768 research outputs found
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 .
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
Towards the solution of noncommutative : 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 by
exploiting Morita equivalence. This duality maps the NC U(1) on the two-torus
with a rational parameter 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 , we are able to construct a series rational approximants
of the original theory, which is finally reached by taking the large limit
at fixed 't Hooft flux. As we shall see, this procedure hides some subletities
since the approach of 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
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
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
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