The renormalization flow in the adjoint SU(2) lattice Higgs model

Applying the Monte Carlo renormalization group method we investigate the flow of coupling constants for the 8⁴ and 16⁴ SU(2) lattice Higgs model with triplet Higgs fields. The couplings of the renormalized actions are determined using Schwinger-Dyson equations. From the flow we find new evidence for the existence of a tricritical point at finite values of the inverse gauge coupling β but no indication for a discontinuity fixed point.     

On Nambu monopole dynamics in a SU(2) lattice Higgs model

It is shown that an SU(2) Higgs model on a lattice is equivalent to the Georgi-Glashow model in the limit of a small coupling constant between the Higgs and gauge fields. It can therefore be concluded that the transition between the confinement and symmetric phases in a 3 + 1 dimensional SU(2) Higgs model at finite temperature is accompanied by condensation of Nambu monopoles. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 9, 577–580 (10 November 1997)     

Phase structure of the SU(2) lattice gauge Higgs theory

Phase structure of the SU(2) lattice gauge Higgs theory is investigated by the Monte Carlo method and by an approximate calculation of an effective potential. Higgs fields are considered in the fundamental representation, and the radial mode of Higgs fields is not frozen. Two different radial measures for a radially varied Higgs field are used.Phase diagrams of the theory are determined, and a strong dependence on the choice of radial measure of scalar fields is manifested.     

SU(2) lattice gauge-Higgs model

Phase diagrams are investigated in theSU(2) gauge-Higgs theory with a defrost radial mode. The Higgs fields are considered in the fundamental representation. Phase diagrams are determined for different values of the scalar self-action constants. It is shown that the lines of first order phase transitions have the end points which are critical points, analogous to a phase diagram of the type “gas-liquid-ice”.     

Mean field theory and the SU(2) adjoint Higgs model

Three versions of the mean field approximation are applied to determine the phase diagram of the SU(2) adjoint Higgs model. In two of these, one with gauge fixing and one without, the Higgs action is integrated exactly. In the third version, the Higgs and Wilson parts of the action are treated on equal footing. The results, when compared to those from Monte Carlo simulations, suggest that more accurate simulations are needed in the crossover region.     

Strong self-coupling expansion in the lattice-regularized standard SU(2) Higgs model

Expectation values at an arbitrary point of the 3-dimensional coupling parameter space in the lattice-regularized SU(2) Higgs model with a doublet scalar field are expressed by a series of expectation values at infinite self-coupling (λ = ∞). Questions of convergence of this “strong self-coupling expansion” (SSCE) are investigated. The SSCE is a potentially useful tool for the study of the γ-dependence at any value (zero or non-zero) of the bare gauge coupling.     

Thermal monopoles in the SU(2) gauge theory on a lattice

Color-magnetic thermal monopoles in SU(2) lattice gluodynamics with improved Simanzik action were studied. The density of the monopoles, the monopole chemical potential, the cluster susceptibility, and the cluster magnetization were studied. These results were compared with results that were reported elsewhere.     

SU(2)Chern-Simons涡旋解的拓扑结构

运用规范势分解理论研究了 Dunne Jackiw Pi Trugenberger 模型中的自对偶方程, 得到一个静态的自对偶Chern Simons多涡旋解, 每个涡旋由5个参数描述。 发现了自对偶解与拓扑数之间的关系, 而拓扑数由Brouwer度与Hopf指标确定。 同时, 也研究了该涡旋解的磁通量的拓扑量子化。The self dual equation and its solution in SU(2) Dunne Jackiw Pi Trugenberger model has Been discussed with special ansatz for the Lie algebraic structures of su(2) and gauge potential decomposition. We obtainer a new concrete self dual equation and found the relationship between SU(2) Chern Simons vortices and topological number which is determined by Hopf indices and Brouwer degrees of  mapping. (two positions, one scale, one phase per vortex and one charge of each vortex) m vortices solutions are discribed by using 5m parameters. The quantization of flux is also studied in this case.     

SU(2) Chern-Simons theory at genus zero

We present a detailed study of the Schrödinger picture space of states in theSU(2) Chern-Simons topological gauge theory in the simplest geometry. The space coincides with that of the solutions of the chiral Ward identities for the WZW model. We prove that its dimension is given by E. Verlinde's formulae.     

Coupled gap equations for the screening masses in the SU(2) Higgs model

The complete set of static screening masses is determined for the SU(2) Higgs model from one-loop coupled gap equations. Results from the version containing scalar fields both in the fundamental and adjoint representations are compared with the model arising when integration over the adjoint scalar field is performed. A non-perturbative and non-linear mapping between the couplings of the two models is proposed which exhibits perfect decoupling of the heavy adjoint scalar field. Also the alternative of a gauge invariant mass resummation is investigated in the high temperature phase. Received: 7 May 1999 / Revised version: 6 July 1999 / Published online: 16 November 1999     

The integrability criterion in SU(2) Chern-Simons gauge theory

We prove that the multiplicity spaces appearing in Chern-Simons theory, as defioned by Segal, vanish unless they are associated to integrable representations. This and other links with conformal field theory are examined.Supported in part by NSF Mathematics Postdoctoral Fellowship DMS-9007255     

Complex singularities in the specific heat of the SU(2) lattice gauge model

A recent Monte Carlo simulation showing a sharp peak versus β in the specific heat for an SU(2) lattice gauge theory is compared with the high temperature expansion. An interpretation based on complex β-plane singularities is proposed.     

SU (3) Chern-Simons field theory in three-manifolds

We present the solution of the non-Abelian SU (3) Chern-Simons field theory defined in a generic three-manifold which is closed, connected and orientable. The surgery rules, which permit us to solve the theory, are derived and several examples of vacuum expectation values of Wilson line operators are computed. The three-manifold invariant associated with the non-Abelian SU (3) Chern-Simons model is defined and its values are computed for various three-manifolds.     

Universality in SU(2) lattice gauge theory

A method of resumming perturbation theory is used to re-analyze previous Monte Carlo data of Bhanot and Dashen. We find no inconsistency with universality. There appears to be a relatively large region where Monte Carlo studies can reliably be done.