Thermal Order in Conformal Theories

Abstract

It is widely expected that at sufficiently high temperatures order is always lost, e.g. magnets loose their ferromagnetic properties. We pose the question of whether this is always the case in the context of quantum field theory in $d$ space dimensions. More concretely, one can ask whether there exist critical points (CFTs) which break some global symmetry at arbitrary finite temperature. The most familiar CFTs do not exhibit symmetry breaking at finite temperature, and moreover, in the context of the AdS/CFT correspondence, critical points at finite temperature are described by an uncharged black brane which obeys a no-hair theorem. Yet, we show that there exist CFTs which have some of their internal symmetries broken at arbitrary finite temperature. Our main example is a vector model which we study both in the epsilon expansion and arbitrary rank as well as the large rank limit (and arbitrary dimension). The large rank limit of the vector model displays a conformal manifold, a moduli space of vacua, and a deformed moduli space of vacua at finite temperature. The appropriate Nambu-Goldstone bosons including the dilaton-like particle are identified. Using these tools we establish symmetry breaking at finite temperature for finite small $\epsilon$. We also prove that a large class of other fixed points, which describe some of the most common quantum magnets, indeed behave as expected and do not break any global symmetry at finite temperature. We discuss some of the consequences of finite temperature symmetry breaking for the spectrum of local operators. Finally, we propose a class of fixed points which appear to be possible candidates for finite temperature symmetry breaking in $d=2$.

arXiv comment66 pages, 3 figures, 3 tables, v3: matches published version

References in corpus (56)

• Gauge Theory Correlators from Non-Critical String Theory
• The Large N Limit of Superconformal Field Theories and Supergravity
• Building an AdS/CFT superconductor
• Generalized Global Symmetries
• Holographic Superconductors
• Breaking an Abelian gauge symmetry near a black hole horizon
• AdS Dual of the Critical O(N) Vector Model
• Exact Results on the Space of Vacua of Four Dimensional SUSY Gauge Theories
• Quantum Field Theory in the Large N Limit: a review
• Theta, Time Reversal, and Temperature
• The Hagedorn Transition, Deconfinement and N=4 SYM Theory
• OPE Convergence in Conformal Field Theory
• Multicritical phenomena in O(n_1)+O(n_2)-symmetric theories
• Comments on Abelian Higgs Models and Persistent Order
• Locality of temperature
• Unitarity violation at the Wilson-Fisher fixed point in 4-epsilon dimensions
• The Conformal Bootstrap at Finite Temperature
• Holographic Phonons
• Anomalies and Bounds on Charged Operators
• A tauberian theorem for the conformal bootstrap
• Is there a monopole problem?
• Circle compactification and 't Hooft anomaly
• Generalized global symmetries and holography
• On the Hohenberg-Mermin-Wagner theorem and its limitations
• Modular Invariance, Tauberian Theorems, and Microcanonical Entropy
• A Nonperturbative Study of Inverse Symmetry Breaking at High Temperatures
• New stability results for Einstein scalar gravity
• On Symmetry Non-Restoration at High Temperature
• Interacting String Multi-verses and Holographic Instabilities of Massive Gravity
• General Properties of Multiscalar RG Flows in $d=4-\epsilon$
• Can Symmetry non-restoration solve the Monopole Problem?
• QCD on a small circle
• Exotic Hairy Black Holes
• Superfluid black branes in AdS_4\times S^7
• Anyonic particle-vortex statistics and the nature of dense quark matter
• Exotic holographic RG flows at finite temperature
• On the CJT Formalism in Multi-Field Theories
• The U.V. Price for Symmetry Non-Restoration
• Quantum Distillation of Hilbert Spaces, Semi-classics and Anomaly Matching
• Wilson Renormalization Group Study of Inverse Symmetry Breaking
• Conformality Loss, Walking, and 4D Complex Conformal Field Theories at Weak Coupling
• Matrix Theory Black Holes and the Gross Witten Transition
• Klebanov-Strassler black hole
• Inverse Symmetry Breaking with 4d Lattice Simulations
• Dynamics of Finite-Temperature CFTs from OPE Inversion Formulas
• Higher Anomalies, Higher Symmetries, and Cobordisms III: QCD Matter Phases Anew
• Holographic quantum criticality from multi-trace deformations
• The Fading of Symmetry Non-restoration at Finite Temperature
• Landau ordering phase transitions beyond the Landau paradigm
• Inverse Symmetry Breaking on the lattice: an accurate MC study
• Metastable Vacua in Large-$N$ QCD${}_3$
• Thermal order in holographic CFTs and no-hair theorem violation in black branes
• Thermal CFTs in momentum space
• Symmetry Nonrestoration in a Gross-Neveu Model with Random Chemical Potential
• Perturbative Critical Behavior from Spacetime Dependent Couplings
• Gravity/Spin-model correspondence and holographic superfluids

Cited by in corpus (41)

• Heavy Operators and Hydrodynamic Tails
• Gravitational shine of dark domain walls
• Universal Asymptotics for High Energy CFT Data
• Thermalization in Large-N CFTs
• Heavy Handed Quest for Fixed Points in Multiple Coupling Scalar Theories in the $\epsilon$ Expansion
• Vector model in various dimensions
• Thermal order in holographic CFTs and no-hair theorem violation in black branes
• Overview of lattice calculations of the $x$-dependence of PDFs, GPDs and TMDs
• Avoided Deconfinement in Randall-Sundrum Models
• A model of persistent breaking of discrete symmetry
• The free and safe fate of symmetry non-restoration
• The fate of the conformal order
• Thermal order in large N conformal gauge theories
• A model of persistent breaking of continuous symmetry
• Bounds on multiscalar CFTs in the epsilon expansion
• The bi-conical vector model at $1/N$
• SUGRA/Strings like to be bald
• Symmetry breaking at high temperatures in large N gauge theories
• Compactified holographic conformal order
• Thermal effects in non-Fermi liquid superconductivity
• A bestiary of black holes on the conifold with fluxes
• Global Electroweak Symmetric Vacuum
• The background field method and critical vector models
• Long-range fermions and critical dualities
• On partition functions and phases of scalars in AdS
• CFT data in the Gross-Neveu model
• Conformal line defects at finite temperature
• Infinite distances in multicritical CFTs and higher-spin holography
• Knitting Wormholes by Entanglement in Supergravity
• Spontaneous breaking of finite group symmetries at all temperatures
• Quantum phase transitions in a bidimensional $O(N)\times {\mathbb{Z}}_2$ scalar field model
• On the trace anomaly of Chaudhuri-Choi-Rabinovici model
• Gapped dilatons in scale invariant superfluids
• Dilaton in scalar QFT: a no-go theorem in $4-\epsilon$ and $3-\epsilon$ dimensions
• Critical long-range vector model in the UV
• Universal fine grained asymptotics of free and weakly coupled Quantum Field Theory
• Universal thermalization dynamics in (1+1)d QFTs
• Phase transitions and remnants of fractionalization at finite temperature in the triangular lattice quantum loop model
• Thermalization and Hydrodynamics of Two-Dimensional Quantum Field Theories
• 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