Abstract:
N=(1,0) supergravity in six dimensions admits AdS_3\times S^3 as a vacuum solution. We extend our recent results presented in hep-th/0212323, by obtaining the complete N=4 Yang-Mills-Chern-Simons supergravity in D=3, up to quartic fermion terms, by S^3 group manifold reduction of the six dimensional theory. The SU(2) gauge fields have Yang-Mills kinetic terms as well as topological Chern-Simons mass terms. There is in addition a triplet of matter vectors. After diagonalisation, these fields describe two triplets of topologically-massive vector fields of opposite helicities. The model also contains six scalars, described by a GL(3,R)/SO(3) sigma model. It provides the first example of a three-dimensional gauged supergravity that can obtained by a consistent reduction of string-theory or M-theory and that admits AdS_3 as a vacuum solution. There are unusual features in the reduction from six-dimensional supergravity, owing to the self-duality condition on the 3-form field. The structure of the full equations of motion in N=(1,0) supergravity in D=6 is also elucidated, and the role of the self-dual field strength as torsion is exhibited.

Abstract:
Recently, gauged supergravities in three dimensions with Yang-Mills and Chern-Simons type interactions have been constructed. In this article, we demonstrate that any gauging of Yang-Mills type with semisimple gauge group G_0, possibly including extra couplings to massive Chern-Simons vectors, is equivalent on-shell to a pure Chern-Simons type gauging with non-semisimple gauge group $G_0 \ltimes T \subset G$, where T is a certain translation group, and where G is the maximal global symmetry group of the ungauged theory. We discuss several examples.

Abstract:
We present a classification of the possible regular, spherically symmetric solutions of the Einstein-Yang-Mills system which is based on a bundle theoretical analysis for arbitrary gauge groups. It is shown that such solitons must be of magnetic type, at least if the magnetic Yang-Mills charge vanishes. Explicit expressions for the Chern-Simons numbers of these selfgravitating Yang-Mills solitons are derived, which involve only properties of irreducible root systems and some information about the asymptotics of the solutions. It turns out, as an example, that the Chern-Simons numbers are always half-integers or integers for the gauge groups $SU(n)$. Possible physical implications of these results, which are based on analogies with the unstable sphaleron solution of the electroweak theory, are briefly indicated.

Abstract:
We prove that three-dimensional N=1 supersymmetric Yang-Mills-Chern-Simons theory is finite to all loops. This leaves open the possibility that different regularization methods give different finite effective actions. We show that for this model dimensional regularization and regularization by dimensional reduction yield the same effective action.

Abstract:
We study one-loop correction to the Chern-Simons coefficient $\kappa=k/4\pi$ in $N=1,2,3$ supersymmetric Yang-Mills Chern-Simons systems. In the pure bosonic case, the shift of the parameter $k$ is known to be $k\rightarrow k + c_v$, where $c_v$ is the quadratic Casimir of the gauge group. In the $N=1$ case, the fermionic contribution cancels the bosonic contribution by half and the shift is $k \rightarrow k+ c_v/2$, making the theory anomalous if $c_v$ is odd. In the $N=2,3$ cases, the fermionic contribution cancels the bosonic contribution completely and there is no correction. We also calculate the mass corrections, showing the supersymmetry is preserved. As the matter fields decouple from the gauge field in the pure Chern-Simons limit, this work sheds some light on the regularization dependency of the correction in pure Chern-Simons systems. We also discuss the implication to the case when the gauge symmetry is spontaneously broken by the Higgs mechanism.

Abstract:
We show explicitly how BV Yang-Mills action emerges as a homotopy generalization of Chern-Simons theory from the algebraic constructions arising from String Field Theory.

Abstract:
We derive some new relationships between matrix models of Chern-Simons gauge theory and of two-dimensional Yang-Mills theory. We show that q-integration of the Stieltjes-Wigert matrix model is the discrete matrix model that describes q-deformed Yang-Mills theory on the 2-sphere. We demonstrate that the semiclassical limit of the Chern-Simons matrix model is equivalent to the Gross-Witten model in the weak coupling phase. We study the strong coupling limit of the unitary Chern-Simons matrix model and show that it too induces the Gross-Witten model, but as a first order deformation of Dyson's circular ensemble. We show that the Sutherland model is intimately related to Chern-Simons gauge theory on the 3-sphere, and hence to q-deformed Yang-Mills theory on the 2-sphere. In particular, the ground state wavefunction of the Sutherland model in its classical equilibrium configuration describes the Chern-Simons free energy. The correspondence is extended to Wilson line observables and to arbitrary simply-laced gauge groups.

Abstract:
We study quantum Chern-Simons theory as the large mass limit of the limit $D\to 3$ of dimensionally regularized topologically massive Yang-Mills theory. This approach can also be interpreted as a BRS-invariant hybrid regularization of Chern-Simons theory, consisting of a higher-covariant derivative Yang-Mills term plus dimensional regularization. Working in the Landau gauge, we compute radiative corrections up to second order in perturbation theory and show that there is no two-loop correction to the one-loop shift $k\rightarrow k+ c_{\scriptscriptstyle V},\,\,k$ being the bare Chern-Simons parameter. In passing we also prove by explicit computation that topologically massive Yang-Mills theory is UV finite.

Abstract:
In this paper we derive in a coordinate-free manner the field equations for a lagrangean consisting of Yang-Mills kinetical term plus Chern-Simons self-coupling term. This equation turns out to be an eigenvalue equation for the covariant laplacian.

Abstract:
Holomorphic quantization of 2+1 dimensional pure Yang-Mills theory is studied with focusing on finite large scales. Previously we have shown that (Yildirim, 2015, Int. J. Mod. Phys A, 30(7), 1550034) topologically massive Yang-Mills theory exhibits a Chern-Simons splitting behavior at large scales, similar to the topologically massive AdS gravity model in its near Chern-Simons limit. This splitting occurs as a sum of two Chern-Simons terms with levels k/2 each. In the pure Chern-Simons limit, the split parts add up to give the original Chern-Simons term in the action. The opposite limit of the gravitational analogue is an Einstein-Hilbert term with a negative cosmological constant, which can be written as subtracted two half Chern-Simons terms. With this motivation, the gauge theory version of this limit is investigated, showing that at large distances, pure Yang-Mills theory acts like a topological theory that consists of split Chern-Simons parts with levels k/2 and -k/2. At very large distances these split terms cancel, making the Yang-Mills theory trivial as expected due to existence of a mass gap. Gauge invariance of the split parts is discussed. It is also shown that, this splitting behavior can be exploited to incorporate link invariants of knot theory, just like in the topologically massive case.