15360602
Two phases for compact U(1) pure gauge theory in three dimensions.
We show that if actions more general than the usual simple plaquette action ({approximately}{ital F}{sup 2}{sub {mu}{nu}}) are considered, then compact U(1) {ital pure} gauge theory in three Euclidean dimensions can have two phases. Both phases are confining phases; however, in one phase the monopole condensate spontaneously {open_quote}{open_quote}magnetizes.{close_quote}{close_quote} For a certain range of parameters the phase transition is continuous, allowing the definition of a strong coupling continuum limit. We note that these observations have relevance to the {open_quote}{open_quote}fictitious{close_quote}{close_quote} gauge field theories of strongly correlated electron systems, such as those describing high-{ital T}{sub {ital c}} superconductors. {copyright} {ital 1996 The American Physical Society.}
120318744
General covariance and open string interactions
Abstract It has been suggested that Witten's open string cubic interaction is independent of the background geometry. We investigate this suggestion in detail with a view to understanding the role of closed strings in Witten's open string field theory. The standard oscillator formulation of the vertex requires the use of a metric, if it is to be generally covariant, indicating that closed string interactions are required. However by changing to variables better suited to treating the midpoint, we show explicitly that it is possible to transform away all reference to the background metric. This supports the assertion that the cubic action (of Horowitz, Lykken, Rohm and Strominger) can also describe closed strings.
13594136
Exact scheme independence at two loops
We further develop an algorithmic and diagrammatic computational framework for very general exact renormalization groups, where the embedded regularisation scheme, parametrised by a general cutoff function and infinitely many higher point vertices, is left unspecified. Calculations proceed iteratively,by integrating by parts with respect to the effective cutoff, thus introducing effective propagators, and differentials of vertices that can be expanded using the flow equations; many cancellations occur on using the fact that the effective propagator is the inverse of the classical Wilsonian two-point vertex. We demonstrate the power of these methods by computing the beta function up to two loops in massless four dimensional scalar field theory, obtaining the expected universal coefficients, independent of the details of the regularisation scheme.
13411572
New Developments in the Continuous Renormalization Group
Over the last several years, there has been a resurgence of interest in using non-perturbative approximation methods based on Wilson's continuous renormalization group. In this lecture, I review progress particularly in the past year, concentrating on theoretical issues in the structure of the exact renormalization group and its approximations.
14167872
Exact scheme independence at one loop
The requirement that the quantum partition function be invariant under a renormalization group transformation results in a wide class of exact renormalization group equations, differing in the form of the kernel. Physical quantities should not be sensitive to the particular choice of the kernel. We demonstrate this scheme independence in four dimensional scalar field theory by showing that, even with a general kernel, the one-loop beta function may be expressed only in terms of the effective action vertices, and thus, under very general conditions, the universal result is recovered.
15153074
An exact RG formulation of quantum gauge theory
A gauge invariant Wilsonian effective action is constructed for pure SU(N) Yang-Mills theory by formulating the corresponding flow equation. Manifestly gauge invariant calculations can be performed i.e. without gauge fixing or ghosts. Regularisation is implemented in a novel way which realises a spontaneously broken SU(N|N) supergauge theory. As an example we sketch the computation of the one-loop ? function, performed for the first time without any gauge fixing.
506054
Supersymmetry and gauge invariance constraints in a U(1) x U(1)'-Higgs superconducting cosmic string model.
A supersymmetric extension of the U(1){times}U(1){prime}-Higgs bosonic superconducting cosmic string model is considered, where the action is constructed from scalar chiral and vector superfields. The chiral superfields are assumed to transform separately under the Abelian gauge groups, and the constraints imposed upon such a model due to renormalizability, supersymmetry, and gauge invariance are examined. For a simple model with a single U(1) chiral superfield and a single U(1){prime} chiral superfield, the Witten mechanism for bosonic superconductivity (giving rise to long-range gauge fields outside of the string) does not exist without the introduction of extra chiral supermultiplets. The simplest model that can accommodate the requisite interactions for a superconducting cosmic string solution with long-range U(1) gauge fields requires five chiral supermultiplets. An investigation of the bosonic sector of this model indicates that a solution is admitted describing a gauge string surrounded by supersymmetric vacuum. By considering the effects of the gauge string background upon the remaining scalar fields of the theory, it is concluded that a parameter range exists for which the U(1) charged scalar fields condense within the core of the string, making it a superconducting string that can carry charge and/or current. It is also found that the neutralmore » scalar field can be associated with particle bound states that are localized within or near the string core. {copyright} {ital 1996 The American Physical Society.}« less