space-time in the presence of field strengths even for theories with gravity.