Chern-Simons Coupling Constant Research Articles

Particle dynamics and geometric optics in Chern–Simons black holes

In this paper we study the effects of the coupling constant of the Chern–Simons modified gravity on some physical properties of black holes. The Hawking mass is one of the proposed definitions of quasilocal mass. We find that, for slowly rotating Chern–Simons black holes, the Hawking mass is independent of the coupling constant. Next, we show the dependence on the centre of mass energy, for two neutral colliding particles, of coupling constant and the rotation parameter. We also investigate energy extraction through Penrose process and find that the energy gain and efficiency of the Penrose process are independent of this coupling constant. Rotation of the polarization vector is also studied for dependence on the Chern–Simons coupling constant.

Atacama Cosmology Telescope: Constraints on cosmic birefringence

We present new constraints on anisotropic birefringence of the cosmic microwave background polarization using two seasons of data from the Atacama Cosmology Telescope covering 456 square degrees of sky. The birefringence power spectrum, measured using a curved-sky quadratic estimator, is consistent with zero. Our results provide the tightest current constraint on birefringence over a range of angular scales between 5 arc minutes and 9°. We improve previous upper limits on the amplitude of a scale-invariant birefringence power spectrum by a factor of between 2 and 3. Assuming a nearly massless axion field during inflation, our result is equivalent to a 2σ upper limit on the Chern-Simons coupling constant between axions and photons of gαγ<4.0×10−2/HI, where HI is the inflationary Hubble scale.Received 1 February 2020Accepted 2 April 2020DOI:https://doi.org/10.1103/PhysRevD.101.083527© 2020 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasCosmic microwave backgroundCosmologyPhysical SystemsAxionsGravitation, Cosmology & Astrophysics

Electrovacuum geometries in five dimensions

The Chong-Cvetic-Lu-Pope 5D rotating charged black hole proves to belong to a set of solutions to Einstein-Maxwell-Chern-Simons (EMCS) equations that share the electromagnetic potential and the Chern-Simons coupling constant but differ in the Kretschmann invariant. This one-parametric family of solutions is found by proposing a properly deformed Plebanski-Demianski Ansatz for modeling the metric tensor. While no black-hole solutions for other values of the Chern-Simons coupling constant are found within this Ansatz, another type of non-static electrovacuum solutions to 5D EMCS equations are obtained, namely Kundt spacetimes sourced by a pure-radiation field.

Exploring String Axions with Gravitational Waves

We explore the string axion dark matter with gravitational waves in Chern–Simons gravity. We show that the parametric resonance of gravitational waves occurs due to the axion coherent oscillation. Remarkably, the circular polarization of gravitational waves is induced by the parity violating Chern–Simons coupling. In fact, the gravitational waves should be enhanced ten times every 10 − 8 pc propagation in the presence of the axion dark matter with mass 10 − 10 eV provided the coupling constant l = 10 8 km . Hence, after 10 kpc propagation, the amplitude of gravitational waves is enhanced significantly and the polarization of gravitational waves becomes circular. However, we have never observed these signatures. This implies that the Chern–Simons coupling constant and/or the abundance of string axions should be constrained much stronger than the current limits.

Topological solutions for the self-dual Chern-Simons $CP(1)$ model with large Chern-Simons coupling constant

Topological solutions for the self-dual Chern-Simons $CP(1)$ model with large Chern-Simons coupling constant

Stationary rotating black holes in theories with gravitational Chern-Simons Lagrangian term

We study the effects of introducing purely gravitational Chern-Simons Lagrangian terms in ordinary Einstein gravity on stationary rotating black hole solutions and on the associated thermodynamical properties, in a generic number of dimensions which support these terms (i.e. in D = 4k-1). We analyze the conditions, namely the number of vanishing angular momenta, under which the contributions of the Chern-Simons term to the equations of motion and the black hole entropy vanish. The particular case of a 7-dimensional theory in which a purely gravitational Chern-Simons term is added to the Einstein-Hilbert Lagrangian in D=7 dimensions is investigated in some detail. As we have not been able to find exact analytic solutions in nontrivial cases, we turn to perturbation theory and calculate the first-order perturbative correction to the Myers-Perry metric in the case where all angular momenta are equal. The expansion parameter is a dimensionless combination linear in the Chern-Simons coupling constant and the angular momentum. Corrections to horizon and ergosurface properties, as well as black hole entropy and temperature, are presented.

Charged rotating Kaluza-Klein multiblack holes and multiblack strings in five-dimensional Einstein-Maxwell theory

We construct exact solutions, which represent regular charged rotating Kaluza-Klein multi-black holes in the five-dimensional pure Einstein-Maxwell theory. Quantization conditions between the mass, the angular momentum, and charges appear from the regularity condition of horizon. We also obtain multi-black string solutions by taking some limits in the solutions. We extend the black hole solutions to the five-dimensional Einstein-Maxwell-Chern-Simons theory with an arbitrary Chern-Simons coupling constant.

Instantonic dyons of Yang–Mills–Chern–Simons models in d = 2n + 1 dimensions, n > 2

We investigate finite energy solutions of Yang–Mills–Chern–Simons systems in odd spacetime dimensions, d = 2n + 1, with n > 2. This can be carried out systematically for all n, but the cases n = 3, 4 corresponding to seven- and nine-dimensional spacetimes are treated concretely. These are static and spherically symmetric configurations, defined in a flat Minkowski background. The value of the electric charge is fixed by the Chern–Simons coupling constant.

Einstein–Yang-Mills–Chern-Simons solutions inD=2n+1dimensions

We investigate finite energy solutions of the Einstein--Yang-Mills--Chern-Simons system in odd spacetime dimensions, $D=2n+1$, with $n&gt;1$. Our configurations are static and spherically symmetric, approaching at infinity a Minkowski spacetime background. In contrast with the Abelian case, the contribution of the Chern-Simons term is nontrivial already in the static, spherically symmetric limit. Both globally regular, particlelike solutions and black holes are constructed numerically for several values of $D$. These solutions carry a nonzero electric charge and have finite mass. For globally regular solutions, the value of the electric charge is fixed by the Chern-Simons coupling constant. The black holes can be thought of as nonlinear superpositions of Reissner-Nordstr\"om and non-Abelian configurations. A systematic discussion of the solutions is given for $D=5$, in which case the Reissner-Nordstr\"om black hole becomes unstable and develops non-Abelian hair. We show that some of these non-Abelian configurations are stable under linear, spherically symmetric perturbations. A detailed discussion of an exact $D=5$ solution describing extremal black holes and solitons is also provided.

Extremal charged rotating black holes in odd dimensions

Employing higher order perturbation theory, we obtain charged rotating black holes in odd dimensions, where the Einstein-Maxwell Lagrangian may be supplemented with a Chern-Simons term. Starting from the Myers-Perry solutions, we use the electric charge as the perturbative parameter, and focus on extremal black holes with equal-magnitude angular momenta. For Einstein-Maxwell-Chern-Simons theory with arbitrary Chern-Simons coupling constant, we perform the perturbations up to third order for any odd dimension. We discuss the physical properties of these black holes and study their dependence on the charge. In particular, we show that the gyromagnetic ratio $g$ of Einstein-Maxwell black holes differs from the lowest order perturbative value $D-2$, and that the first correction term to $g/(D-2)$ is universal.

Constraining parity violation in gravity with measurements of neutron-star moments of inertia

Neutron stars are sensitive laboratories for testing general relativity, especially when considering deviations where velocities are relativistic and gravitational fields are strong. One such deviation is described by dynamical, Chern-Simons modified gravity, where the Einstein-Hilbert action is modified through the addition of the gravitational parity-violating Pontryagin density coupled to a field. This four-dimensional effective theory arises naturally both in perturbative and non-perturbative string theory, loop quantum gravity, and generic effective field theory expansions. We calculate here Chern-Simons modifications to the properties and gravitational fields of slowly spinning neutron stars. We find that the Chern-Simons correction affects only the gravitomagnetic sector of the metric to leading order, thus introducing modifications to the moment of inertia but not to the mass-radius relation. We show that an observational determination of the moment of inertia to an accuracy of 10%, as is expected from near-future observations of the double pulsar, will place a constraint on the Chern-Simons coupling constant of \xi^{1/4} < 5 km, which is at least three-orders of magnitude stronger than the previous strongest bound.

Witten–Nester energy in topologically massive gravity

We formulate topologically massive supergravity with a cosmological constant in the first-order formalism and construct the Noether supercurrent and superpotential associated with its local supersymmetry. Using these results, we construct in ordinary topologically massive gravity the Witten–Nester integral for conserved charges containing spinors which satisfy a generalized version of the Witten equation on the initial value surface. We show that the Witten–Nester charge, represented as an integral over the boundary of the initial value surface, produces the Abbott–Deser–Tekin energy for asymptotically anti-de Sitter spacetimes. We consider all values of the Chern–Simons coupling constant, including the critical value known as the chiral point, and study the cases of standard Brown–Henneaux boundary conditions, as well as their weaker version that allows a slower fall-off. Studying the Witten–Nester energy as a bulk integral over the initial value surface instead, we find a bound on the energy, and through it the sufficient condition for the positivity of the energy. In particular, we find that spacetimes of Petrov type N that admit globally well-defined solutions of the generalized Witten equation have positive energy.

Existence and uniqueness of topological multivortex solutions of the self-dual Chern–Simons [formula omitted] model

In this paper we study the existence and uniqueness of the topological Chern–Simons vortices in the CP ( 1 ) model in R 2 . After reducing the self-dual equations to semilinear elliptic partial differential equations, we show that a topological solution exists, and it is unique up to a real smooth function if the Chern–Simons coupling constant is sufficiently small.

Self-dual vortices in Chern-Simons hydrodynamics

The classical theory of a nonrelativistic charged particle interacting with a U(1) gauge field is reformulated as the Schrödinger wave equation modified by the de Broglie–Bohm nonlinear quantum potential. The model is gauge equivalent to the standard Schrödinger equation with the Planck constant $$\hbar $$ for the deformed strength $$1 - \hbar ^2 $$ of the quantum potential and to the pair of diffusion–antidiffusion equations for the strength $$1 + \hbar ^2 $$ . Specifying the gauge field as the Abelian Chern–Simons (CS) one in 2+1 dimensions interacting with the nonlinear Schrödinger (NLS) field (the Jackiw–Pi model), we represent the theory as a planar Madelung fluid, where the CS Gauss law has the simple physical meaning of creation of the local vorticity for the fluid flow. For the static flow when the velocity of the center-of-mass motion (the classical velocity) is equal to the quantum velocity (generated by the quantum potential velocity of the internal motion), the fluid admits an N-vortex solution. Applying a gauge transformation of the Auberson–Sabatier type to the phase of the vortex wave function, we show that deformation parameter $$\hbar $$ , the CS coupling constant, and the quantum potential strength are quantized. We discuss reductions of the model to 1+1 dimensions leading to modified NLS and DNLS equations with resonance soliton interactions.

Heat kernel coefficients for Chern-Simons boundary conditions in QED

We consider the four-dimensional Euclidean Maxwell theory with a Chern-Simons term on the boundary. The corresponding gauge-invariant boundary conditions become dependent on tangential derivatives. Taking the 4-sphere as a particular example, we calculate explicitly a number of the first heat kernel coefficients and obtain the general formulae that yield any desired coefficient. A remarkable observation is that the coefficient , which defines the 1-loop counterterm and the conformal anomaly, does not depend on the Chern-Simons coupling constant, while the heat kernel itself becomes singular at a certain (critical) value of the coupling. This could be a reflection of a general property of Chern-Simons theories.

On the non-renormalization properties of gauge theories with a Chern-Simons term

Considering three-dimensional Chern-Simons theory, either coupled to matter or with a Yang-Mills term, we show the validity of a trace identity, playing the role of a local form of the Callan-Symanzik equation, in all orders of perturbation theory. From this we deduce the vanishing of the $\beta$-function associated to the Chern-Simons coupling constant and the full finiteness in the case of the Yang-Mills Chern-Simons theory. The main ingredient in the proof of the latter property is the noninvariance of the Chern-Simons form under the gauge transformations. Our results hold for the three-dimensional Chern-Simons model in a general Riemannian manifold.

EFFECTIVE POTENTIAL FOR A NONRELATIVISTIC NON-ABELIAN CHERN-SIMONS MATTER SYSTEM IN CONSTANT BACKGROUND FIELDS

We present the effective potential for nonrelativistic matter coupled to non-Abelian Chern-Simons gauge fields. We perform the calculation using a functional method in constant background fields to satisfy Gauss’s law and to simplify the computation. Both the quantum gauge and matter fields are integrated over. The gauge-fixing is achieved with an Rξ gauge in the ξ→0 limit. Divergences appearing in the matter sector are regulated via operator regularization. We find no correction to the Chern-Simons coupling constant and the system experiences conformal symmetry breaking to one-loop order except at the known value of self-duality. These results agree with previous analysis of the non-Abelian Aharonov-Bohm scattering.

Anyons, modular invariance and anyon gauge for arbitrary rational statistics

We perform the implementation of modular invariance for a system of free anyons on a torus, described by means of the Chern-Simons action, for arbitrary rational Chern-Simons coupling constant. We explain in which sense the “anyon gauge”, in which the wavefunction is multivalued, can be achieved on the torus.

Chern-Simons theory and geometric regularization

We analyze a regularization of Chern-Simons theory based on a geometrical interpretation of the functional integral in the covariant formalism. Perturbative calculations show the existence of two independent finite renormalization of the gauge field and the Chern-Simons coupling constant. Both renormalizations do not depend on the space-time volume and the gauge condition. Coupling constant renormalization, unlike gauge field renormalization, is also independent of the regulating parameters. The method opens the possibility of a non-perturbative approach in the covariant formalism.