Half-BPS supergravity solutions and superalgebras

TL;DR

This paper explores the relationship between specific Lie superalgebras and half-BPS supergravity solutions, classifying subalgebras and conjecturing new solutions in Type IIB and M-theory with varying supersymmetries.

Contribution

It classifies semi-simple subalgebras related to supergravity solutions and proposes the existence of new half-BPS solutions based on this classification.

Findings

Classified semi-simple subalgebras of PSU(2,2|4), OSp(8^*|4), and OSp(8|4,R).

Established correspondence between Lie superalgebras and supergravity solutions.

Conjectured new families of half-BPS solutions in string and M-theory.

Abstract

We establish a correspondence between certain Lie superalgebras with 16 fermionic generators, and half-BPS solutions to supergravities with 32 supersymmetries. Three cases are discussed. For Type IIB supergravity, we relate semi-simple Lie superalgebras H with 16 fermionic generators which are subalgebras of PSU(2,2|4), to families of half-BPS solutions which are invariant under H, and locally asymptotic to AdS_5 x S^5. Similarly, for M-theory, we relate semi-simple Lie superalgebras H with 16 fermionic generators which are subalgebras of OSp(8^*|4) or OSp(8|4,R) to families of half-BPS solutions which are invariant under H, and locally asymptotic to AdS_7 x S^4 or AdS_4 x S^7 respectively. Possible enhancements to more than 16 supersymmetries, such as 24, are also analyzed. The classification of semi-simple subalgebras of PSU(2,2|4), OSp(8^*|4), and OSp(8|4,R) derived in this paper, leads us to conjecture the existence of various new families of half-BPS solutions to Type IIB supergravity and M-theory.