Defect (p,q) Five-branes

TL;DR

This paper constructs a local description of defect (p,q) five-branes using monodromy transformations, revealing their composite nature and introducing a new hyper-Kähler geometry example related to string theory branes.

Contribution

It presents a novel formulation of defect five-branes via monodromy and conjugate transformations, and introduces a new hyper-Kähler ALG space geometry in this context.

Findings

Derived a field configuration for defect (p,q) five-branes.

Identified a new hyper-Kähler ALG space geometry.

Connected the geometry to conjugate configurations of KK5-branes.

Abstract

We study a local description of composite five-branes of codimension two. The formulation is constructed by virtue of $SL(2,{\mathbb Z}) \times SL(2,{\mathbb Z)}$ monodromy associated with two-torus. Applying conjugate monodromy transformations to the complex structures of the two-torus, we obtain a field configuration of a defect $(p,q)$ five-brane. This is a composite state of $p$ defect NS5-branes and $q$ exotic $5^2_2$-branes. We also obtain a new example of hyper-K\"{a}hler geometry. This is an ALG space, a generalization of an ALF space which asymptotically has a tri-holomorphic two-torus action. This geometry appears in the conjugate configuration of a single defect KK5-brane.