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Half-BPS supergravity solutions and superalgebras

Eric D'Hoker, John Estes, Michael Gutperle, Darya Krym, Paul Sorba

TL;DR

The paper develops a systematic program to classify half-BPS solutions in Type IIB supergravity and M-theory by identifying 16-fermion subalgebras of PSU(2,2|4), OSp(8^*|4), and OSp(8|4,ℝ). It derives a finite set of basic subalgebras and direct-sum constructions, associates moduli spaces of regular solutions to each subalgebra, and demonstrates the correspondence between these algebras and known as well as potential new half-BPS backgrounds, including D7-brane scenarios in Type IIB and exceptional D(2,1;c) families in M-theory. The work shows how AdS asymptotics constrain possible symmetries, maps half-BPS operators in the dual CFTs to gravity solutions, and connects to conformal superalgebras across dimensions, outlining both established results (bubbling AdS, Wilson lines, defects) and directions for finding new backgrounds. Overall, it provides a unifying algebraic framework that organizes existing solutions and guides the search for new half-BPS geometries in string/M-theory. The analysis also clarifies when enhanced supersymmetry can occur and how near-horizon brane constructions fit within the established subalgebra classification.

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.

Half-BPS supergravity solutions and superalgebras

TL;DR

The paper develops a systematic program to classify half-BPS solutions in Type IIB supergravity and M-theory by identifying 16-fermion subalgebras of PSU(2,2|4), OSp(8^*|4), and OSp(8|4,ℝ). It derives a finite set of basic subalgebras and direct-sum constructions, associates moduli spaces of regular solutions to each subalgebra, and demonstrates the correspondence between these algebras and known as well as potential new half-BPS backgrounds, including D7-brane scenarios in Type IIB and exceptional D(2,1;c) families in M-theory. The work shows how AdS asymptotics constrain possible symmetries, maps half-BPS operators in the dual CFTs to gravity solutions, and connects to conformal superalgebras across dimensions, outlining both established results (bubbling AdS, Wilson lines, defects) and directions for finding new backgrounds. Overall, it provides a unifying algebraic framework that organizes existing solutions and guides the search for new half-BPS geometries in string/M-theory. The analysis also clarifies when enhanced supersymmetry can occur and how near-horizon brane constructions fit within the established subalgebra classification.

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.

Paper Structure

This paper contains 73 sections, 135 equations, 1 figure, 19 tables.

Table of Contents

  1. Introduction
  2. The half-BPS solution -- superalgebra correspondence
  3. Half-BPS solutions related to D7 branes
  4. Families of half-BPS solutions in M-theory
  5. Organization
  6. Half-BPS configurations in Type IIB
  7. The AdS/CFT correspondence for Type IIB
  8. Half-BPS operators in ${\cal N}=4$ SYM
  9. Intersecting branes in flat space-time
  10. Probe branes in $AdS_{5}\times S^{5}$
  11. Structure of known exact supergravity solutions
  12. Known families of half-BPS solutions
  13. Half-BPS configuration in M-theory
  14. The AdS/CFT correspondence for M-theory
  15. Half-BPS operators in M-theory
  16. ...and 58 more sections

Figures (1)

  • Figure 1: The space of parameters $c_1,c_2,c_3$ and corresponding limiting superalgebras.