Renormalization flow towards gravitational catalysis in the 3d Gross-Neveu model

Abstract

Catalyzed symmetry breaking arises from a parametric enhancement of critical fluctuations independently of the coupling strength. Symmetry-breaking fermionic long-range fluctuations exhibit such an enhancement on negatively curved spaces, as is known from mean-field studies. We study gravitational catalysis from the viewpoint of the functional renormalization group using the 3d Gross-Neveu model as a specific example. We observe gravitational catalysis towards a phase of broken discrete chiral symmetry both on a maximally symmetric (AdS) and on a purely spatially curved manifold for constant negative curvature (Lobachevsky plane). The resulting picture for gravitational catalysis obtained from the renormalization flow is closely related to that of magnetic catalysis. As an application, we estimate the curvature required for subcritical systems of finite length to acquire a gravitionally catalyzed gap.

13 pages, 3 figures

References in corpus (13)

• Exact evolution equation for the effective potential
• Unconventional Integer Quantum Hall effect in graphene
• Interactions and phase transitions on graphene's honeycomb lattice
• Asymptotic safety: a simple example
• The chiral condensate in a constant electromagnetic field
• UV fixed-point structure of the three-dimensional Thirring model
• Critical behavior of the (2+1)-dimensional Thirring model
• Dynamically Induced Zeeman Effect in Massless QED
• Dynamically Generated Anomalous Magnetic Moment in Massless QED
• Quantum critical scaling in magnetic field near the Dirac point in graphene
• Gap generation for Dirac fermions on Lobachevsky plane in a magnetic field
• Gravitational catalysis of chiral and color symmetry breaking of quark matter in hyperbolic space
• The separation of the chiral and deconfinement phase transitions in the curved space-time

Cited by in corpus (12)

• Quantum scalar fields in de Sitter space from the nonperturbative renormalization group
• Renormalization group flow and symmetry restoration in de Sitter space
• Fermions in gravity with local spin-base invariance
• Light charged fermions in quantum gravity
• A curvature bound from gravitational catalysis
• Global surpluses of spin-base invariant fermions
• Spin-base invariance of Fermions in arbitrary dimensions
• Gravitational instantons and anomalous chiral symmetry breaking
• A curvature bound from gravitational catalysis in thermal backgrounds
• Interplay between superconductivity and chiral symmetry breaking in a (2+1)-dimensional model with compactified spatial coordinate
• Magnetic catalysis effect in (2+1)-dimensional Gross--Neveu model with Zeeman interaction
• Fate of chiral symmetry in Riemann-Cartan geometry