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On RG flow of τ RR for supersymmetric field theories in three-dimensions

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Abstract

The coefficient τ RR of the two-point function of the superconformal U(1) R currents of \( \mathcal{N}=2 \) SCFTs in three-dimensions is recently shown to be obtained by differentiating the partition function on a squashed three-sphere with respect to the squashing parameter. With this method, we compute the τ RR for \( \mathcal{N}=2 \) Wess-Zumino models and SQCD numerically for small number of flavors and analytically in the large number limit. We study the behavior of τ RR under an RG flow by adding superpotentials to the theories. While the τ RR decreases for the gauge theories, we find an \( \mathcal{N}=2 \) Wess-Zumino model whose τ RR increases along the RG flow. Since τ RR is proportional to the coefficient C T of the two-point correlation function of the stress-energy tensors for \( \mathcal{N}=2 \) superconformal field theories, this rules out the possibility of C T being a measure of the degrees of freedom which monotonically decreases along RG flows in three-dimensions.

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Authors and Affiliations

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

    Tatsuma Nishioka

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

    Kazuya Yonekura

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  1. Tatsuma Nishioka
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  2. Kazuya Yonekura
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Correspondence to Kazuya Yonekura.

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ArXiv ePrint: 1303.1522

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Nishioka, T., Yonekura, K. On RG flow of τ RR for supersymmetric field theories in three-dimensions. J. High Energ. Phys. 2013, 165 (2013). https://doi.org/10.1007/JHEP05(2013)165

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