Colour-Twist Operators I: Spectrum and Wave Functions

Abstract

We introduce a new class of operators in any theory with a 't Hooft large-$N$ limit that we call colour-twist operators. They are defined by twisting the colour-trace with a global symmetry transformation and are continuously linked to standard, un-twisted single-trace operators. In particular, correlation functions between operators that are twisted by an R-symmetry of $\mathcal{N}=4$ SYM extend those in the $\gamma$-deformed theory. The most general deformation also breaks the Lorentz symmetry but preserves integrability in the examples we consider. In this paper, we focus on colour-twist operators in the fishnet model. We exemplify our approach for the simplest colour-twist operators with one and two scalar fields, which we study non-perturbatively using field-theoretical as well as integrability methods, finding a perfect match. We also propose the quantisation condition for the Baxter equation appearing in the integrability calculation in the fishnet model. The results of this paper constitute a crucial step towards building the separation of variable construction for the correlation functions by means of the Quantum Spectral Curve approach.

arXiv comment66 pages, 20 figures

References in corpus (40)

• Entanglement Entropy and Quantum Field Theory
• Towards a derivation of holographic entanglement entropy
• Deforming field theories with $U(1)\times U(1)$ global symmetry and their gravity duals
• Separation of Variables. New Trends.
• Lax Pair for Strings in Lunin-Maldacena Background
• Integrability for the Full Spectrum of Planar AdS/CFT
• Quantum spectral curve for AdS_5/CFT_4
• Light-ray operators in conformal field theory
• Holographic Calculations of Renyi Entropy
• Beauty and the Twist: The Bethe Ansatz for Twisted N=4 SYM
• New integrable non-gauge 4D QFTs from strongly deformed planar N=4 SYM
• Notes on the scattering amplitude / Wilson loop duality
• Quantum spectral curve for arbitrary state/operator in AdS${}_5$/CFT${}_4$
• From correlation functions to scattering amplitudes
• A General Proof of the Quantum Null Energy Condition
• Gauge-string duality for (non)supersymmetric deformations of N=4 Super Yang-Mills theory
• The cusp anomalous dimension at three loops and beyond
• T-system on T-hook: Grassmannian Solution and Twisted Quantum Spectral Curve
• Quantum Spectral Curve and the Numerical Solution of the Spectral Problem in AdS5/CFT4
• Strongly γ-deformed N=4 SYM as an integrable CFT
• NNLO BFKL Pomeron eigenvalue in N=4 SYM
• Integrability of Conformal Fishnet Theory
• Quantum Spectral Curve and Structure Constants in N=4 SYM: Cusps in the Ladder Limit
• Handling Handles: Nonplanar Integrability in $\mathcal{N}=4$ Supersymmetric Yang-Mills Theory
• Twist operators in higher dimensions
• TBA, NLO Luscher correction, and double wrapping in twisted AdS/CFT
• New Construction of Eigenstates and Separation of Variables for SU(N) Quantum Spin Chains
• PSU(2,2|4) Character of Quasiclassical AdS/CFT
• Scattering Amplitudes -- Wilson Loops Duality for the First Non-planar Correction
• Exact Correlation Functions in Conformal Fishnet Theory
• Y-system and beta-deformed N=4 Super-Yang-Mills
• The Holographic Fishchain
• Handling Handles. Part II. Stratification and Data Analysis
• Review of AdS/CFT Integrability, Chapter III.7: Hirota Dynamics for Quantum Integrability
• Finite-size effect for four-loop Konishi of the beta-deformed N=4 SYM
• Quantum Fishchain in $Ad{S}_5$
• Review of AdS/CFT Integrability, Chapter III.5: Luscher corrections
• The Holographic Dual of Strongly γ-deformed N=4 SYM Theory: Derivation, Generalization, Integrability and Discrete Reparametrization Symmetry
• Scalar Insertions in Cusped Wilson Loops in the Ladders Limit of Planar N=4 SYM
• Inheritance principle and Non-renormalization theorems at finite temperature

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• Orthogonality of Q-Functions up to Wrapping in Planar N=4 Super Yang-Mills Theory