Anomalies, conformal manifolds, and spheres
The twopoint 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 ahlerHodge 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 WessZumino consistency conditions, but can be ruled outmore »
 Authors:

^{[1]};
^{[2]};
^{[3]};
^{[3]};
^{[4]};
^{[5]}
 Perimeter Inst. for Theoretical Physics, Waterloo, ON (Canada)
 Princeton Univ., NJ (United States). Dept. of Physics
 Weizmann Inst. of Science, Rehovot (Israel)
 School of Natural Sciences, Princeton, NJ (United States). Inst. for Advanced Study
 MaxPlanck Inst. for Gravitational Physics, Golm (Germany). AlbertEinsteinInst.
 Publication Date:
 Grant/Contract Number:
 SC0009988; 335182; 884/11; 2010/629; 1989/14
 Type:
 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 10298479
 Publisher:
 Springer Berlin
 Research Org:
 Institute for Advanced Study, Princeton
 Sponsoring Org:
 USDOE Office of Science (SC); Israel Science Foundation; GermanIsraeli Foundation for Scienti c Research and Development (GIF); Industry Canada; Ministry of Research and Innovation
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Supersymmetric gauge theory; Anomalies in Field and String Theories
 OSTI Identifier:
 1327006
Gomis, Jaume, Hsin, PoShen, Komargodski, Zohar, Schwimmer, Adam, Seiberg, Nathan, and Theisen, Stefan. Anomalies, conformal manifolds, and spheres. United States: N. p.,
Web. doi:10.1007/JHEP03(2016)022.
Gomis, Jaume, Hsin, PoShen, Komargodski, Zohar, Schwimmer, Adam, Seiberg, Nathan, & Theisen, Stefan. Anomalies, conformal manifolds, and spheres. United States. doi:10.1007/JHEP03(2016)022.
Gomis, Jaume, Hsin, PoShen, Komargodski, Zohar, Schwimmer, Adam, Seiberg, Nathan, and Theisen, Stefan. 2016.
"Anomalies, conformal manifolds, and spheres". United States.
doi:10.1007/JHEP03(2016)022. https://www.osti.gov/servlets/purl/1327006.
@article{osti_1327006,
title = {Anomalies, conformal manifolds, and spheres},
author = {Gomis, Jaume and Hsin, PoShen and Komargodski, Zohar and Schwimmer, Adam and Seiberg, Nathan and Theisen, Stefan},
abstractNote = {The twopoint 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 ahlerHodge 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 WessZumino consistency conditions, but can be ruled out by a more detailed analysis.},
doi = {10.1007/JHEP03(2016)022},
journal = {Journal of High Energy Physics (Online)},
number = 3,
volume = 2016,
place = {United States},
year = {2016},
month = {3}
}