On the equivalence of bound state solutions

TL;DR

This paper demonstrates the equivalence of various bound state solutions of branes in supergravity theories using two different methods, enhancing understanding of their relationships in different dimensions.

Contribution

It establishes the equivalence of multiple bound state solutions obtained via zero mode analysis and T-duality techniques in ten- and eleven-dimensional supergravity.

Findings

Proves equivalence of (M2,M5) and related solutions in eleven dimensions.

Shows equivalence of ((F,D1),D3) and (p,q) 5-brane bound states in ten dimensions.

Comments on V-duality and boosted solutions in supergravity.

Abstract

In this paper we show the equivalence of various (non-threshold) bound state solutions of branes, or equivalently branes in background potentials, in ten- and eleven-dimensional supergravity. We compare solutions obtained in two very different ways. One method uses a zero mode analysis to make an Ansatz which makes it possible to solve the full non-linear supergravity equations. The other method utilises T-duality techniques to turn on the fields on the brane. To be specific, in eleven dimensions we show the equivalence for the (M2,M5) bound state, or equivalently an M5-brane in a C_3 field, where we also consider the (MW,M2,M2',M5) solution, which can be obtained from the (M2,M5) bound state by a boost. In ten dimensions we show the equivalence for the ((F,D1),D3) bound state as well as the bound states of (p,q) 5-branes with lower dimensional branes in type IIB, corresponding to D3-branes in B_2 and C_2 fields and (p,q) 5-branes in B_2, C_2 and C_4 fields. We also comment on the recently proposed V-duality related to infinitesimally boosted solutions.