Supersymmetry on curved spaces and superconformal anomalies

Davide Cassani*, Dario Martelli

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

44 Citations (Scopus)

Abstract

We study the consequences of unbroken rigid supersymmetry of fourdimensional field theories placed on curved manifolds. We show that in Lorentzian signature the background vector field coupling to the R-current is determined by the Weyl tensor of the background metric. In Euclidean signature, the same holds if two supercharges of opposite R-charge are preserved, otherwise the (anti-) self-dual part of the vector fieldstrength is fixed by the Weyl tensor. As a result of this relation, the trace and R-current anomalies of superconformal field theories simplify, with the trace anomaly becoming purely topological. In particular, in Lorentzian signature, or in the presence of two Euclidean supercharges of opposite R-charge, supersymmetry of the background implies that the term proportional to the central charge c vanishes, both in the trace and R-current anomalies. This is equivalent to the vanishing of a superspace Weyl invariant. We comment on the implications of our results for holography.

Original languageEnglish
Article number25
Number of pages30
JournalJournal of High Energy Physics
Volume2013
Issue number10
DOIs
Publication statusPublished - 3 Oct 2013

Keywords

  • Supersymmetric gauge theory
  • Anomalies in Field and String Theories
  • AdS-CFT Correspondence
  • Differential and Algebraic Geometry
  • HOLOGRAPHIC RENORMALIZATION
  • GAUGED SUPERGRAVITY
  • CONFORMAL SUPERGRAVITY
  • COEFFICIENTS
  • MANIFOLDS
  • SYMMETRY
  • FIELDS

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