Definition of Chern-Simons Terms in Thermal QED_3 Revisited

We present two compact derivations of the correct definition of the Chern-Simons term in the topologically non trivial context of thermal $QED_3$. One is based on a transgression descent from a D=4 background connection, the other on embedding the abelian model in SU(2). The results agree with earlier cohomology conclusions and can be also used to justify a recent simple heuristic approach. The correction to the naive Chern-Simons term, and its behavior under large gauge transformations are displayed.Comment: 9 pages, RevTex, no figures, new derivation from non abelian embedding adde

Polyakov conjecture and 2+1 dimensional gravity coupled to particles

A proof is given of Polyakov conjecture about the auxiliary parameters of the SU(1,1) Riemann-Hilbert problem for general elliptic singularities. Such a result is related to the uniformization of the the sphere punctured by n conical defects. Its relevance to the hamiltonian structure of 2+1 dimensional gravity in the maximally slicing gauge is stressed.Comment: Talk by P. Menotti at Int. Europhysics Conference on High Energy Physics, Budapest 12-18 July 2001, 5 pages late

Towards the solution of noncommutative YM2YM_2: Morita equivalence and large N-limit

In this paper we shall investigate the possibility of solving U(1) theories on the non-commutative (NC) plane for arbitrary values of $\theta$ by exploiting Morita equivalence. This duality maps the NC U(1) on the two-torus with a rational parameter $\theta$ to the standard U(N) theory in the presence of a 't Hooft flux, whose solution is completely known. Thus, assuming a smooth dependence on $\theta$, we are able to construct a series rational approximants of the original theory, which is finally reached by taking the large $N-$limit at fixed 't Hooft flux. As we shall see, this procedure hides some subletities since the approach of $N$ to infinity is linked to the shrinking of the commutative two-torus to zero-size. The volume of NC torus instead diverges and it provides a natural cut-off for some intermediate steps of our computation. In this limit, we shall compute both the partition function and the correlator of two Wilson lines. A remarkable fact is that the configurations, providing a finite action in this limit, are in correspondence with the non-commutative solitons (fluxons) found independently by Polychronakos and by Gross and Nekrasov, through a direct computation on the plane.Comment: 21 pages, JHEP3 preprint tex-forma

New supersymmetric Wilson loops in ABJ(M) theories

We present two new families of Wilson loop operators in N= 6 supersymmetric Chern-Simons theory. The first one is defined for an arbitrary contour on the three dimensional space and it resembles the Zarembo's construction in N=4 SYM. The second one involves arbitrary curves on the two dimensional sphere. In both cases one can add certain scalar and fermionic couplings to the Wilson loop so it preserves at least two supercharges. Some previously known loops, notably the 1/2 BPS circle, belong to this class, but we point out more special cases which were not known before. They could provide further tests of the gauge/gravity correspondence in the ABJ(M) case and interesting observables, exactly computable by localizationComment: 9 pages, no figure. arXiv admin note: text overlap with arXiv:0912.3006 by other author

Proof of Polyakov conjecture for general elliptic singularities

A proof is given of Polyakov conjecture about the auxiliary parameters of the SU(1,1) Riemann-Hilbert problem for general elliptic singularities. Its relevance to 2+1 dimensional gravity and to the uniformization of the sphere punctured by n conical defects is stressed

Partition functions of chiral gauge theories on the two dimensional torus and their duality properties

Two different families of abelian chiral gauge theories on the torus are investigated: the aim is to test the consistency of two-dimensional anomalous gauge theories in the presence of global degrees of freedom for the gauge field. An explicit computation of the partition functions shows that unitarity is recovered in particular regions of parameter space and that the effective dynamics is described in terms of fermionic interacting models. For the first family, this connection with fermionic models uncovers an exact duality which is conjectured to hold in the nonabelian case as well.Comment: RevTex, 13 pages, references adde