475 research outputs found
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
Knizhnik-Zamolodchikov-Bernard equations connected with the eight-vertex model
Using quasiclassical limit of Baxter's 8 - vertex R - matrix, an elliptic
generalization of the Knizhnik-Zamolodchikov equation is constructed. Via
Off-Shell Bethe ansatz an integrable representation for this equation is
obtained. It is shown that there exists a gauge transformation connecting this
equation with Knizhnik-Zamolodchikov-Bernard equation for SU(2)-WZNW model on
torus.Comment: 20 pages latex, macro: tcilate
Recursive representation of the torus 1-point conformal block
The recursive relation for the 1-point conformal block on a torus is derived
and used to prove the identities between conformal blocks recently conjectured
by R. Poghossian. As an illustration of the efficiency of the recurrence method
the modular invariance of the 1-point Liouville correlation function is
numerically analyzed.Comment: 14 pages, 1 eps figure, misprints corrected and a reference adde
Higher Equations of Motion in N = 1 SUSY Liouville Field Theory
Similarly to the ordinary bosonic Liouville field theory, in its N=1
supersymmetric version an infinite set of operator valued relations, the
``higher equations of motions'', holds. Equations are in one to one
correspondence with the singular representations of the super Virasoro algebra
and enumerated by a couple of natural numbers . We demonstrate
explicitly these equations in the classical case, where the equations of type
survive and can be interpreted directly as relations for classical
fields. General form of the higher equations of motion is established in the
quantum case, both for the Neveu-Schwarz and Ramond series.Comment: Two references adde
Bootstrap in Supersymmetric Liouville Field Theory. I. NS Sector
A four point function of basic Neveu-Schwarz exponential fields is
constructed in the N = 1 supersymmetric Liouville field theory. Although the
basic NS structure constants were known previously, we present a new
derivation, based on a singular vector decoupling in the NS sector. This allows
to stay completely inside the NS sector of the space of states, without
referencing to the Ramond fields. The four-point construction involves also the
NS blocks, for which we suggest a new recursion representation, the so-called
elliptic one. The bootstrap conditions for this four point correlation function
are verified numerically for different values of the parameters
Modular anomaly equations in N =2* theories and their large-N limit
We propose a modular anomaly equation for the prepotential of the N=2* super Yang-Mills theory on R^4 with gauge group U(N) in the presence of an Omega-background. We then study the behaviour of the prepotential in a large-N limit, in which N goes to infinity with the gauge coupling constant kept fixed. In this regime instantons are not suppressed. We focus on two representative choices of gauge theory vacua, where the vacuum expectation values of the scalar fields are distributed either homogeneously or according to the Wigner semi-circle law. In both cases we derive an all-instanton exact formula for the prepotential. As an application, we show that the gauge theory partition function on S^4 at large N localises around a Wigner distribution for the vacuum expectation values leading to a very simple expression in which the instanton contribution becomes independent of the coupling constant
Matone's relation of N=2 super Yang-Mills and spectrum of Toda chain
In N=2 super Yang-Mills theory, the Matone's relation relates instanton
corrections of the prepotential to instanton corrections of scalar field
condensation . This relation has been proved to hold for Omega
deformed theories too, using localization method. In this paper, we first give
a case study supporting the relation, which does not rely on the localization
technique. Especially, we show that the magnetic expansion also satisfies a
relation of Matone's type. Then we discuss implication of the relation for the
spectrum of periodic Toda chain, in the context of recently proposed
Nekrasov-Shatashvili scheme.Comment: 17 pages; v2 minor changes, references added; v3 more material added
in 2nd section, clarification in 4th sectio
Five-dimensional AGT Conjecture and the Deformed Virasoro Algebra
We study an analog of the AGT relation in five dimensions. We conjecture that
the instanton partition function of 5D N=1 pure SU(2) gauge theory coincides
with the inner product of the Gaiotto-like state in the deformed Virasoro
algebra. In four dimensional case, a relation between the Gaiotto construction
and the theory of Braverman and Etingof is also discussed.Comment: 12 pages, reference added, minor corrections (typos, notation
changes, etc
A New 2d/4d Duality via Integrability
We prove a duality, recently conjectured in arXiv:1103.5726, which relates
the F-terms of supersymmetric gauge theories defined in two and four dimensions
respectively. The proof proceeds by a saddle point analysis of the
four-dimensional partition function in the Nekrasov-Shatashvili limit. At
special quantized values of the Coulomb branch moduli, the saddle point
condition becomes the Bethe Ansatz Equation of the SL(2) Heisenberg spin chain
which coincides with the F-term equation of the dual two-dimensional theory.
The on-shell values of the superpotential in the two theories are shown to
coincide in corresponding vacua. We also identify two-dimensional duals for a
large set of quiver gauge theories in four dimensions and generalize our proof
to these cases.Comment: 19 pages, 2 figures, minor corrections and references adde
Penner Type Matrix Model and Seiberg-Witten Theory
We discuss the Penner type matrix model recently proposed by Dijkgraaf and
Vafa for a possible explanation of the relation between four-dimensional gauge
theory and Liouville theory by making use of the connection of the matrix model
to two-dimensional CFT. We first consider the relation of gauge couplings
defined in UV and IR regimes of N_f = 4, N = 2 supersymmetric gauge theory
being related as . We then use this relation to discuss the action of modular
transformation on the matrix model and determine its spectral curve.
We also discuss the decoupling of massive flavors from the N_f = 4 matrix
model and derive matrix models describing asymptotically free N = 2 gauge
theories. We find that the Penner type matrix theory reproduces correctly the
standard results of N = 2 supersymmetric gauge theories.Comment: 22 pages; v2: references added, typos corrected; v3: a version to
appear in JHE
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