215 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
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
Boundary Action of N=2 Super-Liouville Theory
We derive a boundary action of N=2 super-Liouville theory which preserves
both N=2 supersymmetry and conformal symmetry by imposing explicitly and . The resulting boundary action shows a new duality
symmetry.Comment: 15 pages; One reference is adde
Fractional Superstrings with Space-Time Critical Dimensions Four and Six
We propose possible new string theories based on local world-sheet symmetries
corresponding to extensions of the Virasoro algebra by fractional spin
currents. They have critical central charges and Minkowski
space-time dimensions for an integer. We present evidence
for their existence by constructing modular invariant partition functions and
the massless particle spectra. The dimension and strings have
space-time supersymmetry.Comment: 9 page
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
Generalized matrix models and AGT correspondence at all genera
We study generalized matrix models corresponding to n-point Virasoro
conformal blocks on Riemann surfaces with arbitrary genus g. Upon AGT
correspondence, these describe four dimensional N=2 SU(2)^{n+3g-3} gauge
theories with generalized quiver diagrams. We obtain the generalized matrix
models from the perturbative evaluation of the Liouville correlation functions
and verify the consistency of the description with respect to degenerations of
the Riemann surface. Moreover, we derive the Seiberg-Witten curve for the N=2
gauge theory as the spectral curve of the generalized matrix model, thus
providing a check of AGT correspondence at all genera.Comment: 19 pages; v2: version to appear in JHE
Genus-one correction to asymptotically free Seiberg-Witten prepotential from Dijkgraaf-Vafa matrix model
We find perfect agreements on the genus-one correction to the prepotential of
SU(2) Seiberg-Witten theory with N_f=2, 3 between field theoretical and
Dijkgraaf-Vafa-Penner type matrix model results.Comment: 12 pages; v2: minor revision; v3: more structured, submitted versio
On 3d extensions of AGT relation
An extension of the AGT relation from two to three dimensions begins from
connecting the theory on domain wall between some two S-dual SYM models with
the 3d Chern-Simons theory. The simplest kind of such a relation would
presumably connect traces of the modular kernels in 2d conformal theory with
knot invariants. Indeed, the both quantities are very similar, especially if
represented as integrals of the products of quantum dilogarithm functions.
However, there are also various differences, especially in the "conservation
laws" for integration variables, which hold for the monodromy traces, but not
for the knot invariants. We also discuss another possibility: interpretation of
knot invariants as solutions to the Baxter equations for the relativistic Toda
system. This implies another AGT like relation: between 3d Chern-Simons theory
and the Nekrasov-Shatashvili limit of the 5d SYM.Comment: 23 page
S-duality and 2d Topological QFT
We study the superconformal index for the class of N=2 4d superconformal
field theories recently introduced by Gaiotto. These theories are defined by
compactifying the (2,0) 6d theory on a Riemann surface with punctures. We
interpret the index of the 4d theory associated to an n-punctured Riemann
surface as the n-point correlation function of a 2d topological QFT living on
the surface. Invariance of the index under generalized S-duality
transformations (the mapping class group of the Riemann surface) translates
into associativity of the operator algebra of the 2d TQFT. In the A_1 case, for
which the 4d SCFTs have a Lagrangian realization, the structure constants and
metric of the 2d TQFT can be calculated explicitly in terms of elliptic gamma
functions. Associativity then holds thanks to a remarkable symmetry of an
elliptic hypergeometric beta integral, proved very recently by van de Bult.Comment: 25 pages, 11 figure
Nekrasov Functions and Exact Bohr-Sommerfeld Integrals
In the case of SU(2), associated by the AGT relation to the 2d Liouville
theory, the Seiberg-Witten prepotential is constructed from the Bohr-Sommerfeld
periods of 1d sine-Gordon model. If the same construction is literally applied
to monodromies of exact wave functions, the prepotential turns into the
one-parametric Nekrasov prepotential F(a,\epsilon_1) with the other epsilon
parameter vanishing, \epsilon_2=0, and \epsilon_1 playing the role of the
Planck constant in the sine-Gordon Shroedinger equation, \hbar=\epsilon_1. This
seems to be in accordance with the recent claim in arXiv:0908.4052 and poses a
problem of describing the full Nekrasov function as a seemingly straightforward
double-parametric quantization of sine-Gordon model. This also provides a new
link between the Liouville and sine-Gordon theories.Comment: 10 page
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