811 research outputs found
Wilson Loops and Chiral Correlators on Squashed Sphere
We study chiral deformations of and supersymmetric
gauge theories obtained by turning on
interactions with the superfield. Using localization, we
compute the deformed gauge theory partition function and the
expectation value of circular Wilson loops on a squashed four-sphere. In
the case of the deformed theory, exact formulas for and
are derived in terms of an underlying interacting matrix model replacing
the free Gaussian model describing the theory. Using the AGT
correspondence, the -deformations are related to the insertions of
commuting integrals of motion in the four-point CFT correlator and chiral
correlators are expressed as -derivatives of the gauge theory partition
function on a finite -background. In the so called Nekrasov-Shatashvili
limit, the entire ring of chiral relations is extracted from the
-deformed Seiberg-Witten curve. As a byproduct of our analysis we
show that gauge theories on rational -backgrounds are dual to
CFT minimal models.Comment: 33 pages, 2 figure, in this version we have added two new references
and a detailed comparison with the results obtained in one of these tw
Exotic prepotentials from D(-1)D7 dynamics
We compute the partition functions of D(-1)D7 systems describing the
multi-instanton dynamics of SO(N) gauge theories in eight dimensions. This is
the simplest instance of the so called exotic instantons. In analogy with the
Seiberg-Witten theory in four space-time dimensions, the prepotential and
correlators in the chiral ring are derived via localization formulas and found
to satisfy relations of the Matone type. Exotic prepotentials of SO(N) gauge
theories with N=2 supersymmetries in four-dimensions are also discussed.Comment: 19 page
Structure Constants in the Super-Liouville Field Theory
The symmetry algebra of Super-Liouville field theory in two dimensions
is the infinite dimensional superconformal algebra, which allows one to
prove, that correlation functions, containing degenerated fields obey some
partial linear differential equations. In the special case of four point
function, including a primary field degenerated at the first level, this
differential equations can be solved via hypergeometric functions. Taking into
account mutual locality properties of fields and investigating s- and t-
channel singularities we obtain some functional relations for three- point
correlation functions. Solving this functional equations we obtain three-point
functions in both Neveu-Schwarz and Ramond sectors.Comment: LaTeX file, 17 pages, no figure
Perturbation theory in radial quantization approach and the expectation values of exponential fields in sine-Gordon model
A perturbation theory for Massive Thirring Model (MTM) in radial quantization
approach is developed. Investigation of the twisted sector in this theory
allows us to calculate the vacuum expectation values of exponential fields of the sine-Gordon theory in first order over Massive Thirring
Models coupling constant. It appears that the apparent difficulty in radial
quantization of massive theories, namely the explicite ''time'' dependence of
the Hamiltonian, may be successfully overcome. The result we have obtained
agrees with the exact formula conjectured by Lukyanov and Zamolodchikov and
coincides with the analogous calculations recently carried out in dual angular
quantization approach by one of the authors.Comment: 16 pages, no figures, LaTe
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