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     

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.     

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.     

Chiral magnetic effect in SU(2) lattice gluodynamics at zero temperature

The chiral magnetic effect is the appearance of a quark electric current along a magnetic-field direction in topologically nontrivial gauge fields. There is evidence that this effect is observed in collisions between heavy ions at the RHIC collider. The features of the chiral magnetic effect in SU(2) lattice gluodynamics at zero temperature have been investigated. It has been found that the electric current increases in the magnetic-field direction owing to quantum fluctuations of gluon fields. Fluctuations of the local charge density and chirality also increase with the magnetic field strength, which is a signature of the chiral magnetic effect.     

Chern-Simons states at genus one

We present a rigorous analysis of the Schrödinger picture quantization for theSU(2) Chern-Simons theory on 3-manifold torusxline, with insertions of Wilson lines. The quantum states, defined as gauge covariant holomorphic functionals ofsu(2)-connections on the torus, are expressed by degree 2k theta-functions satisfying additional conditions. The conditions are obtained by splitting the space of semistablesu(2)-connections into nine submanifolds and by analyzing the behavior of states at four codimension 1 strata. We construct the Knizhnik-Zamolodchikov-Bernard connection allowing to compare the states for different complex structures of the torus and different positions of the Wilson lines. By letting two Wilson lines come together, we prove a recursion relation for the dimensions of the spaces of states which, together with the (unproven) absence of states for spins>1/2 level implies the Verlinde dimension formula.     

Quantization ofSL(2,R) Chern-Simons theory

In this paper we consider the bosonic sector of the electroweak theory. It has been shown in the work of Ambjorn and Olesen that when the Higgs mass equals to the mass of theZ boson, the model in two dimensions subject to the 't Hooft periodic boundary condition may be reduced to a Bogomol'nyi system and that the solutions of the system are vortices in a dual superconductor. We shall prove using a constrained variational reformulation of the problem the existence of such vortices. Our conditions for the existence of solutions are necessary and sufficient when the vortex numberN=1,2.Research supported in part by NSF grant DMS-88-02858 and DOE grant DE-FG02-86ER250125     

Fluctuations in SU(2) Yang-Mills theory

The nonlinear differential equation resulting from the use of the ’t Hooft-Corrigan-Fairlie-Wilczek ansatz in SU(2) Yang-Mills gauge theory is solved by the bilinear operator method. The solutions which are singular are interpreted as fluctuations involving no flux transport. However, these objects may play a tunnelling role similar to that of merons.     

N = 4 supergravity theory with local SU(2) × SU(2) invariance

N = 4 supergravity theory has been formulated in two different equivalent forms, which may be expected to become inequivalent when the internal symmetry is gauged. The extension of the first form to include local SO(4) internal symmetry is known. In this paper the extension of the second form to local SU(2) × SU(2) invariance is given, and is indeed inequivalent to the first form. The second form is in general parity non-conserving, while both forms have scalar field potentials that are unbounded from below.     

Vector and Spinor Decomposition of SU（2） Gauge Potential, Their Equivalence, and Knot Structure in SU（2） Chern-Simons Theory

In this paper, spinor and vector decompositions of SU（2） gauge potential are presented and their equivalence is constructed using a simply proposal. We also obtain the action of Faddeev nonlinear 0（3） sigma model from the SU（2） mass/ve gauge field theory, which is proposed according to the gauge invariant principle. At last, the knot structure in SU（2） Chern-Simons filed theory is discussed in terms of the Φ-mapping topological current theory, The topological charge of the knot is characterized by the Hopf indices and the Brouwer degrees of Φ-mapping.     

Finite temperature SU(2) lattice gauge theory

We discuss SU(2) lattice gauge theories at non-zero temperature and prove several rigorous results including i) the absence of confinement for sufficiently high temperature in the pure gauge theory, and ii) the absence of spontaneous chiral symmetry breaking for sufficiently high temperature in the theory with massless fundamental representation fermions.     

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.     

Topology and zero modes in the SU(2) lattice gauge vacuum

Evidence is presented that the Atiyah-Singer index theorem is effectively restored on the lattice for numerically accessible values of the lattice spacing (corresponding to β 4/g² ⩾2.4). It is shown explicitly how topological lattice artifacts decouple from the long-distance fermionic physics. Evidence is presented that while the spontaneous breaking of chiral symmetry does receive contributions of a topological origin, these are not the only contributions.