Brane Transitions from Exceptional Groups

TL;DR

This paper explores new brane transitions related to exceptional groups, extending previous work on D5 and E7 cases, and proposes a local rule for understanding these transitions within M-theory and quantum algebraic frameworks.

Contribution

It generalizes the study of brane transitions to exceptional groups, specifically E7, and introduces a local rule to better understand these novel transitions.

Findings

Identification of new brane transitions within exceptional Weyl groups.

Extension of the quantum curve analysis from D5 to E7 cases.

Proposal of a local rule for brane transitions based on combined results.

Abstract

It is a well-known result by Hanany and Witten that, when two five-branes move across each other, D3-branes stretching between them are generated. Later the same brane configurations played a crucial role in understanding the worldvolume theory of multiple M2-branes. Recently the partition function of multiple M2-branes was transformed to the Fredholm determinant for quantum algebraic curves, where the characteristic 3/2 power law of degrees of freedom is reproduced and the determinant enjoys a large symmetry given by exceptional Weyl groups. The large exceptional Weyl group reproduces the Hanany-Witten brane transitions and, besides, contains brane transitions unknown previously. Aiming at understanding the new brane transitions better, we generalize our previous study on the D5 quantum curve to the E7 case, which requires delicate handling of degeneracies. By combining the results of these two cases, we propose a "local" rule for the brane transitions.