Thermal order in large N conformal gauge theories

Abstract

In this work we explore the possibility of spontaneous breaking of global symmetries at all nonzero temperatures for conformal field theories (CFTs) in $D=4$ space-time dimensions. We show that such a symmetry-breaking indeed occurs in certain families of non-supersymmetric large $N$ gauge theories at a planar limit. We also show that this phenomenon is accompanied by the system remaining in a persistent Brout-Englert-Higgs (BEH) phase at any temperature. These analyses are motivated by the work done in arXiv:2005.03676 where symmetry-breaking was observed in all thermal states for certain CFTs in fractional dimensions. In our case, the theories demonstrating the above features have gauge groups which are specific products of $SO(N)$ in one family and $SU(N)$ in the other. Working in a perturbative regime at the $N\to \infty$ limit, we show that the beta functions in these theories yield circles of fixed points in the space of couplings. We explicitly check this structure up to two loops and then present a proof of its survival under all loop corrections. We show that under certain conditions, an interval on this circle of fixed points demonstrates both the spontaneous breaking of a global symmetry as well as a persistent BEH phase at all nonzero temperatures. The broken global symmetry is ${\mathbb{Z}}_2$ in one family of theories and $U(1)$ in the other. The corresponding order parameters are expectation values of the determinants of bifundamental scalar fields in these theories. We characterize these symmetries as baryon-like symmetries in the respective models.

arXiv comment116 pages, v4: typos have been corrected, comments and references have been added, version matches with the published one

References in corpus (56)

• Building an AdS/CFT superconductor
• Holographic Superconductors
• Breaking an Abelian gauge symmetry near a black hole horizon
• 4d Conformal Field Theories and Strings on Orbifolds
• On Conformal Theories in Four Dimensions
• d=3 Bosonic Vector Models Coupled to Chern-Simons Gauge Theories
• Two-loop Renormalization Group Equations in General Gauge Field Theories
• Large N limit of orbifold field theories
• Comments on Abelian Higgs Models and Persistent Order
• Unitarity violation at the Wilson-Fisher fixed point in 4-epsilon dimensions
• Holographic Phonons
• New Methods in QFT and QCD: From Large-N Orbifold Equivalence to Bions and Resurgence
• Baryon Spectra and AdS/CFT Correspondence
• Perturbative Search for Fixed Lines in Large N Gauge Theories
• (In)validity of large N orientifold equivalence
• Is there a monopole problem?
• Gauge/Gravity Duality and Warped Resolved Conifold
• Large N Field Theory and AdS Tachyons
• Circle compactification and 't Hooft anomaly
• Perturbative Gauge Theory and Closed String Tachyons
• Duality of Non-Supersymmetric Large N Gauge Theories
• Necessary and sufficient conditions for non-perturbative equivalences of large N orbifold gauge theories
• Dibaryons, Branes, And Strings In AdS Orbifold Models
• Universality of Phases in QCD and QCD-like Theories
• A Nonperturbative Study of Inverse Symmetry Breaking at High Temperatures
• Thermal Order in Conformal Theories
• Unrestored Electroweak Symmetry
• Non-perturbative equivalences among large N gauge theories with adjoint and bifundamental matter fields
• Interacting String Multi-verses and Holographic Instabilities of Massive Gravity
• An Analysis of Scheme Transformations in the Vicinity of an Infrared Fixed Point
• Orbifold equivalence and the sign problem at finite baryon density
• Exotic Hairy Black Holes
• Superfluid black branes in AdS_4\times S^7
• Scheme Transformations in the Vicinity of an Infrared Fixed Point
• Exotic holographic RG flows at finite temperature
• Symmetry-breaking vacua and baryon condensates in AdS/CFT
• The U.V. Price for Symmetry Non-Restoration
• Conformality Loss, Walking, and 4D Complex Conformal Field Theories at Weak Coupling
• Quantum Distillation of Hilbert Spaces, Semi-classics and Anomaly Matching
• Klebanov-Strassler black hole
• On non-supersymmetric conformal manifolds: field theory and holography
• Dualities and Phases of 3D N=1 SQCD
• Higher Anomalies, Higher Symmetries, and Cobordisms III: QCD Matter Phases Anew
• Phase structure of complete asymptotically free SU($N_c$) theories with quarks and scalar quarks
• The Fading of Symmetry Non-restoration at Finite Temperature
• Inverse Symmetry Breaking on the lattice: an accurate MC study
• Baryonic branches and resolutions of Ricci-flat Kahler cones
• RG Limit Cycles and Unconventional Fixed Points in Perturbative QFT
• Spontaneous Conformal Symmetry Breaking in Fishnet CFT
• On the Question of an Ultraviolet Zero of the Beta Function of the $\lambda ({\vec{\varphi }}^2{)}_4^2$ Theory
• The fate of the conformal order
• Symmetry Nonrestoration in a Gross-Neveu Model with Random Chemical Potential
• SUGRA/Strings like to be bald
• Symmetry Non Restoration and Inverse Symmetry Breaking on the lattice
• New and Old Fermionic Dualities from 3d Bosonization
• Generalization of QCD${}_3$ Symmetry-Breaking and Flavored Quiver Dualities

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