New dynamics and dualities in supersymmetric chiral gauge theories

Journal of High Energy Physics, Sep 2011

We analyze the phase structure of supersymmetric chiral gauge theories with gauge group SU(N), an antisymmetric, and F ≤ N + 3 flavors, in the presence of a cubic superpotential. When F = N + 3 the theory flows to a superconformal fixed point in the infrared, and new dual descriptions of this theory are uncovered. The theory with odd N admits a self-dual magnetic description. For general N, we find an infinite family of magnetic dual descriptions, characterized by arbitrarily large gauge groups and additional classical global symmetries that are truncated by nonperturbative effects. The infrared dynamics of these theories are analyzed using a-maximization, which supports the claim that all these theories flow to the same superconformal fixed point. A very rich phase structure is found when the number of flavors is reduced below N + 3, including a new self-dual point, transitions from conformal to confining, and a nonperturbative instability for F ≤ N. We also give examples of chiral theories with antisymmetrics that have nonchiral duals.

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New dynamics and dualities in supersymmetric chiral gauge theories

Nathaniel Craig 0 2 Rouven Essig 1 Anson Hook 1 Gonzalo Torroba 1 Open Access 0 Department of Physics and Astronomy, Rutgers University , Piscataway, NJ 08854, U.S.A 1 Physics Department and SLAC National Accelerator Laboratory, Stanford University , Stanford, CA 94309, U.S.A 2 School of Natural Sciences, Institute for Advanced Study , Princeton, NJ 08540, U.S.A We analyze the phase structure of supersymmetric chiral gauge theories with gauge group SU(N ), an antisymmetric, and F N + 3 flavors, in the presence of a cubic superpotential. When F = N + 3 the theory flows to a superconformal fixed point in the infrared, and new dual descriptions of this theory are uncovered. The theory with odd N admits a self-dual magnetic description. For general N , we find an infinite family of magnetic dual descriptions, characterized by arbitrarily large gauge groups and additional classical global symmetries that are truncated by nonperturbative effects. The infrared dynamics of these theories are analyzed using a-maximization, which supports the claim that all these theories flow to the same superconformal fixed point. A very rich phase structure is found when the number of flavors is reduced below N +3, including a new self-dual point, transitions from conformal to confining, and a nonperturbative instability for F N . We also give examples of chiral theories with antisymmetrics that have nonchiral duals. Contents 1 Introduction 2 A self-dual chiral theory 2.1 The electric theory 2.2 The magnetic dual theory 2.3 Consistency checks of the duality 3 An infinite family of dual theories 3.1 Duality from product gauge groups 3.1.1 The limit Sp(N+K4) SU(N) 3.1.2 The limit SU(N) Sp(N+K4) 3.2 Perturbative analysis of the magnetic theory 3.3 Nonperturbative effects and truncation of global symmetries 4 Dynamics at the superconformal fixed point 4.1 a-maximization in the electric theory 4.2 a-maximization in the magnetic theory for general K 5 The phase structure for F < N + 3 flavors 5.1 F = N + 2 flavors from integrating out P and one Q 5.1.1 Magnetic description 5.1.2 Phase structure 5.1.3 The superconformal index 5.2 F = N + 2 flavors from integrating out one Q and one Q 5.2.1 Magnetic description 5.2.2 Phase structure 5.3 The theory with F < N + 2 flavors 6 Generalizations and chiral/nonchiral dualities 6.1 An infinite family of duals 6.1.1 Tests of the duality 6.1.2 Adding baryonic deformations 6.2 Chiral/nonchiral dualities 7 Conclusions and future directions A Product gauge group flows for F < N + 3 A central problem in quantum field theory is to understand the phases of interacting gauge theories. While results on nonsupersymmetric theories are mostly numerical, theories with N = 1 supersymmetry (four supercharges) have holomorphic quantities which, in some cases, can be used to determine the vacuum structure. During the last decades, enormous progress on N = 1 theories has been made following the work of Seiberg [13]. Seiberg duality has now become a key tool for analyzing strongly coupled effects. Chiral gauge theories exhibit many fascinating phenomena, and have important theoretical and phenomenological applications. Starting from the pioneering works of [4, 5], dynamical supersymmetry breaking was found in chiral theories, providing one of the main motivations for their subsequent study. For reviews and references see [68]. Furthermore, intriguing dualities and nonperturbative effects have been found in these theories, like chiral-nonchiral dualities [913], mixed phases [14], and new phase transitions between conformal and confining theories (as we shall also find in this work). Various other examples have been studied for instance in [15, 16]. However, a general understanding of the infrared (IR) dynamics of chiral theories is still lacking, as is a systematic procedure to obtain dual theories. Progress in obtaining dual theories was made by Berkooz [17], who proposed to deconfine fields transforming in 2-index representations. The deconfinement method will also play an important part in this paper. In this work, we present new dualities and dynamical effects in chiral gauge theories with an SU(N ) gauge group and matter in the antisymmetric and (anti) fundamental representations. Related work on this class of models appears in [14, 1719]. Cancellation of gauge anomalies restricts the matter content to We will focus on the case F N + 3 and add a cubic superpotential W QAQ for some of the quarks, described in section 2. The first part of the work (sections 24) analyzes the dynamics for F = N + 3, while the phase structure when F < N + 3 is studied in section 5. The case F > N + 3 will be studied in [20]. First, in section 2 we argue that for N odd and F = N + 3 this theory has a dual magnetic description in terms of an SU(N ) gauge theory that includes additional mesons, baryons and cubic interactions. This reveals that this theory, which features a nonzero superpotential (...truncated)


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Nathaniel Craig, Rouven Essig, Anson Hook, Gonzalo Torroba. New dynamics and dualities in supersymmetric chiral gauge theories, Journal of High Energy Physics, 2011, pp. 46, Volume 2011, Issue 9, DOI: 10.1007/JHEP09(2011)046