Gravitational instantons and anomalous chiral symmetry breaking

Abstract

We study anomalous chiral symmetry breaking in two-flavour QCD induced by gravitational and QCD-instantons within asymptotically safe gravity within the functional renormalisation group approach. Similarly to QCD-instantons, gravitational ones, associated to a K3-surface connected by a wormhole-like throat in flat spacetime, generate contributions to the 't~Hooft coupling proportional to $\exp (-1/g_N)$ with the dimensionless Newton coupling $g_N$. Hence, in the asymptotically safe gravity scenario with a non-vanishing fixed point coupling $g_N^{\ast }$, the induced 't Hooft coupling is finite at the Planck scale, and its size depends on the chosen UV-completion. Within this scenario the gravitational effects on anomalous $U(1{)}_A$-breaking at the Planck scale may survive at low energy scales. In turn, fermion masses of the order of the Planck scale cannot be present. This constrains the allowed asymptotically safe UV-completion of the Gravity-QCD system. We map-out the parameter regime that is compatible with the existence of light fermions in the low-energy regime.

arXiv comment14 pages, 7 figures

References in corpus (72)

• Exact evolution equation for the effective potential
• QCD Phenomenology based on a Chiral Effective Lagrangian
• Non-Perturbative Renormalization Flow in Quantum Field Theory and Statistical Physics
• Instantons in QCD
• Nonperturbative Evolution Equation for Quantum Gravity
• The Exact Renormalisation Group and Approximate Solutions
• Aspects of the Functional Renormalisation Group
• The QCD phase structure at finite temperature and density
• An Introduction to the Nonperturbative Renormalization Group
• Non-Trivial Ultraviolet Fixed Point in Quantum Gravity
• Introduction to the functional RG and applications to gauge theories
• Instantons at work
• Flow Equations for N Point Functions and Bound States
• Fundamentals of the Exact Renormalization Group
• Fermion Interactions and Universal Behavior in Strongly Interacting Theories
• Chiral symmetry breaking in continuum QCD
• Lectures on the functional renormalization group method
• Non-perturbative quark, gluon and meson correlators of unquenched QCD
• Renormalization Flow of Bound States
• From Quarks and Gluons to Hadrons: Chiral Symmetry Breaking in Dynamical QCD
• Renormalisation group and the Planck scale
• Chiral phase structure of QCD with many flavors
• Asymptotic safety of gravity-matter systems
• Local Quantum Gravity
• Towards apparent convergence in asymptotically safe quantum gravity
• One force to rule them all: asymptotic safety of gravity with matter
• Asymptotic freedom of Yang-Mills theory with gravity
• Dynamical symmetry breaking in curved spacetime -review-
• Universality of spontaneous chiral symmetry breaking in gauge theories
• Light fermions in quantum gravity
• Asymptotically safe cosmology - a status report
• Exact flow equation for composite operators
• Viability of quantum-gravity induced ultraviolet completions for matter
• Quantum gravity and Standard-Model-like fermions
• Chiral fermions in asymptotically safe quantum gravity
• Towards a renormalizable standard model without fundamental Higgs scalar
• The Vacuum Structure of Vector Mesons in QCD
• Global solutions of functional fixed point equations via pseudo-spectral methods
• Nambu-Jona-Lasinio Model in Curved Space-Time
• Fierz-complete NJL model study III: Emergence from quark-gluon dynamics
• Solving functional flow equations with pseudo-spectral methods
• Atiyah-Patodi-Singer index from the domain-wall fermion Dirac operator
• Phase structure of renormalizable four-fermion models in spacetimes of constant curvature
• Exact Flow Equations and the U(1)-Problem
• Chiral gap effect in curved space
• A curvature bound from gravitational catalysis
• Analysis of the Wilsonian Effective Potentials in Dynamical Chiral Symmetry Breaking
• Phase structure of NJL model with weak renormalization group
• Dynamical Symmetry Breaking in Spaces with Constant Negative Curvature
• Temperature- and Curvature Dependence of the Chiral Symmetry Breaking in 2D Gauge Theories
• The Atiyah-Patodi-Singer index and domain-wall fermion Dirac operators
• Three Dimensional Gross-Neveu Model on Curved Spaces
• Gap generation for Dirac fermions on Lobachevsky plane in a magnetic field
• Curvature Induced Phase Transition in a Four-Fermion Theory Using the Weak Curvature Expansion
• Weak solution of the non-perturbative renormalization group equation to describe the dynamical chiral symmetry breaking
• Partial bosonisation for the two-dimensional Hubbard model: How well does it work?
• Resolving phase transitions with Discontinuous Galerkin methods
• Geometrically induced magnetic catalysis and critical dimensions
• Temperature induced phase transitions in four fermion models in curved space-time
• Gravitational catalysis of chiral and color symmetry breaking of quark matter in hyperbolic space
• Chiral symmetry breaking in gauged $\mathbf{NJL}$ model in curved spacetime
• Approach to D-dimensional Gross-Neveu model at finite temperature and curvature
• Gauge and gravitational instantons: From 3-forms and fermions to Weak Gravity and flat axion potentials
• The separation of the chiral and deconfinement phase transitions in the curved space-time
• Renormalization flow towards gravitational catalysis in the 3d Gross-Neveu model
• Gauged NJL model at strong curvature
• Observable consequences of quantum gravity: Can light fermions exist?
• Quantum spacetime and the renormalization group: Progress and visions
• Bound states in Functional Renormalization Group
• Curvature-induced phase transitions in the inflationary universe - Supersymmetric Nambu-Jona-Lasinio Model in de Sitter spacetime -
• Topological and Curvature Effects in a Multi-fermion Interaction Model
• Topological Origin of Chiral Symmetry Breaking in QCD and in Gravity

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• The Asymptotically Safe Standard Model: From quantum gravity to dynamical chiral symmetry breaking
• Asymptotic freedom and safety in quantum gravity
• A curvature bound from gravitational catalysis in thermal backgrounds
• Quantum gravity phenomenology at the dawn of the multi-messenger era -- A review
• Is asymptotically safe inflation eternal?
• Mod-two APS index and domain-wall fermion
• Scaling solutions for asymptotically free quantum gravity
• Understanding the index theorems with massive fermions
• Fate of chiral symmetry in Riemann-Cartan geometry
• Asymptotically Safe Gravity-Fermion systems on curved backgrounds