Quiver Matrix Mechanics for IIB String Theory (I): Wrapping Membranes and Emergent Dimension

TL;DR

This paper introduces a non-perturbative, supersymmetric quiver matrix mechanics model for type IIB string theory, capturing membrane wrapping and emergent dimensions through a discrete approach that aligns with continuum Yang-Mills theory.

Contribution

It develops a novel discrete matrix mechanics framework for IIB string theory, explicitly constructs membrane states, and demonstrates emergent dimensions in a non-perturbative setting.

Findings

Constructed explicit solitonic membrane states

Achieved SL(2,Z)-invariant spectrum with correct tension

Demonstrated emergent flat dimension as torus shrinks

Abstract

In this paper we present a discrete, non-perturbative formulation for type IIB string theory. Being a supersymmetric quiver matrix mechanics model in the framework of M(atrix) theory, it is a generalization of our previous proposal of compactification via orbifolding for deconstructed IIA strings. In the continuum limit, our matrix mechanics becomes a $(2+1)$-dimensional Yang-Mills theory with 16 supercharges. At the discrete level, we are able to construct explicitly the solitonic states that correspond to membranes wrapping on the compactified torus in target space. These states have a manifestly $SL(2,\integer)$-invariant spectrum with correct membrane tension, and give rise to an emergent flat dimension when the compactified torus shrinks to vanishing size.