Spontaneous Conformal Symmetry Breaking in Fishnet CFT

Abstract

Quantum field theories with exact but spontaneously broken conformal invariance have an intriguing feature: their vacuum energy (cosmological constant) is equal to zero. Up to now, the only known ultraviolet complete theories where conformal symmetry can be spontaneously broken were associated with supersymmetry (SUSY), with the most prominent example being the $\mathcal{N}$=4 SUSY Yang-Mills. In this Letter we show that the recently proposed conformal "fishnet" theory supports at the classical level a rich set of flat directions (moduli) along which conformal symmetry is spontaneously broken. We demonstrate that, at least perturbatively, some of these vacua survive in the full quantum theory (in the planar limit, at the leading order of $1/N_c$ expansion) without any fine tuning. The vacuum energy is equal to zero along these flat directions, providing the first non-SUSY example of a four-dimensional quantum field theory with "natural" breaking of conformal symmetry.

arXiv commentJournal version

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Cited by in corpus (12)

• Massive Conformal Symmetry and Integrability for Feynman Integrals
• Scale and Weyl Invariance in Einstein-Cartan Gravity
• Massive Fishnets
• The Loom for General Fishnet CFTs
• Thermal order in large N conformal gauge theories
• Exact quantum conformal symmetry, its spontaneous breakdown, and gravitational Weyl anomaly
• Integrability for Feynman Integrals
• Twistor fishnets
• Instability of complex CFTs with operators in the principal series
• Amplitudes in fishnet theories in diverse dimensions and Box ladder diagrams
• Dilaton in scalar QFT: a no-go theorem in $4-\epsilon$ and $3-\epsilon$ dimensions
• A Large Twist Limit for Any Operator