# Spontaneous Conformal Symmetry Breaking in Fishnet CFT

## TL;DR

This paper demonstrates that the fishnet conformal field theory can spontaneously break conformal symmetry at the classical level with some vacua surviving quantum corrections, resulting in a zero vacuum energy without supersymmetry.

## Contribution

It shows for the first time that a non-supersymmetric four-dimensional quantum field theory can naturally exhibit spontaneous conformal symmetry breaking with zero vacuum energy.

## Key findings

- Existence of flat directions where conformal symmetry is broken.
- Some vacua persist quantum mechanically without fine tuning.
- Vacuum energy remains zero along these flat directions.

## 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.