Rotational Invariance in the M(atrix) Formulation of Type IIB Theory

TL;DR

This paper explores how rotational invariance manifests in the matrix model formulation of type IIB string theory, revealing a surprising emergence of full O(8) symmetry from duality principles.

Contribution

It demonstrates the emergence of full rotational symmetry in type IIB matrix models via electric-magnetic duality, contrasting with the manifest symmetry in other formulations.

Findings

Full O(8) symmetry arises from duality in type IIB matrix models.

Transverse dimensions are realized differently in IIB compared to IIA.

Rotational invariance is not manifest but emerges through duality.

Abstract

The matrix model formulation of M-theory can be generalized by compactification to ten-dimensional type II string theory, formulated in the infinite momentum frame. Both the type IIA and IIB string theories can be formulated in this way. In the M-theory and type IIA cases, the transverse rotational invariance is manifest, but in the IIB case, one of the transverse dimensions materializes in a completely different way from the other seven. The full O(8) rotational symmetry then follows in a surprising way from the electric-magnetic duality of supersymmetric Yang-Mills field theory.