Integrable Fishnet from $\gamma$-Deformed $\mathcal{N}=2$ Quivers

Abstract

We introduce bi-fermion fishnet theories, a class of models describing integrable sectors of four-dimensional gauge theories with non-maximal supersymmetry. Bi-fermion theories are characterized by a single complex scalar field and two Weyl fermions interacting only via chiral Yukawa couplings. The latter generate oriented Feynman diagrams forming hexagonal lattices, whose fishnet structure signals an underlying integrability that we exploit to compute anomalous dimensions of BMN-vacuum operators. Furthermore, we investigate Lunin-Maldacena deformations of $\mathcal{N}=2$ superconformal field theories with deformation parameter $\gamma$ and prove that bi-fermion models emerge in the limit of large imaginary $\gamma$ and vanishing 't Hooft coupling $g$, with $g{e}^{-i\gamma /2}$ fixed. Finally, we explicitly find non-trivial conformal fixed points and compute the scaling dimensions of operators for any $\gamma$ and in presence of double-trace deformations.

6 pages, 3 figures, 1 table; published version

References in corpus (17)

• High energy QCD as a completely integrable model
• Dual Superconformal Symmetry from AdS5 x S5 Superstring Integrability
• New integrable non-gauge 4D QFTs from strongly deformed planar N=4 SYM
• Bethe Ansatz for QCD Pomeron,
• Yangian Symmetry for Fishnet Feynman Graphs
• From Euclidean Sources to Lorentzian Spacetimes in Holographic Conformal Field Theories
• Holographic Aspects of Four Dimensional $\mathcal{N}=2$ SCFTs and their Marginal Deformations
• Bi-scalar integrable CFT at any dimension
• Non-conformality of gamma_i-deformed N=4 SYM theory
• Secret Symmetries of Type IIB Superstring Theory on AdS3 x S3 x M4
• Integrability in N=2 superconformal gauge theories
• RG stability of integrable fishnet models
• Yangian Symmetry of String Theory on $Ad{S}_3\times S^3\times S^3\times S^1$ with Mixed 3-form Flux
• One-loop Wilson loops and the particle-interface potential in AdS/dCFT
• The S-matrix algebra of the AdS2 X S2 superstring
• Quantum Spectral Curve of $\gamma$-twisted $\mathcal{N}=4$ SYM theory and fishnet CFT
• A Requiem for $Ad{S}_4\times \mathbb{C}{P}^3$ Fermionic self-T-duality

Cited by in corpus (26)

• Exactly solvable magnet of conformal spins in four dimensions
• Structure Constants in $\mathcal{N}=4$ SYM at Finite Coupling as Worldsheet $g$-Function
• Thermodynamic Bethe Ansatz for Fishnet CFT
• Holographic Complex Conformal Field Theories
• Exactly solvable single-trace four point correlators in $\chi$CFT${}_4$
• Integrated correlators from integrability: Maldacena-Wilson line in $\mathcal{N}=4$ SYM
• Yangian Bootstrap for Massive Feynman Integrals
• Massive Fishnets
• The Loom for General Fishnet CFTs
• Hexagonalization of Fishnet integrals I: mirror excitations
• Instability of complex CFTs with operators in the principal series
• Twistor fishnets
• The four-point function of determinant operators in $\mathcal{N}=4$ SYM
• Amplitudes in fishnet theories in diverse dimensions and Box ladder diagrams
• Conformal quantum mechanics & the integrable spinning Fishnet
• Wilson loop correlators in $\mathcal{N}=2$ superconformal quivers
• Fishnet four-point integrals: integrable representations and thermodynamic limits
• Correlation functions of determinant operators in conformal fishnet theory
• Loop Operators in Three-Dimensional $\mathcal{N}=2$ Fishnet Theories
• Bootstrability in Defect CFT: Integrated Correlators and Sharper Bounds
• Regge amplitudes in Generalized Fishnet and Chiral Fishnet Theories
• Chiral correlators in $\mathcal{N}=2$ superconformal quivers
• A Large Twist Limit for Any Operator
• Non-Local Symmetries of Planar Feynman Integrals
• Wilson loops as defects in N=2 conformal field theories
• Non-perturbative Aspects of Quantum Field Theories from Holography