Deformation of $D_p$-Brane Worldvolume in Weakly Curved Background

TL;DR

This paper investigates how weakly curved NS-NS backgrounds deform the worldvolume of Dp-branes, proposing a new open string metric approach and revealing that a spherical D5-brane behaves like an extremal black 5-brane at small radius, linking non-commutative gauge theories to gravity.

Contribution

It introduces an alternative derivation of the open string metric in weakly curved backgrounds and applies it to analyze D5-brane deformation, connecting non-commutative gauge theories with gravity duals.

Findings

Spherical D5-brane acts like an extremal black 5-brane as radius approaches zero.

Proposed a new formalism for open string metric in weakly curved backgrounds.

Demonstrated gauge/gravity duality with non-commutative, non-associative gauge theory.

Abstract

We study a $D_p$-brane in a parallelizable NS-NS background. The article starts with a brief review of the non-associative deformation of $D$-brane worldvolume in presence of torsion \cite{cornalba}. We suggest an alternative form and heuristic derivation of the open string metric for weakly curved backgrounds, by promoting the constant two-form in the flat space formula to a dynamical two-form and then Taylor expanding the bulk fields in Riemann Normal Coordinates at the origin. For weakly curved backgrounds, terms only upto the leading order in the NS-NS field strength or torsion contribute. This formalism differs from the author's earlier works in a collaboration \cite{richa}. We use the open string metric proposed in this paper to determine the deformation of $D_5$-brane for a particular NS-NS background. It turns out that a spherical $D_5$-brane with torsion acts like an extremal black 5-brane in the limit of radius $r \rightarrow 0$. This is an interesting case of gauge/gravity duality with an intractable non-commutative and non-associative gauge theory on a $D_p$-brane with torsion, which is equivalent to a simpler and ordinary gravity theory on the extremal black brane.