Matrix Description of Intersecting M5 Branes
Shamit Kachru, Yaron Oz, Zheng Yin
TL;DR
This work develops a matrix/DLCQ description of 3+1d ${\cal N}=2$ superconformal fixed points arising from intersecting M5 branes, recasting the physics on the intersection as supersymmetric quantum mechanics on the Higgs branch of a 4d ${\cal N}=1$ gauge theory defined by D0 probes in a D4/D4' background. The authors derive the probe dynamics, specify the F-term constraints, and analyze the Higgs-branch moduli space, including its branch structure and dimensions, to extract multiplicities and scaling dimensions of chiral primaries via compact-cohomology at the origin. They discuss decoupling criteria for matrix descriptions of SUSY field theories by comparing to the $(2,0)$ theory and examining potential metric divergences along tubes between branches, providing a framework to define intrinsic intersection dynamics decoupled from bulk gravity. Overall, the paper offers a concrete, non-Lagrangian route to define and study the operator content of these tensionless-string theories through a D0-brane matrix quantum mechanics approach, with implications for the broader DLCQ program in M-theory.
Abstract
Novel 3+1 dimensional N=2 superconformal field theories (with tensionless BPS string solitons) are believed to arise when two sets of M5 branes intersect over a 3+1 dimensional hyperplane. We derive a DLCQ description of these theories as supersymmetric quantum mechanics on the Higgs branch of suitable 4d N=1 supersymmetric gauge theories. Our formulation allows us to determine the scaling dimensions of certain chiral primary operators in the conformal field theories. We also discuss general criteria for quantum mechanical DLCQ descriptions of supersymmetric field theories (and the resulting multiplicities and scaling dimensions of chiral primary operators).