Symmetry breaking at high temperatures in large N gauge theories

Abstract

Considering marginally relevant and relevant deformations of the weakly coupled $(3+1)$-dimensional large $N$ conformal gauge theories introduced in arXiv:2011.13981, we study the patterns of phase transitions in these systems that lead to a symmetry-broken phase in the high temperature limit. These deformations involve only the scalar fields in the models. The marginally relevant deformations are obtained by varying certain double trace quartic couplings between the scalar fields. The relevant deformations, on the other hand, are obtained by adding masses to the scalar fields while keeping all the couplings frozen at their fixed point values. At the $N\to \infty$ limit, the RG flows triggered by these deformations approach the aforementioned weakly coupled CFTs in the UV regime. These UV fixed points lie on a conformal manifold with the shape of a circle in the space of couplings. In certain parameter regimes a subset of points on this manifold exhibits thermal order characterized by the spontaneous breaking of a global ${\mathbb{Z}}_2$ or $U(1)$ symmetry and Higgsing of a subset of gauge bosons at all nonzero temperatures. We show that the RG flows triggered by the marginally relevant deformations lead to a weakly coupled IR fixed point which lacks the thermal order. Thus, the systems defined by these RG flows undergo a transition from a disordered phase at low temperatures to an ordered phase at high temperatures. This provides examples of both inverse symmetry breaking and symmetry nonrestoration. For the relevant deformations, we demonstrate that a variety of phase transitions are possible depending on the signs and magnitudes of the masses (squared) added to the scalar fields. Using thermal perturbation theory, we derive the approximate values of the critical temperatures for all these phase transitions. All the results are obtained at the $N\to \infty$ limit.

40 pages

References in corpus (15)

• Asymptotic safety guaranteed
• Theoretical uncertainties for cosmological first-order phase transitions
• On the validity of perturbative studies of the electroweak phase transition in the Two Higgs Doublet model
• Thermodynamics of a two-step electroweak phase transition
• Large N Field Theory and AdS Tachyons
• On the perturbative expansion at high temperature and implications for cosmological phase transitions
• Thermal Order in Conformal Theories
• Orbifold equivalence and the sign problem at finite baryon density
• QCD on a small circle
• Thermal order in holographic CFTs and no-hair theorem violation in black branes
• RG Limit Cycles and Unconventional Fixed Points in Perturbative QFT
• The free and safe fate of symmetry non-restoration
• The fate of the conformal order
• Thermal order in large N conformal gauge theories
• SUGRA/Strings like to be bald

Cited by in corpus (9)

• A model of persistent breaking of discrete symmetry
• Casimir Energy and Modularity in Higher-dimensional Conformal Field Theories
• A model of persistent breaking of continuous symmetry
• Towards TeV-Scale Supersymmetric Electroweak Baryogenesis
• Spontaneous breaking of finite group symmetries at all temperatures
• Quantum phase transitions in a bidimensional $O(N)\times {\mathbb{Z}}_2$ scalar field model
• Finite size effects in the phase transition patterns of coupled scalar field systems
• The quest for a conifold conformal order
• Symmetry breaking patterns for two coupled complex scalar fields at finite temperature and in an external magnetic field