Counting supersymmetric branes

TL;DR

This paper classifies maximal supergravity solutions, focusing on branes of low co-dimension, and provides a group-theoretic counting method based on E11 and duality transformations, extending previous wrapping rules.

Contribution

It introduces a group theory derivation for counting supersymmetric branes of co-dimension at most two, extending existing wrapping rules and constructing explicit supergravity solutions.

Findings

Classified supergravity solutions with co-dimension ≤ 2.

Developed a group-theoretic counting method based on E11.

Constructed explicit solutions for co-dimension two branes.

Abstract

Maximal supergravity solutions are revisited and classified, with particular emphasis on objects of co-dimension at most two. This class of solutions includes branes whose tension scales with g_s^{-\sigma} for \sigma>2. We present a group theory derivation of the counting of these objects based on the corresponding tensor hierarchies derived from E11 and discrete T- and U-duality transformations. This provides a rationale for the wrapping rules that were recently discussed for \sigma<4 in the literature and extends them. Explicit supergravity solutions that give rise to co-dimension two branes are constructed and analysed.