Non-conformality of gamma_i-deformed N=4 SYM theory

Abstract

We show that the gamma_i-deformation, which was proposed as candidate gauge theory for a non-supersymmetric three-parameter deformation of the AdS/CFT correspondence, is not conformally invariant due to a running double-trace coupling - not even in the 't Hooft limit. Moreover, this non-conformality cannot be cured when we extend the theory by adding at tree-level arbitrary multi-trace couplings that obey certain minimal consistency requirements. Our findings suggest a possible connection between this breakdown of conformal invariance and a puzzling divergence recently encountered in the integrability-based descriptions of two-loop finite-size corrections for the single-trace operator of two identical chiral fields. We propose a test to clarify this.

LaTeX, feynmp, 25 pages, 1 figure; v2: formulations improved, references added, typos corrected, 27 pages; v3: typos corrected, one reference added, matches published version

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• Holographic Evidence for Non-Supersymmetric Conformal Manifolds
• The complete one-loop dilatation operator of planar real beta-deformed N=4 SYM theory
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• Exactly solvable single-trace four point correlators in $\chi$CFT${}_4$
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• Quantum Spectral Curve of $\gamma$-twisted $\mathcal{N}=4$ SYM theory and fishnet CFT
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• Massive Fishnets
• The One-Loop Spectral Problem of Strongly Twisted $\mathcal{N}$=4 Super Yang-Mills Theory
• Solving the Hagedorn temperature of AdS5/CFT4 via the Quantum Spectral Curve: Chemical potentials and deformations
• Exact scattering amplitudes in conformal fishnet theory
• Yangian Ward Identities for Fishnet Four-Point Integrals
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• One-Loop Non-Planar Anomalous Dimensions in Super Yang-Mills Theory
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• Integrability treatment of AdS/CFT orbifolds
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• Regge amplitudes in Generalized Fishnet and Chiral Fishnet Theories
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• $T^3$ deformations and $\beta$-deformed geometries
• Spectral curve for gamma-deformed AdS/CFT
• Beta deformed sigma model and strong deformation coupling limit