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 O(2, 2; Z) = SL(2, Z) × SL(2, Z) 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 fivebranes. 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.

Unwinding strings in semi-flatland

“…In the semi-flat limit, a fiber-wise T-duality on the shrinking cycle relates the I 1 degeneration to a NS5-brane with monodromy ρ → ρ + 1 [25,26] (see also [27]). In this case, however, the exact solution breaks all the isometries of the fiber torus.…”

T-duality transformations for the NS5-brane along angular directions

“…where the latter corresponds to a so-called non-geometric background [16-18, 6, 19]. Corrections to the smearing-approximation for this chain of Tduality transformations have been studied for instance in [9,[20][21][22][23][24][25][26], and in the context of Double Field Theory (DFT) this point has been addressed for instance in [27,28,26,29]. In this work we want to go one step further back and investigate T-duality transformations for the uncompactified NS5-brane solution along angular directions.…”

Gravity theory on Poisson manifold with R‐flux

“…Solutions of particular interest are the analogue of the fundamental string solution and the NS5-brane solution that should be charged under the R-flux, since such objects are speculated to exhibit exotic geometrical properties [33][34][35][36][37][38][39][40][41][42][43]. An open question is whether our framework provides a geometrical meaning for those non-geometric objects.…”