skip to main content


Title: Anomalies, conformal manifolds, and spheres

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 $M$ 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 $N$ = (2; 2) and $N$ = (0; 2) supersymmetric theories in d = 2 and $N$ = 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 K ahler-Hodge and we further argue that it has vanishing K ahler class. For $N$ = (2; 2) theories in d = 2 and N = 2 theories in d = 4 we also show that the relation between the sphere partition function and the K ahler potential of $M$ follows immediately from the appropriate sigma models that we construct. Ultimately, along the way we find several examples of potential trace anomalies that obey the Wess-Zumino consistency conditions, but can be ruled outmore » by a more detailed analysis.« less
 [1] ;  [2] ;  [3] ;  [3] ;  [4] ;  [5]
  1. Perimeter Inst. for Theoretical Physics, Waterloo, ON (Canada)
  2. Princeton Univ., NJ (United States). Dept. of Physics
  3. Weizmann Inst. of Science, Rehovot (Israel)
  4. School of Natural Sciences, Princeton, NJ (United States). Inst. for Advanced Study
  5. Max-Planck Inst. for Gravitational Physics, Golm (Germany). Albert-Einstein-Inst.
Publication Date:
OSTI Identifier:
Grant/Contract Number:
SC0009988; 335182; 884/11; 2010/629; 1989/14
Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2016; Journal Issue: 3; Journal ID: ISSN 1029-8479
Springer Berlin
Research Org:
Institute for Advanced Study, Princeton
Sponsoring Org:
USDOE Office of Science (SC); Israel Science Foundation; German-Israeli Foundation for Scienti c Research and Development (GIF); Industry Canada; Ministry of Research and Innovation
Country of Publication:
United States
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS Supersymmetric gauge theory; Anomalies in Field and String Theories