Negative Branes, Supergroups and the Signature of Spacetime

TL;DR

This paper explores how negative branes in string theory relate to exotic spacetime signatures, holography of supergroup gauge theories, and potential non-perturbative definitions of these theories.

Contribution

It demonstrates the connection between negative branes and spacetime signature change, and derives holographic duals and Seiberg-Witten curves for supergroup gauge theories.

Findings

Negative branes induce spacetime signature change near their worldvolumes.

Supergroup gauge theories are holographically dual to exotic string theory backgrounds.

The Seiberg-Witten curve for $ abla N|M)$ theories is derived using multiple methods.

Abstract

We study the realization of supergroup gauge theories using negative branes in string theory. We show that negative branes are intimately connected with the possibility of timelike compactification and exotic spacetime signatures previously studied by Hull. Isolated negative branes dynamically generate a change in spacetime signature near their worldvolumes, and are related by string dualities to a smooth M-theory geometry with closed timelike curves. Using negative D3 branes, we show that $SU(0|N)$ supergroup theories are holographically dual to an exotic variant of type IIB string theory on $dS_{3,2} \times \bar S^5$, for which the emergent dimensions are timelike. Using branes, mirror symmetry and Nekrasov's instanton calculus, all of which agree, we derive the Seiberg-Witten curve for $\mathcal N=2 ~SU(N|M)$ gauge theories. Together with our exploration of holography and string dualities for negative branes, this suggests that supergroup gauge theories may be non-perturbatively well-defined objects, though several puzzles remain.