BPS solutions of a D5-brane worldvolume in a D3-brane background from superalgebras

TL;DR

The authors extend the D5-brane BPS analysis from flat to curved backgrounds by examining a D5 in a D3-brane geometry, both near-horizon and non-near-horizon. They derive a D5 energy bound via a Hamiltonian decomposition and identify a topological central charge $Z_{el}$ (and its near-horizon specialization $Z_9$) that arises as a central charge in the maximally extended worldvolume algebra. In the near-horizon limit, the worldvolume algebra is $OSp(4^*|4)$ extended to $OSp(1|16)$, with $Z_9$ interpreted as strings ending on the D5; in the non-near-horizon case the algebra contracts to $OSp(1|8)$, and the central charges describe more general brane intersections, including 1/8-BPS states. Together, the results provide a coherent framework linking BPS bounds, first-order embedding equations, and brane-intersection physics in curved backgrounds, with potential applicability to broader brane configurations.

Abstract

The BPS method is used to find BPS solutions of the worldvolume theory of a D5-brane in the near horizon geometry of a D3-brane. The BPS bound is interpreted in terms of the `maximally extended' D5 worldvolume supersymmetry algebra in the corresponding curved background, which is OSp(1|16). This algebra is an extension of the worldvolume superalgebra OSp(4^*|4). The analysis is generalized to the non-near horizon case.