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Anomalies, conformal manifolds, and spheres

  • Jaume GomisEmail author
  • Po-Shen Hsin
  • Zohar Komargodski
  • Adam Schwimmer
  • Nathan Seiberg
  • Stefan Theisen
Open Access
Regular Article - Theoretical Physics

Abstract

The two-point function of exactly marginal operators leads to a universal contribution to the trace anomaly in even dimensions. We study aspects of this trace anomaly, emphasizing its interpretation as a sigma model, whose target space \( \mathrm{\mathcal{M}} \) is the space of conformal field theories (a.k.a. the conformal manifold). When the underlying quantum field theory is supersymmetric, this sigma model has to be appropriately supersymmetrized. As examples, we consider in some detail \( \mathcal{N}=\left(2,\;2\right) \) and \( \mathcal{N}=\left(0,\;2\right) \) supersymmetric theories in d = 2 and \( \mathcal{N}=2 \) supersymmetric theories in d = 4. This reasoning leads to new information about the conformal manifolds of these theories, for example, we show that the manifold is Kähler-Hodge and we further argue that it has vanishing Kähler class. For \( \mathcal{N}=\left(2,\;2\right) \) theories in d = 2 and \( \mathcal{N}=2 \) theories in d = 4 we also show that the relation between the sphere partition function and the Kähler potential of \( \mathrm{\mathcal{M}} \) follows immediately from the appropriate sigma models that we construct. Along the way we find several examples of potential trace anomalies that obey the Wess-Zumino consistency conditions, but can be ruled out by a more detailed analysis.

Keywords

Supersymmetric gauge theory 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) 2016

Authors and Affiliations

  • Jaume Gomis
    • 1
    Email author
  • Po-Shen Hsin
    • 2
  • Zohar Komargodski
    • 3
  • Adam Schwimmer
    • 3
  • Nathan Seiberg
    • 4
  • Stefan Theisen
    • 5
  1. 1.Perimeter Institute for Theoretical PhysicsWaterlooCanada
  2. 2.Department of PhysicsPrinceton UniversityPrincetonU.S.A.
  3. 3.Weizmann Institute of ScienceRehovotIsrael
  4. 4.School of Natural SciencesInstitute for Advanced StudyPrincetonU.S.A.
  5. 5.Max-Planck-Institut für GravitationsphysikAlbert-Einstein-InstitutGolmGermany

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