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Contact terms, unitarity, and F -maximization in three-dimensional superconformal theories

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Abstract

We consider three-dimensional \( \mathcal{N}=2 \) superconformal field theories on a threesphere and analyze their free energy F as a function of background gauge and supergravity fields. A crucial role is played by certain local terms in these background fields, including several Chern-Simons terms. The presence of these terms clarifies a number of subtle properties of F . This understanding allows us to prove the F -maximization principle. It also explains why computing F via localization leads to a complex answer, even though we expect it to be real in unitary theories. We discuss several corollaries of our results and comment on the relation to the F -theorem.

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Authors and Affiliations

  1. Weizmann Institute of Science, Rehovot, 76100, Israel

    Cyril Closset & Zohar Komargodski

  2. Department of Physics, Princeton University, Princeton, NJ, 08544, U.S.A.

    Thomas T. Dumitrescu

  3. Institute for Advanced Study, Princeton, NJ, 08540, U.S.A.

    Guido Festuccia, Zohar Komargodski & Nathan Seiberg

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  1. Cyril Closset
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  2. Thomas T. Dumitrescu
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  3. Guido Festuccia
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  4. Zohar Komargodski
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  5. Nathan Seiberg
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Correspondence to Cyril Closset.

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ArXiv ePrint: 1205.4142

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Closset, C., Dumitrescu, T.T., Festuccia, G. et al. Contact terms, unitarity, and F -maximization in three-dimensional superconformal theories. J. High Energ. Phys. 2012, 53 (2012). https://doi.org/10.1007/JHEP10(2012)053

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