Arxiv: Spontaneous Conformal Symmetry Breaking in Fishnet
CERN-TH-2019-147 Spontaneous Conformal Symmetry Breaking in Fishnet CFT Georgios K. Karananas,1, ∗ Vladimir Kazakov,2, 3, 4, y and Mikhail Shaposhnikov5, z 1Arnold Sommerfeld Center, Ludwig-Maximilians-Universit¨atM¨unchen,Theresienstraße 37, 80333, M¨unchen,Germany 2Laboratoire de Physique de l'Ecole´ Normale Sup´erieure, 24 rue Lhomond, F-75231 Paris Cedex 05, France 3PSL Research University, CNRS, Sorbonne Universit´e 4CERN Theory Department, CH-1211 Geneva 23, Switzerland 5Institute of Physics, Laboratory of Particle Physics and Cosmology, Ecole´ Polytechnique F´ed´erale de Lausanne (EPFL), CH-1015, Lausanne, Switzerland Quantum field theories with exact but spontaneously broken conformal invariance have an in- triguing 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. INTRODUCTION vant for the explanation of the amazing smallness of the cosmological constant. Conformal Field Theories (CFTs) represent an indis- A systematic way to construct effective field theories pensable tool to address the behavior of many systems in enjoying exact but spontaneously broken CI was de- the vicinity of the critical points associated with phase scribed in [6], following the ideas of [7, 8] (for further transitions.
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