Effective Action For Gauge Fields Research Articles

Anomalous Lorentz and CPT violation

If there exists Lorentz and CPT violation in nature, then it is crucial to discover and understand the underlying mechanism. In this contribution, we discuss one such mechanism which relies on four-dimensional chiral gauge theories defined over a spacetime manifold with topology ℛ3 × S1 and periodic spin structure for the compact dimension. It can be shown that the effective gauge-field action contains a local Chern-Simons-like term which violates Lorentz and CPT invariance. For arbitrary Abelian U(1) gauge fields with trivial holonomies in the compact direction, this anomalous Lorentz and CPT violation has recently been established perturbatively with a Pauli–Villars-type regularization and nonperturbatively with a lattice regularization based on Ginsparg-Wilson fermions.

Anomalous Lorentz and CPT violation from a local Chern–Simons-like term in the effective gauge-field action

We consider four-dimensional chiral gauge theories defined over a spacetime manifold with topology R3×S1 and periodic boundary conditions over the compact dimension. The effective gauge-field action is calculated for Abelian U(1) gauge fields Aμ(x) which depend on all four spacetime coordinates (including the coordinate x4∈S1 of the compact dimension) and have vanishing components A4(x) (implying trivial holonomies in the 4-direction). Our calculation shows that the effective gauge-field action contains a local Chern–Simons-like term which violates Lorentz and CPT invariance. This result is established perturbatively with a generalized Pauli–Villars regularization and nonperturbatively with a lattice regularization based on Ginsparg–Wilson fermions.

Heavy quark induced effective action for gauge fields in the $SU(N_c)\otimes U(1)$ model and the low-energy structure of heavy quark current correlators

We calculate the low-energy limit of heavy quark current correlators within an expansion in the inverse heavy quark mass. The induced low-energy currents built from the gluon fields corresponding to the initial heavy quark currents are obtained from an effective action for gauge fields in the one-loop approximation at the leading order of the 1/m expansion. Explicit formulae for the low-energy spectra of electromagnetic and tensor heavy quark current correlators are given. Consequences of the appearance of a nonvanishing spectral density below the two-particle threshold for high precision phenomenology of heavy quarks are discussed quantitatively.

A CPT anomaly

We consider chiral gauge theories defined over a four-dimensional spacetime manifold with a Cartesian product structure for at least one compact spatial dimension. For a simple setup, we calculate the effective gauge field action by integrating out the chiral fermions, while maintaining gauge invariance. Due to a combination of infrared and ultraviolet effects, there appears a CPT-odd term in the effective gauge field action. This CPT anomaly could occur in chiral gauge theories relevant to elementary particle physics, provided the spacetime manifold has the appropriate topology. Two possible applications for cosmology are discussed.

Threshold effects in open-string theory

We analyze the one-loop effective gauge-field action in Z 2-orbifold compactifications of type-I theory. We show how, for non-abelian group factors, the threshold effects are ultraviolet finite though given entirely by a six-dimensional field theory expression.

The effective gauge field action of a system of non-relativistic electrons

We consider a system of free, non-relativistic electrons at zero temperature and positive density, coupled to an arbitrary, external electromagnetic vector potential,A. By integrating out the electron degrees of freedom we obtain the effective action forA. We show that, in the scaling limit, this effective action is quadratic inA and can be viewed as an integral over the Fermi sphere of effective actions of (1+1)-dimensional, chiral schwinger models. We use this result to elucidate Luther-Haldane bosonization of systems of non-relativistic electrons. We also study systems of weakly coupled interacting electrons for which the BCS channel is turned off. Using the quadratic dependence of the effective action onA, we show that, in the scaling limit, the RPA yields the dominant contribution.

Perturbative analysis for Kaplan's lattice chiral fermions.

Perturbation theory for lattice fermions with domain wall mass terms is developed and is applied to investigate the chiral Schwinger model formulated on the lattice by Kaplan's method. We calculate the effective action for gauge fields to one loop, and find that it contains a longitudinal component even for anomaly-free cases. From the effective action we obtain gauge anomalies and Chern-Simons currents without ambiguity. We also show that the current corresponding to the fermion number has a nonzero divergence and it flows off the wall into the extra dimension. Similar results are obtained for a proposal by Shamir, who used a constant mass term with free boundaries instead of domain walls.

Superconductivity, Faraday effect, and optical absorption in the commensurate flux phase of the t-J model.

Using a large-{ital N} slave-boson formulation of the {ital t}-{ital J} model on the square lattice that has explicit spinon-holon decoupling of the correlated electron, we study the stability and electromagnetic response of the commensurate flux phase in the limit near half filling. A region of stability for the flux phase is found located between a dimer phase region near half filling and a fluxless metallic phase region far from half filling. The commensurate flux phase itself is found to be a superconductor of the anyon type. Furthermore, it is shown that the parity--time-reversal--violating characteristic of this phase results in a frequency-dependent Faraday effect. This effect manifests itself as a zero-field Hall effect in the low-frequency limit, where the off-diagonal conductance scales with the hole concentration. Associated with this result, it is also found that the commensurate flux phase supports a series of optical absorption peaks at energies on the order of {ital J}. Lastly, inclusion of instanton tunneling events in the effective gauge-field action results in the confinement of the spinon and holon degrees of freedom. This confinement effect, however, weakens exponentially as one approaches the Mott transition. The present results are discussed in the context of the high-{italmore » T}{sub {ital c}} superconducting oxides.« less

Analysis of the lattice-chiral-fermion proposal of Aoki, Funakubo, and Kashiwa.

We examine the lattice-chiral-fermion scheme proposed by Aoki, Funakubo, and Kashiwa (AFK) in the context of chiral QED in two and four dimensions. In four dimensions, we find that, although the AFK scheme ensures gauge invariance by rendering amplitudes transverse, it does not improve their ultraviolet behavior; as in the Wilson theory, the effective vacuum polarization is quadratically divergent. In both two and four dimensions, we find that there are contributions to the effective gauge-field action beyond those analyzed by AFK. These contributions are not accessible through finite-order perturbation theory.

Parity anomaly and fermion-boson transmutation in 3-dimensional lattice QED

We calculate the effective gauge field action due to a single two-component fermion of mass m and charge e, using a cubic lattice as an ultra-violet regulator and Wilson type fermion actions to avoid a doubling of fermion species. In the limit where the cutoff is removed, we find that the answer is finite but not unique: the various lattice fermion actions belong to different universality classes labelled by an integer n. In all cases, the parity invariance of the classical (continuum) action at m = 0 is violated bu quantum effects, i.e. there is an anomaly. In addition, for n ≠ 0, a Chern-Simons term is generated at large m, and this implies a non-zero photon mass, deconfinement and unusual spin and statistics of charged particles. In particular, for the class of actions with n = −1, we show by a straightforward semi-classical argument that the fundamental fermion is converted to a particle with spin 0.

The anomalous effective action in three-dimensional gauge theories

We analyse the effective action for gauge fields in odd dimensions, obtained by integrating out the fermions in the Feynman path integral. In particular, we discuss the generation of a Chern-Simons term by massless fermions minimally coupled to an Abelian gauge field. We review two methods of revealing the presence of a Chern-Simons term in the effective action: first, as the consequence of a nontrivial holonomy of the fermionic ground state, then as the result of the generation of an anomalous imaginary part of the effective action. We derive the most general form of the anomalous effective action at the lowest nontrivial order of a derivative expansion in time. We discuss the implications of our analysis for the theory of the fractional quantum Hall effect as well as for the quantization of anomalous theories.

SU(2) gauge symmetry and anomaly of the [formula omitted] antiferromagnetic Heisenberg model in 2 + 1 dimensions

On the basis of the local SU (2) symmetry of the Heisenberg model, we show that the model, in a continuum limit, reduces to a problem of massless fermions coupled to an SU(2) gauge field in three space-time dimensions. The effective gauge field action changes by ± π ⦶ n ⦶ under a large gauge transformation with winding number n. To restore the gauge invariance, a parity- nonconserving, topological term is needed in the effective action. The physical implications are conjectured.

Parity violation and gauge noninvariance of the effective gauge field action in three dimensions

The effective gauge field action due to fermions coupled to $\mathrm{SU}(N)$ gauge fields in three dimensions is found to change by $\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}|n|$ under a homotopically nontrivial gauge transformation with winding number $n$. This gauge noninvariance can be eliminated by adding a parity-violating topological term to the action, or by regulating the theory in a way which produces this term automatically in the effective action. The Euler-Heisenberg effective action is calculated in the SU(2) theory and in QED.

Gauge Noninvariance and Parity Nonconservation of Three-Dimensional Fermions

The effective gauge field action due to an odd number of fermion species in three-dimensional $\mathrm{SU}(N)$ gauge theories is shown to change by $\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}|n|$ under a homotopically nontrivial gauge transformation with winding number $n$. Gauge invariance can be restored by use of Pauli-Villars regularization, which, however, introduces parity nonconservation in the form of a parity-nonconserving, topological term in the effective action.