Non-abelian self-duality from self-interaction

The non-abelian self-dual action in three dimensions is derived using the self-interaction mechanism.Comment: Latex, 7 page

A normal coordinate expansion of the gauge potential

In this pedagogical note, I present a method for constructing a fully covariant normal coordinate expansion of the gauge potential on a curved space-time manifold. Although the content of this paper is elementary, the results may prove useful in some applications and have not, to the best of my knowledge, been discussed in the literature

A New Approach to Axial Vector Model Calculations II

We further develop the new approach, proposed in part I (hep-th/9807072), to computing the heat kernel associated with a Fermion coupled to vector and axial vector fields. We first use the path integral representation obtained for the heat kernel trace in a vector-axialvector background to derive a Bern-Kosower type master formula for the one-loop amplitude with $M$ vectors and $N$ axialvectors, valid in any even spacetime dimension. For the massless case we then generalize this approach to the full off-diagonal heat kernel. In the D=4 case the SO(4) structure of the theory can be broken down to $SU(2) \times SU(2)$ by use of the 't Hooft symbols. Various techniques for explicitly evaluating the spin part of the path integral are developed and compared. We also extend the method to external fermions, and to the inclusion of isospin. On the field theory side, we obtain an extension of the second order formalism for fermion QED to an abelian vector-axialvector theory.Comment: Sequel to hep-th/9807072, references added, some clarifications and corrections, 29 pages, RevTex, 8 diagrams using epsfig.st

Quantum discontinuity between zero and infinitesimal graviton mass with a Lambda term

We show that the recently demonstrated absence of the usual discontinuity for massive spin 2 with a Lambda term is an artifact of the tree approximation, and that the discontinuity reappears at one loop.Comment: 8 pages, revtex 3.1, title changed (version to appear in Phys. Rev. Lett.

Gauge Dependence in Chern-Simons Theory

We compute the contribution to the modulus of the one-loop effective action in pure non-Abelian Chern-Simons theory in an arbitrary covariant gauge. We find that the results are dependent on both the gauge parameter ($\alpha$) and the metric required in the gauge fixing. A contribution arises that has not been previously encountered; it is of the form $(\alpha / \sqrt{p^2}) \epsilon _{\mu \lambda \nu} p^\lambda$. This is possible as in three dimensions $\alpha$ is dimensionful. A variant of proper time regularization is used to render these integrals well behaved (although no divergences occur when the regularization is turned off at the end of the calculation). Since the original Lagrangian is unaltered in this approach, no symmetries of the classical theory are explicitly broken and $\epsilon_{\mu \lambda \nu}$ is handled unambiguously since the system is three dimensional at all stages of the calculation. The results are shown to be consistent with the so-called Nielsen identities which predict the explicit gauge parameter dependence using an extension of BRS symmetry. We demonstrate that this $\alpha$ dependence may potentially contribute to the vacuum expectation values of products of Wilson loops.Comment: 17 pp (including 3 figures). Uses REVTeX 3.0 and epsfig.sty (available from LANL). Latex thric

Effective Lagrangian from Higher Curvature Terms: Absence of vDVZ Discontinuity in AdS Space

We argue that the van Dam-Veltman-Zakharov discontinuity arising in the $M^2 \to 0$ limit of the massive graviton through an explicit Pauli-Fierz mass term could be absent in anti de Sitter space. This is possible if the graviton can acquire mass spontaneously from the higher curvature terms or/and the massless limit $M^2\to 0$ is attained faster than the cosmological constant $\Lambda \to 0$. We discuss the effects of higher-curvature couplings and of an explicit cosmological term ($\Lambda$) on stability of such continuity and of massive excitations.Comment: 23 pages, Latex, the version to appear in Class. Quant. Gra

Off-Diagonal Elements of the DeWitt Expansion from the Quantum Mechanical Path Integral

The DeWitt expansion of the matrix element M_{xy} = \left\langle x \right| \exp -[\case{1}{2} (p-A)^2 + V]t \left| y \right\rangle, $(p=-i\partial)$ in powers of $t$ can be made in a number of ways. For $x=y$ (the case of interest when doing one-loop calculations) numerous approaches have been employed to determine this expansion to very high order; when $x \neq y$ (relevant for doing calculations beyond one-loop) there appear to be but two examples of performing the DeWitt expansion. In this paper we compute the off-diagonal elements of the DeWitt expansion coefficients using the Fock-Schwinger gauge. Our technique is based on representing $M_{xy}$ by a quantum mechanical path integral. We also generalize our method to the case of curved space, allowing us to determine the DeWitt expansion of \tilde M_{xy} = \langle x| \exp \case{1}{2} [\case{1}{\sqrt {g}} (\partial_\mu - i A_\mu)g^{\mu\nu}{\sqrt{g}}(\partial_\nu - i A_\nu) ] t| y \rangle by use of normal coordinates. By comparison with results for the DeWitt expansion of this matrix element obtained by the iterative solution of the diffusion equation, the relative merit of different approaches to the representation of $\tilde M_{xy}$ as a quantum mechanical path integral can be assessed. Furthermore, the exact dependence of $\tilde M_{xy}$ on some geometric scalars can be determined. In two appendices, we discuss boundary effects in the one-dimensional quantum mechanical path integral, and the curved space generalization of the Fock-Schwinger gauge.Comment: 16pp, REVTeX. One additional appendix concerning end-point effects for finite proper-time intervals; inclusion of these effects seem to make our results consistent with those from explicit heat-kernel method

Accelerated Universe from Gravity Leaking to Extra Dimensions

We discuss the idea that the accelerated Universe could be the result of the gravitational leakage into extra dimensions on Hubble distances rather than the consequence of non-zero cosmological constant.Comment: 20 pages, 6 figure

Two-Loop Quantum Corrections of Scalar QED with Non-Minimal Chern-Simons Coupling

We investigate two-loop quantum corrections to non-minimally coupled Maxwell-Chern-Simons theory. The non-minimal gauge interaction represents the magnetic moment interaction between the charged scalar and the electromagnetic field. We show that the one-loop renormalizability of the theory found in previous work does not survive to the two-loop level. However, with an appropriate choice of the non-minimal coupling constant, it is possible to renormalize the two-loop effective potential and hence render it potentially useful for a detailed analysis of spontaneous symmetry breaking induced by radiative corrections.Comment: 29 pages, including 21 figures. One author added, some formulae corrected and references adde