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Journal of High Energy Physics

, 2018:122 | Cite as

\( \mathcal{N}=1 \) Liouville SCFT in four dimensions

  • Tom LevyEmail author
  • Yaron Oz
  • Avia Raviv-Moshe
Open Access
Regular Article - Theoretical Physics
  • 50 Downloads

Abstract

We construct a four supercharges Liouville superconformal field theory in four dimensions. The Liouville superfield is chiral and its lowest component is a log-correlated complex scalar whose real part carries a background charge. The action consists of a supersymmetric Paneitz operator, a background supersymmetric \( \mathcal{Q} \)-curvature charge and an exponential potential. It localizes semiclassically on solutions that describe curved superspaces with a constant complex supersymmetric \( \mathcal{Q} \)-curvature. The theory is nonunitary with a continuous spectrum of scaling dimensions. We study the dynamics on the supersymmetric 4-sphere, show that the classical background charge is not corrected quantum mechanically and calculate the super-Weyl anomaly. We derive an integral form for the correlation functions of vertex operators.

Keywords

Conformal Field Theory Supergravity Models Field Theories in Higher Dimensions Anomalies in Field and String Theories 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.Raymond and Beverly Sackler School of Physics and AstronomyTel-Aviv UniversityTel-AvivIsrael

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