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Published January 2017 | Submitted + Published
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Shortening Anomalies in Supersymmetric Theories

Gomis, Jaume
Komargodski, Zohar ORCID icon
Ooguri, Hirosi ORCID icon
Seiberg, Nathan ORCID icon
Wang, Yifan ORCID icon

Abstract

We present new anomalies in two-dimensiona N=(2,2) superconformal theories. They obstruct the shortening conditions of chiral and twisted chiral multiplets at coincident points. This implies that marginal couplings cannot be promoted to background superfields in short representations. Therefore, standard results that follow from N=(2,2) spurion analysis are invalidated. These anomalies appear only if supersymmetry is enhanced beyond N=(2,2). These anomalies explain why the conformal manifolds of the K3 and T^4 sigma models are not Kähler and do not factorize into chiral and twisted chiral moduli spaces and why there are no N=(2,2) gauged linear sigma models that cover these conformal manifolds. We also present these results from the point of view of the Riemann curvature of conformal manifolds.

Additional Information

© 2017 The Author(s). 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. Article funded by SCOAP3. Received: 08 December 2016; Accepted: 17 December 2016; First Online: 17 January 2017. We thank Kevin Costello, David Morrison, Kyriakos Papadodimas, Ronen Plesser, Adam Schwimmer, Stefan Theisen, and Edward Witten for useful discussions. J.G.'s research was supported in part by the Perimeter Institute for Theoretical Physics. Research at Perimeter Institute is supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Research and Innovation. Z.K. is supported in part by an Israel Science Foundation center for excellence grant and by the I-CORE program of the Planning and Budgeting Committee and the Israel Science Foundation (grant number 1937/12). Z.K. is also supported by the ERC STG grant 335182 and by the United States-Israel BSF grant 2010/629. H.O. is supported in part by U.S. Department of Energy grant DE-SC0011632, by the Simons Investigator Award, by the World Premier International Research Center Initiative, MEXT, Japan, by JSPS Grant-in-Aid for Scientific Research C-26400240, and by JSPS Grant-in-Aid for Scientific Research on Innovative Areas 15H05895. N.S. was supported in part by DOE grant DE-SC0009988. Y.W. was supported by the NSF grant PHY-1620059 and by the Simons Foundation Grant #488653. H.O. thanks the hospitality of the Institute for Advanced Study and Harvard University, where he spent his sabbatical in 2015 - 2016, and of the Aspen Center for Physics, which is supported by the National Science Foundation grant PHY-1066293. N.S. thanks the hospitality of the Weizmann Institute of Science during the completion of this work.

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Published - art_3A10.1007_2FJHEP01_282017_29067.pdf

Submitted - 1611.03101v1.pdf

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