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

The Canonical Structure of the Superstring Action

We consider the canonical structure of the Green-Schwarz superstring in $9 + 1$ dimensions using the Dirac constraint formalism; it is shown that its structure is similar to that of the superparticle in $2 + 1$ and $3 + 1$ dimensions. A key feature of this structure is that the primary Fermionic constraints can be divided into two groups using field-independent projection operators; if one of these groups is eliminated through use of a Dirac Bracket (DB) then the second group of primary Fermionic constraints becomes first class. (This is what also happens with the superparticle action.) These primary Fermionic first class constraints can be used to find the generator of a local Fermionic gauge symmetry of the action. We also consider the superstring action in other dimensions of space-time to see if the Fermionic gauge symmetry can be made simpler than it is in $2 + 1$, $3 + 1$ and $9 + 1$ dimensions. With a $3 + 3$ dimensional target space, we find that such a simplification occurs. We finally show how in five dimensions there is no first class Fermionic constraint.Comment: 24 pages, Latex2e; further comments and clarifications adde

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

The effect of small-amplitude time-dependent changes to the surface morphology of a sphere

Typical approaches to manipulation of flow separation employ passive means or active techniques such as blowing and suction or plasma acceleration. Here it is demonstrated that the flow can be significantly altered by making small changes to the shape of the surface. A proof of concept experiment is performed using a very simple time-dependent perturbation to the surface of a sphere: a roughness element of 1% of the sphere diameter is moved azimuthally around a sphere surface upstream of the uncontrolled laminar separation point, with a rotational frequency as large as the vortex shedding frequency. A key finding is that the non-dimensional time to observe a large effect on the lateral force due to the perturbation produced in the sphere boundary layers as the roughness moves along the surface is ˆt =tU_(∞)/D ≈4. This slow development allows the moving element to produce a tripped boundary layer over an extended region. It is shown that a lateral force can be produced that is as large as the drag. In addition, simultaneous particle image velocimetry and force measurements reveal that a pair of counter-rotating helical vortices are produced in the wake, which have a significant effect on the forces and greatly increase the Reynolds stresses in the wake. The relatively large perturbation to the flow-field produced by the small surface disturbance permits the construction of a phase-averaged, three-dimensional (two-velocity component) wake structure from measurements in the streamwise/radial plane. The vortical structure arising due to the roughness element has implications for flow over a sphere with a nominally smooth surface or distributed roughness. In addition, it is shown that oscillating the roughness element, or shaping its trajectory, can produce a mean lateral force

Treatment of a System with Explicitly Broken Gauge Symmetries

A system in which the free part of the action possesses a gauge symmetry that is not respected by the interacting part presents problems when quantized. We illustrate how the Dirac constraint formalism can be used to address this difficulty by considering an antisymmetric tensor field interacting with a spinor field.Comment: 10 pages, LaTeX2e, typos correcte

The Effective Potential in Non-Conformal Gauge Theories

By using the renormalization group (RG) equation it has proved possible to sum logarithmic corrections to quantities that arise due to quantum effects in field theories. In particular, the effective potential V in the Standard Model in the limit that there are no massive parameters in the classical action (the "conformal limit") has been subject to this analysis, as has the effective potential in a scalar theory with a quartic self coupling and in massless scalar electrodynamics. Having multiple coupling constants and/or mass parameters in the initial action complicates this analysis, as then several mass scales arise. We show how to address this problem by considering the effective potential in scalar electrodynamics when the scalar field has a tree level mass term. In addition to summing logarithmic corrections by using the RG equation, we also consider the consequences of the condition V'(v)=0 where v is the vacuum expectation value of the scalar. If V is expanded in powers of the logarithms that arise, then it proves possible to show that either v is zero or that V is independent of the scalar. (That is, either there is no spontaneous symmetry breaking or the vacuum expectation value is not determined by minimizing V as V is "flat".