Dual Superconformal Symmetry of $\mathcal{N}=2$ Chern-Simons theory with Fundamental Matter at Large $N$

Abstract

Dual conformal symmetry and Yangian symmetry are symmetries of amplitudes that have aided the study of scattering amplitudes in highly supersymmetric theories like $\mathcal{N}=4$ SYM and ABJM. However, in general such symmetries are absent from the theories with lesser or no supersymmetry. In this paper, we show that the tree level $2\to 2$ scattering amplitude in the 3d $\mathcal{N}=2$ Chern-Simons theory coupled to a fundamental chiral multiplet is dual superconformal invariant. In the 't Hooft large $N$ limit, the $2\to 2$ scattering amplitude in this theory has been shown to be tree-level exact in non-anyonic channels, while having only an overall multiplicative coupling dependent renormalisation in the anyonic channel. Therefore, the dual superconformal symmetry that we demonstrate in this paper is all loop exact. This is unlike the previously studied highly supersymmetric theories where dual superconformal symmetry is anomalous at loop levels. Furthermore, we reverse the argument to study the extent to which dual superconformal invariance fixes the scattering amplitude in an $\mathcal{N}=2$ supersymmetric theory. We demonstrate that requiring the dual superconformal invariance completely fixes the momentum dependence of the $2\to 2$ amplitude, while the coupling constant dependence remain unfixed. Further, we use a combination of parity invariance, unitarity and self-duality of the amplitude to constrain the coupling dependence of scattering amplitude.

arXiv commentV2 Published version

References in corpus (50)

• Dual superconformal symmetry of scattering amplitudes in N=4 super-Yang-Mills theory
• A Duality Web in 2+1 Dimensions and Condensed Matter Physics
• Chern-Simons Theory with Vector Fermion Matter
• Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory
• Fermionic T-Duality, Dual Superconformal Symmetry, and the Amplitude/Wilson Loop Connection
• Level/rank Duality and Chern-Simons-Matter Theories
• Seiberg Duality in Chern-Simons Theory
• d=3 Bosonic Vector Models Coupled to Chern-Simons Gauge Theories
• Constraining conformal field theories with a slightly broken higher spin symmetry
• Particle-Vortex Duality from 3d Bosonization
• Comments on 3d Seiberg-like dualities
• Correlation Functions of Large N Chern-Simons-Matter Theories and Bosonization in Three Dimensions
• Baryons, monopoles and dualities in Chern-Simons-matter theories
• Time-Reversal Breaking in QCD${}_4$, Walls, and Dualities in 2+1 Dimensions
• Comments on Global Symmetries, Anomalies, and Duality in (2+1)d
• From correlation functions to Wilson loops
• The Thermal Free Energy in Large N Chern-Simons-Matter Theories
• Chern-Simons-matter dualities with $SO$ and $USp$ gauge groups
• Chern Simons duality with a fundamental boson and fermion
• Correlators of Large N Fermionic Chern-Simons Vector Models
• Phases of large $N$ vector Chern-Simons theories on $S^2\times S^1$
• Tree-level Recursion Relation and Dual Superconformal Symmetry of the ABJM Theory
• On the Higher-Spin Spectrum in Large N Chern-Simons Vector Models
• Scattering in Mass-Deformed N>=4 Chern-Simons Models
• More Abelian Dualities in 2+1 Dimensions
• Supersymmetric Chern-Simons Theories with Vector Matter
• Unitarity, Crossing Symmetry and Duality of the S-matrix in large N Chern-Simons theories with fundamental matter
• ABJM amplitudes and the positive orthogonal grassmannian
• Disorder Operators in Chern-Simons-Fermion Theories
• Yangian Symmetry for Bi-Scalar Loop Amplitudes
• On the fermionic T-duality of the AdS_4 \times CP^3 sigma-model
• On Integrable Backgrounds Self-dual under Fermionic T-duality
• Duality and Higher Temperature Phases of Large $N$ Chern-Simons Matter Theories on $S^2\times S^1$
• Unitarity, Crossing Symmetry and Duality in the scattering of $\mathcal{N}=1$ Susy Matter Chern-Simons theories
• Chern Simons Bosonization along RG Flows
• On AdS_4 x CP^3 T-duality
• Self-Duality of Green-Schwarz Sigma-Models
• Non-Abelian 3d Bosonization and Quantum Hall States
• Embedding three-dimensional bosonization dualities into string theory
• Chern-Simons-Fermion Vector Model with Chemical Potential
• Anomalous Dimensions in Non-Supersymmetric Bifundamental Chern-Simons Theories
• Poles in the $S$-Matrix of Relativistic Chern-Simons Matter theories from Quantum Mechanics
• Transport in Chern-Simons-Matter Theories
• Bosonizing three-dimensional quiver gauge theories
• Scattering Amplitude and Bosonization Duality in General Chern-Simons Vector Models
• A Note on Large N Thermal Free Energy in Supersymmetric Chern-Simons Vector Models
• All tree level scattering amplitudes in Chern-Simons theories with fundamental matter
• On the ABJM four-point amplitude at three loops and BDS exponentiation
• Large N Chern-Simons with massive fundamental fermions - A model with no bound states
• Complete factorization in minimal N=4 Chern-Simons-matter theory

Cited by in corpus (12)

• Constraining momentum space correlators using slightly broken higher spin symmetry
• Line operators in Chern-Simons-Matter theories and Bosonization in Three Dimensions II -Perturbative Analysis and All-loop Resummation
• Correlation functions in $\mathcal{N}=2$ Supersymmetric vector matter Chern-Simons theory
• Fermi seas from Bose condensates in Chern-Simons matter theories and a bosonic exclusion principle
• Matter Chern Simons Theories in a Background Magnetic Field
• The large $N$ phase diagram of $\mathcal{N}=2$ $SU(N)$ Chern-Simons theory with one fundamental chiral multiplet
• Mass-deformed $\mathcal{N}=3$ Supersymmetric Chern-Simons-Matter Theory
• Mapping Large N Slightly Broken Higher Spin (SBHS) theory correlators to Free theory correlators
• Scattering Amplitudes in $\mathcal{N}=3$ Supersymmetric $SU(N)$ Chern-Simons-Matter Theory at Large $N$
• The Hilbert Space of large $N$ Chern-Simons matter theories
• Hidden sectors of Chern-Simons Matter theories and Exact Holography
• On thermal correlators and bosonization duality in Chern-Simons theories with massive fundamental matter