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\( \mathcal{Z} \) extremization in chiral-like Chern-Simons theories

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Abstract

We study the localized free energy on S 3 of three-dimensional \( \mathcal{N} \) = 2 ChernSimons matter theories at weak coupling. We compute the two loop R charge in three different ways, namely by the standard perturbative approach, by extremizing the localized partition function at finite N and by applying the standard ansatz for the saddle point approximation for large N. We show that the latter approach does not reproduce the expected result when chiral theories are considered. We circumvent these problems by restoring a reflection symmetry on the eigenvalues in the free energy. Thanks to this symmetrization we find that the three methods employed agree. In particular we match the computation for a model whose four dimensional parent is the quiver gauge theory describing D3 branes probing the Hirzebruch surface. We conclude by commenting on the application of our results and to the strong coupling regime.

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Authors and Affiliations

  1. Department of Physics, University of California, San Diego La Jolla, CA, 92093-0354, U.S.A

    Antonio Amariti

  2. Instituut voor Theoretische Fysica, Katholieke Universiteit Leuven, Celestijnenlaan 200D, B-3001, Leuven, Belgium

    Massimo Siani

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  1. Antonio Amariti
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  2. Massimo Siani
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Correspondence to Massimo Siani.

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ArXiv ePrint: 1109.4152

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Amariti, A., Siani, M. \( \mathcal{Z} \) extremization in chiral-like Chern-Simons theories. J. High Energ. Phys. 2012, 171 (2012). https://doi.org/10.1007/JHEP06(2012)171

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  • DOI: https://doi.org/10.1007/JHEP06(2012)171

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