Topological Invariants, Instantons and Chiral Anomaly on Spaces with Torsion

Abstract

In a spacetime with nonvanishing torsion there can occur topologically stable configurations associated with the frame bundle which are independent of the curvature. The relevant topological invariants are integrals of local scalar densities first discussed by Nieh and Yan (N-Y). In four dimensions, the N-Y form $N=(T^a\wedge T_a-R_{ab}\wedge e^a\wedge e^b)$ is the only closed 4-form invariant under local Lorentz rotations associated with the torsion of the manifold. The integral of $N$ over a compact D-dimensional (Euclidean) manifold is shown to be a topological invariant related to the Pontryagin classes of SO(D+1) and SO(D). An explicit example of a topologically nontrivial configuration carrying nonvanishing instanton number proportional to $\int N$ is costructed. The chiral anomaly in a four-dimensional spacetime with torsion is also shown to contain a contribution proportional to $N$, besides the usual Pontryagin density related to the spacetime curvature. The violation of chiral symmetry can thus depend on the instanton number of the tangent frame bundle of the manifold. Similar invariants can be constructed in D>4 dimensions and the existence of the corresponding nontrivial excitations is also discussed.

6 pages, RevTeX, no figures, two columns

Cited by in corpus (130)

• f(T) teleparallel gravity and cosmology
• Physical Aspects of the Space-Time Torsion
• Teleparallel equivalent of Gauss-Bonnet gravity and its modifications
• Torsional Anomalies, Hall Viscosity, and Bulk-boundary Correspondence in Topological States
• Cosmological applications of $F(T,T_G)$ gravity
• Fermions in Ashtekar-Barbero Connections Formalism for Arbitrary Values of the Immirzi Parameter
• Interaction of the Barbero--Immirzi Field with Matter and Pseudo-Scalar Perturbations
• The First Law of Black Hole Mechanics for Fields with Internal Gauge Freedom
• Magnetic monopoles revisited: Models and searches at colliders and in the Cosmos
• Barbero-Immirzi field in canonical formalism of pure gravity
• Peccei--Quinn mechanism in gravity and the nature of the Barbero--Immirzi parameter
• Thermal transport, geometry, and anomalies
• Torsion, Parity-odd Response and Anomalies in Topological States
• Modified teleparallel theories of gravity -- Gauss-Bonnet and trace extensions
• Topological Interpretation of Barbero-Immirzi Parameter
• Emergent spacetime and gravitational Nieh-Yan anomaly in chiral $p+ip$ Weyl superfluids and superconductors
• Comment on: Topological Invariants, instantons, and the chiral anomaly on spaces with torsion
• Mixed axial-torsional anomaly in Weyl semimetals
• The quadratic spinor Lagrangian, axial torsion current, and generalizations
• On the chiral anomaly in non-Riemannian spacetimes
• Einstein-Cartan gravity, Asymptotic Safety, and the running Immirzi parameter
• Emergent gravity and chiral anomaly in Dirac semimetals in the presence of dislocations
• Torsional Landau levels and geometric anomalies in condensed matter Weyl systems
• Axions in gravity with torsion
• Continuous phase transition and critical behaviors of 3D black hole with torsion
• Holographic currents in first order Gravity and finite Fefferman-Graham expansions
• Supersymmetric Particle in a Spacetime with Torsion and the Index Theorem
• Emergent gravity in the cubic tight-binding model of Weyl semimetal in the presence of elastic deformations
• Phase transition and entropy spectrum of BTZ black hole in three-dimensional gravity with torsion
• Generalized Second Law of Thermodynamic in Modified Teleparallel Theory
• Local supersymmetry without SUSY partners
• Some exact solutions with torsion in 5-D Einstein-Gauss-Bonnet gravity
• Static and rotating black strings in dynamical Chern-Simons modified gravity
• The role of temperature dependent string-inspired CPT violating backgrounds in leptogenesis and the chiral magnetic effect
• Fermion Helicity Flip Induced by Torsion Field
• On thermal Nieh-Yan anomaly in Weyl superfluids
• Topological magnetotorsional effect in Weyl semimetals
• Reply to the comment by D. Kreimer and E. Mielke
• Torsion in string-inspired cosmologies and the universe dark sector
• Topological parameters in gravity
• Solutions on a brane in a bulk spacetime with Kalb-Ramond field
• Holographic correspondence in topological superconductors
• A solution of the strong CP problem via the Peccei-Quinn mechanism through the Nieh-Yan modified gravity and cosmological implications
• Torsion-induced gravitational $\theta$ term and gravitoelectromagnetism
• Viscoelastic-electromagnetism and Hall viscosity
• Comments on Heterotic Flux Compactifications
• Non-zero torsion and late cosmology
• Index Theorems on Torsional Geometries
• Negative thermal magnetoresistivity as a signature of chiral anomaly in Weyl superconductors
• The Chiral Heat Effect
• Luminal Propagation of Gravitational Waves in Scalar-tensor Theories: The Case for Torsion
• Some Aspects of Holst and Nieh-Yan Terms in General Relativity with Torsion
• Implications of axionic hair on shadow of M87*
• de Sitter group and Einstein-Hilbert Lagrangian
• Adler-Bell-Jackiw anomaly, the Nieh-Yan form, and vacuum polarization
• Unimodular Einstein--Cartan gravity: Dynamics and conservation laws
• On thermal Nieh-Yan anomaly in topological Weyl materials
• Dimensionless physics
• Hamiltonian approach to the torsional anomalies and its dimensional ladder
• A new functional flow equation for Einstein-Cartan quantum gravity
• Induced gravitational topological term and the Einstein-Cartan modified theory
• Hamiltonian study for Chern-Simons and Pontryagin theories
• Anomalous Hall viscosity at the Weyl semimetal/insulator transition
• The Topological Structure of Nieh-Yan Form and Chiral Anomaly in Spaces with Torsion
• Chiral Anomaly in Contorted Spacetimes
• The Immirzi Parameter as an Instanton Angle
• Torsional Topological Invariants
• Gravitomagnetic Helicity
• Fermions in (Anti) de Sitter Gravity in Four Dimensions
• Gravitational Constant and Torsion
• On chiral responses to geometric torsion
• Geometric Model of Topological Insulators from the Maxwell Algebra
• Hyperscaling violating black holes in scalar-torsion theories
• Barbero-Immirzi parameter, manifold invariants and Euclidean path integrals
• On the addition of torsion to chiral gravity
• The Holst Action by the Spectral Action Principle
• Axion gravitodynamics, Lense-Thirring effect, and gravitational waves
• (Super)-Gravities Beyond 4 Dimensions
• Anomalous chiral transport with vorticity and torsion: Cancellation of two mixed gravitational anomaly currents in rotating chiral $p+ip$ Weyl condensates
• Some cosmological models coming from gravitational theories having torsional degrees of freedom
• The method of covariant symbols in curved space-time
• (Super-)Gravities of a different sort
• Gravity Asymptotics with Topological Parameters
• On selfdual spin-connections and Asymptotic Safety
• Chiral Torsional Effects in Anomalous Fluids in Thermal Equilibrium
• Quantum realizations of Hilbert-Palatini second-class constraints
• Torsion, Dirac Field, Dark Matter and Dark Radiation
• Solar neutrinos, helicity effects and new affine gravity with torsion II
• Faddeev-Jackiw quantization of topological invariants: Euler and Pontryagin classes
• A relation between the Barbero-Immirzi parameter and the standard model
• Supergravity as a constrained BF theory
• Fractional Quantum Hall Effect for Extended Objects: from Skyrmionic Membranes to Dyonic Strings
• Torsion and anomalies in the warped limit of Lifschitz theories
• On Nieh-Yan Transport
• The type II Weyl semimetals at low temperatures: chiral anomaly, elastic deformations, zero sound
• Massive torsion modes, chiral gravity, and the Adler-Bell-Jackiw anomaly
• Duality and higher Buscher rules in p-form gauge theory and linearized gravity
• Alternative approach to the regularization of odd dimensional AdS gravity
• Deformed BF theory as a theory of gravity and supergravity
• A black hole solution in conformal supergravity
• Parity violation in Poincaré gauge gravity
• Geometric supergravitty
• Torsion, energy magnetization and thermal Hall effect
• Quantum-Ordering Ambiguities in Weak Chern-Simons 4D Gravity and Metastability of the Condensate-Induced Inflation
• On Torsion Contribution to Chiral Anomaly via Nieh-Yan Term
• Generalized Chern-Simons Modified Gravity in First-Order Formalism
• Torsional instanton effects in quantum gravity
• de Sitter Spaces
• Post-Riemannian Merger of Yang-Mills Interactions with Gravity
• Unconventional Supersymmetry via the Dressing Field Method
• Phonon helicity and Nieh-Yan Anomaly in the Kramers-Weyl semimetals of Chiral Crystals
• Canonical and symplectic analysis for three dimensional gravity without dynamics
• Asymptotically AdS black hole with a conformally-coupled scalar field in the first-order formalism of gravity
• Symmetries and observables in topological gravity
• Generalizations of the Nieh-Yan topological invariant
• Dark Energy from Topology
• Comments On Torsion and MacDowell-Mansouri gravity
• Self duality in unconventional conformal supersymmetry
• Topological symmetry-restored phase of gravity
• Holography of dislocations and ring defects in Einstein-Gauss-Bonnet AdS gravity
• Euler and Pontryagin currents of the Dirac operator
• Self-Excited Gravitational Instantons
• Hamiltonian Analysis of $R+T^2$ Action
• A gauge theoretical view of the charge concept in Einstein gravity
• Noncommutative $D=5$ Chern-Simons Gravity: Kaluza-Klein Reduction and Chiral Gravitational Anomaly
• A topological origin for Dark Energy
• Geometric Baryogenesis with Chiral-Time Equivalence
• Induced gauge interactions revisited
• Thermal response of the Nieh-Yan term
• Connection dynamics of a gauge theory of gravity coupled with matter