Hyper-Kähler with torsion, T-duality, and defect (p, q) five-branes

Abstract

We investigate a five-branes interpretation of hyper-Kähler geometry with torsion (HKT). This geometry is obtained by conformal transformation of the Taub-NUT space which represents a Kaluza-Klein five-brane. This HKT would represent an NS5-brane on the Taub-NUT space. In order to explore the HKT further, we compactify one transverse direction, and study the (Formula presented.) monodromy structure associated with two-torus. Performing the conjugate transformation, we obtain a new solution whose physical interpretation is a defect (p, q) five-brane on the ALG space. Throughout this analysis, we understand that the HKT represents a coexistent state of two kinds of five-branes. This situation is different from composite states such as (p, q) five-branes or (p, q) seven-branes in type IIB theory. We also study the T-dualized system of the HKT. We again find a new solution which also indicates another defect (p, q) five-brane on the ALG space.