2019/05/17 by Ofer Aharony, Adar Sharon · 34 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Chern–Simons theory #Combinatorics #Conjecture #Coupling (piping) #Degenerate energy levels #Fixed point #Gauge theory #Mathematical analysis #Mathematical physics #Mathematics #Physics #Physics of Superconductivity and Magnetism #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #Renormalization group #Supersymmetry #hep-th
paper · pdf · doi:10.1007/jhep07(2019)160
published in Journal of High Energy Physics 2019(7) (Springer Nature)
arxiv created 2019/05/17 · openalex created_date 2019/05/29 · openalex publication_date 2019/07/01 · arxiv updated 2019/09/04 · openalex updated_date 2026/08/05
A bstract We discuss 3 d N <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 1 supersymmetric SU( N ) and U( N ) Chern-Simons-matter theories, with N f matter superfields in the fundamental representation of SU( N ) or U( N ). In the large N ’t Hooft limit with fixed ’t Hooft coupling λ these theories have one (for N f = 1) or two (for N f > 1) exactly marginal deformations in the superpotential. At finite N these couplings acquire a beta function. We compute the beta function exactly for λ = 0, at leading order in 1 /N . For N f = 1 we find four fixed points, one of which is triply-degenerate. We show that at large N there are at most six fixed points for any λ, and conjecture that there are exactly six, with three of them stable (including a point with enhanced N <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 2 supersymmetry). The strong-weak coupling dualities of N <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 1 Chern-Simons-matter theories map each of these fixed points to a dual one. We show that at large N the phase structure near each of the three stable fixed points is different. For N f > 1 we analyze the fixed points at weak coupling, and we work out the action of the strong-weak coupling duality on the marginal and relevant superpotential couplings at large N (which was previously known only for N f = 1). In addition, we compute in these theories the 2-point and 3-point functions of the lowest gauge-invariant singlet superfield at large N , for all values of λ and of the superpotential couplings, and use them to test the large N dualities. This computation is one of the ingredients needed for a computation of the beta function at order 1 /N for all λ, which we leave for future work. We also discuss Chern-Simons-matter theories with extra Hubbard-Stratonovich type singlet fields, and suggest dualities between them.