Curious aspects of three-dimensional \( \mathcal{N}=1 \) SCFTs

Journal of High Energy Physics, Aug 2018

Abstract We study the dynamics of certain 3d \( \mathcal{N}=1 \) time reversal invariant theories. Such theories often have exact moduli spaces of supersymmetric vacua. We propose several dualities and we test these proposals by comparing the deformations and supersymmetric ground states. First, we consider a theory where time reversal symmetry is only emergent in the infrared and there exists (nonetheless) an exact moduli space of vacua. This theory has a dual description with manifest time reversal symmetry. Second, we consider some surprising facts about \( \mathcal{N}=2 \) U(1) gauge theory coupled to two chiral superfields of charge 1. This theory is claimed to have emergent SU(3) global symmetry in the infrared. We propose a dual Wess-Zumino description (i.e. a theory of scalars and fermions but no gauge fields) with manifest SU(3) symmetry but only \( \mathcal{N}=1 \) supersymmetry. We argue that this Wess-Zumino model must have enhanced supersymmetry in the infrared. Finally, we make some brief comments about the dynamics of \( \mathcal{N}=1 \) SU(N) gauge theory coupled to Nf quarks in a time reversal invariant fashion. We argue that for Nf < N there is a moduli space of vacua to all orders in perturbation theory but it is non-perturbatively lifted.

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Curious aspects of three-dimensional \( \mathcal{N}=1 \) SCFTs

Journal of High Energy Physics August 2018, 2018:4 | Cite as Curious aspects of three-dimensional \( \mathcal{N}=1 \) SCFTs AuthorsAuthors and affiliations Davide GaiottoZohar KomargodskiJingxiang Wu Open Access Regular Article - Theoretical Physics First Online: 02 August 2018 Received: 13 June 2018 Accepted: 21 July 2018 22 Downloads Abstract We study the dynamics of certain 3d \( \mathcal{N}=1 \) time reversal invariant theories. Such theories often have exact moduli spaces of supersymmetric vacua. We propose several dualities and we test these proposals by comparing the deformations and supersymmetric ground states. First, we consider a theory where time reversal symmetry is only emergent in the infrared and there exists (nonetheless) an exact moduli space of vacua. This theory has a dual description with manifest time reversal symmetry. Second, we consider some surprising facts about \( \mathcal{N}=2 \) U(1) gauge theory coupled to two chiral superfields of charge 1. This theory is claimed to have emergent SU(3) global symmetry in the infrared. We propose a dual Wess-Zumino description (i.e. a theory of scalars and fermions but no gauge fields) with manifest SU(3) symmetry but only \( \mathcal{N}=1 \) supersymmetry. We argue that this Wess-Zumino model must have enhanced supersymmetry in the infrared. Finally, we make some brief comments about the dynamics of \( \mathcal{N}=1 \) SU(N) gauge theory coupled to Nf quarks in a time reversal invariant fashion. We argue that for Nf < N there is a moduli space of vacua to all orders in perturbation theory but it is non-perturbatively lifted. Keywords Duality in Gauge Field Theories Nonperturbative Effects Supersymmetric Gauge Theory Supersymmetry and Duality  ArXiv ePrint: 1804.02018 Download to read the full article text Notes Open Access 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. References [1] M.T. Grisaru, W. Siegel and M. Roček, Improved methods for supergraphs, Nucl. Phys. B 159 (1979) 429 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar [2] N. Seiberg, Naturalness versus supersymmetric nonrenormalization theorems, Phys. Lett. B 318 (1993) 469 [hep-ph/9309335] [INSPIRE]. [3] N. Seiberg, Exact results on the space of vacua of four-dimensional SUSY gauge theories, Phys. Rev. D 49 (1994) 6857 [hep-th/9402044] [INSPIRE]. [4] V. Bashmakov, J. Gomis, Z. Komargodski and A. 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Davide Gaiotto, Zohar Komargodski, Jingxiang Wu. Curious aspects of three-dimensional \( \mathcal{N}=1 \) SCFTs, Journal of High Energy Physics, 2018, 4, DOI: 10.1007/JHEP08(2018)004