Spontaneous conformal symmetry breaking in fishnet CFT

Georgios K Karananas,Vladimir Kazakov,Mikhail Shaposhnikov

doi:10.1016/j.physletb.2020.135922

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 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/Nc 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.

Highlights

Conformal Field Theories (CFTs) represent an indispensable tool to address the behavior of many systems in the vicinity of the critical points associated with phase transitions
In this Letter we show that there exists a nonsupersymmetric CFT with these properties—the recently proposed strongly γ deformed N = 4 SUSY Yang-Mills (SYM), dubbed Conformal Fishnet Theory (FCFT)
We will be able to demonstrate this perturbatively in the coupling constant. The reasons for these rather surprising properties for a non-SUSY theory are: i) its UV-finiteness; ii) the fact that the FCFT has a large moduli space, which increases the chances of finding directions along which conformal invariance (CI) may be broken even without resorting to unnatural tunings; iii) the supersymmetric stabilization mechanism of the parent theory is replaced by the absence of certain dangerous loop diagrams that would normally lift the classical flat directions in the Coleman-Weinberg (CW) effective potential [16]

Summary

Introduction

The reasons for these rather surprising properties for a non-SUSY theory are: i) its UV-finiteness; ii) the fact that the FCFT has a large moduli space, which increases the chances of finding directions along which CI may be broken even without resorting to unnatural tunings; iii) the supersymmetric stabilization mechanism of the parent theory is replaced by the absence of certain dangerous loop diagrams that would normally lift the classical flat directions in the Coleman-Weinberg (CW) effective potential [16] This self-protection mechanism is not powerful enough to completely liberate the FCFT from all multiloop corrections on top of arbitrary flat directions, even in the planar limit. The FCFT can be extremely useful as it provides the so far unique possibility to test certain ideas of potential phenomenological value in the non-SUSY world

Fishnet CFT

Flat vacua

Classical flat vacua

Quantum Coleman-Weinberg effective potential

Conclusions and open problems