Symmetries of N = (1,0) supergravity backgrounds in six dimensions

Kuzenko S. M., Lindstrom U., Raptakis E. S. N., Tartaglino-Mazzucchelli G.

JOURNAL OF HIGH ENERGY PHYSICS, vol.2021, no.3, 2021 (SCI-Expanded) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 2021 Issue: 3
  • Publication Date: 2021
  • Doi Number: 10.1007/jhep03(2021)157
  • Journal Name: JOURNAL OF HIGH ENERGY PHYSICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, INSPEC, zbMATH, Directory of Open Access Journals
  • Keywords: Extended Supersymmetry, Higher Spin Symmetry, Supergravity Models, Superspaces, SUPERCONFORMAL TENSOR CALCULUS, HIGHER-SPIN SUPERALGEBRAS, KILLING TENSORS, GAUGE-THEORY, SUPERSPACE, MULTIPLETS, SUPERFIELDS, COUPLINGS, R2-ACTION, GEOMETRY
  • Middle East Technical University Affiliated: Yes

Abstract

General N = (1, 0) supergravity-matter systems in six dimensions may be described using one of the two fully fledged superspace formulations for conformal supergravity: (i) SU(2) superspace; and (ii) conformal superspace. With motivation to develop rigid supersymmetric field theories in curved space, this paper is devoted to the study of the geometric symmetries of supergravity backgrounds. In particular, we introduce the notion of a conformal Killing spinor superfield E-alpha, which proves to generate extended superconformal transformations. Among its cousins are the conformal Killing vector xi (a) and tensor zeta (a(n)) superfields. The former parametrise conformal isometries of supergravity backgrounds, which in turn yield symmetries of every superconformal field theory. Meanwhile, the conformal Killing tensors of a given background are associated with higher symmetries of the hypermultiplet. By studying the higher symmetries of a non-conformal vector multiplet we introduce the concept of a Killing tensor superfield. We also analyse the problem of computing higher symmetries for the conformal d'Alembertian in curved space and demonstrate that, beyond the first-order case, these operators are defined only on a limited class of backgrounds, including all conformally flat ones.