Journal
JOURNAL OF HIGH ENERGY PHYSICS
Volume -, Issue 3, Pages -Publisher
SPRINGER
DOI: 10.1007/JHEP03(2016)022
Keywords
Supersymmetric gauge theory; Anomalies in Field and String Theories
Categories
Funding
- DOE [DE-SC0009988]
- ERC STG [335182]
- Israel Science Foundation [884/11, 1989/14]
- United States-Israel Bi- national Science Foundation (BSF) [2010/629]
- I-CORE Program of the Planning and Budgeting Committee
- Physics Department of Princeton University
- GIF - the German-Israeli Foundation for Scientific Research and Development
- Perimeter Institute for Theoretical Physics
- Government of Canada through Industry Canada
- Province of Ontario through the Ministry of Research and Innovation
- NSERC
- ERA grant by the Province of Ontario
- European Research Council (ERC) [335182] Funding Source: European Research Council (ERC)
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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 A1 = 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 Kahler-Hodge and we further argue that it has vanishing Kahler class. For D = (2, 2) theories in N = 2 and N = 2 theories in d = 4 we also show that the relation between the sphere partition function and the Kahler potential of.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.
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