Topological Mass Term Research Articles

Topological mass quantization and parity violation in 2 + 1 dimensional QED

We give a quantization condition for the coefficient of the topological mass term and a topological argument for the necessity of parity violation in a 2 + 1 dimensional QED, and in general in an odd number of dimensions. We also point out and rectify a technical flaw in the standard argument for the SU(2) nonperturbative anomaly.

Variational approach to (2+1)-dimensional QED with topological mass term.

Using a variational method worked out in a previous paper, we study (2+1)-dimensional QED with topological mass term. We find that for massive fermions the state with a constant magnetic field lies below the perturbative ground state. We investigate the possible existence of partially occupied zero modes.

Topological mass term for gravity induced by matter

The contribution of massive fermions and topologically massive gauge fields to a Chern-Simons term for the graviton is computed to one-loop order in three dimensions. Invariance under large coordinate transformations places restrictions on the number of these massive matter fields. The parity anomaly for massless fermions is determined, and a possible parity anomaly for massless gauge fields is suggested.

Non-Abelian adiabatic phases and the fractional quantum Hall effect.

An explicit realization of $\mathrm{U}(n)$ quantum holonomy is presented in the context of nonrelativistic (2 + 1)-dimensional electrodynamics and used to construct the adiabatic effective action. It is shown that the U(1) subgroup of the $\mathrm{U}(n)$ holonomy gives rise to an effective Chern-Simons topological mass term and its relationship with the fractional quantum Hall effect is discussed.

P-Form electrodynamics

A generalization of gauge theory in which the gauge potential1-form is replaced by a p-form is studied. Charged particles are then replaced by elementary extended objects of dimension p−1. It is shown that this extension is compatible with space-time locality only if the gauge group is U(1). A source which is a closed p−1 surface has zero total charge and corresponds to a particle-antiparticle pair. Its quantum rate of production in an external uniform field is evaluated semiclassically. The analog of the Dirac magnetic pole is constructed. It is another extended object, of dimension n−p−3, where n is the dimension of space-time. The “electric” and “magnetic” charges obey the Dirac quantization condition. This condition is derived in two different ways. One method makes use of local gauge patches and the other brings in singular gauge transformations. A topological mass term is introduced and it is shown that it can coexist with a magnetic pole when n=2p+1, provided the topological mass is quantized.

The absence of radiative corrections from higher-order loops to the topological mass in (2 + 1)-dimensional electrodynamics

A proof is presented that there are no radiative corrections from higher loops to the topological mass term of abelian gauge theory in 2 + 1 dimensions, thus the coefficient of the topological mass term at one-loop order is exact to all higher orders.

N⩾=2 supersymmetric Chern-Simons terms as d=3 extended conformal supergravity

The authors present supersymmetric Chern-Simons terms for N>or=2 extended supergravity in d=3 dimensions and show that they are the gauge actions of N>or=2 conformal supergravity. In these models, gravitational and gauge Chern-Simons terms (which, when coupled to other systems, give rise to self-dual vectors and/or topological mass terms) are unified by supersymmetry.

No more corrections to the topological mass term in QED 3

We consider the theory of a photon interacting with scalar, spinor, and/or vector fields with arbitrary gauge-invariant interactions, in three spacetime dimensions. We show that to all orders in perturbation theory, all corrections to the topological mass term (beyond the known one-loop correction) vanish identically.

Bose-Fermi correspondence and Kac-Moody algebras in four dimensions

The Schwinger terms in current-algebra commutation relations generated by a topological mass term in the Yang-Mills Lagrangian are analyzed. It is shown how the Schwinger terms modify the geometry of gauge-group orbits in the space of vector potentials. In 4+1 space-time dimensions the topological mass leads to a current algebra in 3+1 dimensions which in the case of an external Abelian monopole field is identical to a current algebra constructed from a four-component fermion field. The current algebra is a direct generalization of the standard Kac-Moody algebra in 1+1 dimensions.

Topological mass terms and the high temperature limit of chiral gauge theories

It is shown that in the high temperature limit of a 4D chiral gauge theory with non-zero chemical potential, a topological mass term is generated for the gauge field. This mass is imaginary and may signal an instability of non-trivial gauge configurations.

Odd-Dimensional Anomaly at High Temperature

By the study on high temperature behavior of the vacuum expectation value of the fermionic current vector in four-dimensional space-time, we have demonstrated that in the effective Lagrangian of three-dimensional gauge theories, except the usual Yang-Mills expression, there must also exist the unconventional three-dimensional Chern-Simons topological mass term which violates parity conservation.

Radiatively induced topological mass terms in (2+1)-dimensional gauge theories.

We show that no topological mass terms are induced radiatively to the two-loop order in either Abelian or non-Abelian gauge theories of 2+1 dimensions with massive fermions if the Pauli-Villars regularization is used consistently for fermion loops. We study the case where gauge bosons have no topological mass at the tree level.

Induced Chern-Simons terms at high temperatures and finite densities.

The CP nonconserving portion of the gauge-field effective action for an even number of left-handed SU(2) fermion doublets, with nonzero chemical potentials ..mu../sup i/, is calculated to leading order in the inverse temperature, T/sup -1/. It is shown to be i summation/sub i/ (..mu../sup 1//T)W(A), where W(A) is the Chern-Simons topological mass term. This result is also shown to be a consequence of the U(1)/sub L/ anomaly at zero temperature, but with ..mu..not =0. Because of the i in front of the Chern-Simons term, this produces magnetic screening only if ..mu.. is complex.

Lower dimensional gravity

Gravity theory on a line and in the plane is reviewed. The triviality of the planar Einstein model is avoided by adding sources and a topological mass term. A constant curvature model for two dimensional space-time, analogous to the theory in three dimensional space-time, is proposed.

Abelian gauge structure inside nonabelian gauge theories

We show that the inclusion of topological lagrangians in nonabelian gauge theories introduces certain topologically nontrivial abelian background fields in the configuration space of these theories. In particular, the θ-term and the topological mass term lead, respectively, to a vortex and a monopole in gauge orbit space in 3 + 1 and 2 + 1 dimensions. The identification of the theta-vacuum effect with a kind of Bohm-Aharonov effect in gauge-orbit space motivates a discussion on the possibility of solving the strong CP problem dynamically.

Analytic study of θ vacua on the lattice

A new definition of the topological charge density for four-dimensional lattice gauge theory is given. Using a systematic expansion we find a cusp in the vacuum energy at θ = π signaling the spontaneous breaking of CP there. Unlike its two-dimensional analogue (QED 2), QCD confines at θ = π. As a by-product an expression for the topological mass term for (2+1)-dimensional lattice gauge theory is obtained.

The effective action for photons in (2 + 1) dimensions

The topological mass term in the Euler-Heisenberg effective action for (2 + 1)-dimensional spinor QED is studied by functional and canonical methods. The mass term is associated with a quantum Hall effect in the vacuum, and with a vacuum charge in the special case of a pure magnetic field. This charge is shown to become depleted at non-zero temperature.

GaugedN=4supergravity in six dimensions

We obtain $N=4$ gauged supergravity in $d=6$ dimensions from dimensional reduction of $N=2$, $d=7$ gauged supergravity. Starting from a topological mass term in the $d=7$ theory one gets an $N=4$, $d=6$ irreducible model with a two-parameter potential and a local SU(2) in which an antisymmetric rank-two tensor absorbs a Higgs-vector field and becomes massive. Without a topological mass term in $d=7$ we get the reducible coupling of pure gauged $N=4$ supergravity to a vector multiplet. We also consider various truncations to matter-coupled $N=2$ theories. The pure gauged $N=4$ supergravity gauges the superalgebra ${F}_{4}$.

Anomalies and fermion zero modes on strings and domain walls

the parity anomaly in 2n + 1 dimensions, and the Dirac index density in 2n + 2 dimensions can be understood in terms of the physics of fermion zero modes on strings and domain walls. We show that the Dirac equation possesses chiral zero modes in the presence of strings in 2n +2 dimensions (such as occur in axion theories) or domain walls in 2n + 1 dimensions. We show that the anomalies due to the chiral zero modes are exactly cancelled by anomalies due to the coupling of axion-like fields to the Dirac index density or by anomalies due to the induced topological mass term. Anomalies arise when the quantum-mechanical vacuum functional of a field theory fails to have all the symmetries of the classical lagrangian from which it is derived. Ifthe symmetry in question is a gauge symmetry associated with a dynamical gauge field, the anomaly is intolerable and must be eliminated. The usual method is direct cancellation by the addition of extra fermion species with appropriate quantum numbers. In this paper, we will show that in certain contexts involving defects (i.e. strings and domain walls), anomalies arise which may be compensated by quantum number flows in the higher-dimensional space in which the defect is embedded, rather than cancelled. This phenomenon gives a particularly simple physical interpretation of the recently discovered mathematical connection between chiral anomalies in 2n +2 dimensions, parity anomalies in 2n + l dimensions and gravitational and non-abelian anomalies in 2n dimensions [1-5]. It also suggests some interesting phenomenological possibilities for the axion strings which may have played a role in the development of density perturbations in the early universe

Topologically massive spin 5/2 theory

A three-dimensional gauge invariant action describing massive pure spin 5/2 excitations is obtained. However, unlike the corresponding topologically massive spin 3/2 case, an auxiliary spinor field is required here. Both topological mass and kinetic terms are invariant under the usual local gauge transformations of the spin 5/2 field; the former is also invariant under a local algebraic conformal transformation.