A piece of cake: the ground-state energies in gamma_i-deformed N=4 SYM theory

Abstract

In the non-supersymmetric gamma_i-deformed N=4 SYM theory, the scaling dimensions of the operators tr[Z^L] composed of L scalar fields Z receive finite-size wrapping and prewrapping corrections in the 't Hooft limit. In this paper, we calculate these scaling dimensions to leading wrapping order directly from Feynman diagrams. For L>=3, the result is proportional to the maximally transcendental `cake' integral. It matches with an earlier result obtained from the integrability-based Luescher corrections, TBA and Y-system equations. At L=2, where the integrability-based equations yield infinity, we find a finite rational result. This result is renormalization-scheme dependent due to the non-vanishing beta-function of an induced quartic scalar double-trace coupling, on which we have reported earlier. This explicitly shows that conformal invariance is broken - even in the 't Hooft limit.

21 pages, LaTeX, BibTeX, pstricks, feynmp

References in corpus (6)

• Twisting the Mirror TBA
• Finite-size effects in the superconformal beta-deformed N=4 SYM
• Y-system and beta-deformed N=4 Super-Yang-Mills
• Twisted Bethe equations from a twisted S-matrix
• Single impurity operators at critical wrapping order in the beta-deformed N=4 SYM
• The complete one-loop dilatation operator of planar real beta-deformed N=4 SYM theory

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• Strongly γ-deformed N=4 SYM as an integrable CFT
• Almost abelian twists and AdS/CFT
• Bi-scalar integrable CFT at any dimension
• Yangian Symmetry for Bi-Scalar Loop Amplitudes
• Basso-Dixon Correlators in Two-Dimensional Fishnet CFT
• Exact Correlation Functions in Conformal Fishnet Theory
• On a CFT limit of planar ${\gamma }_i$-deformed $\mathcal{N}=4$ SYM theory
• The complete one-loop dilatation operator of planar real beta-deformed N=4 SYM theory
• Spontaneous Conformal Symmetry Breaking in Fishnet CFT
• Quantum Spectral Curve of $\gamma$-twisted $\mathcal{N}=4$ SYM theory and fishnet CFT
• Solving the Hagedorn temperature of AdS5/CFT4 via the Quantum Spectral Curve: Chemical potentials and deformations
• Massive Fishnets
• Exact scattering amplitudes in conformal fishnet theory
• Hexagonalization of Fishnet integrals I: mirror excitations
• N=4 SYM Quantum Spectral Curve in BFKL regime
• One-Loop Partition Functions in Deformed $\mathcal{N}=4$ SYM Theory
• Correlation functions of determinant operators in conformal fishnet theory
• Dilaton in scalar QFT: a no-go theorem in $4-\epsilon$ and $3-\epsilon$ dimensions
• A hitchhiker's guide to quantum field theoretic aspects of $\mathcal{N}=4$ SYM theory and its deformations
• Holographic backgrounds from D-brane probes