32 research outputs found
An Algorithm for the Microscopic Evaluation of the Coefficients of the Seiberg-Witten Prepotential
A procedure, allowing to calculate the coefficients of the SW prepotential in
the framework of the instanton calculus is presented. As a demonstration
explicit calculations for 2, 3 and 4- instanton contributions are carried out.Comment: LaTeX, 23 pages; typos are corrected, determinant formula is
simplifie
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
N=1 Superpotentials from Multi-Instanton Calculus
In this paper we compute gaugino and scalar condensates in N=1 supersymmetric
gauge theories with and without massive adjoint matter, using localization
formulae over the multi--instanton moduli space. Furthermore we compute the
chiral ring relations among the correlators of the theory and check
this result against the multi-instanton computation finding agreement.Comment: 31 pages, uses youngtab.sty, some explanations added, version to
appear in JHE
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
Instanton on toric singularities and black hole countings
We compute the instanton partition function for U(N) gauge
theories living on toric varieties, mainly of type
including or O_{\PP_1}(-p) surfaces. The results provide
microscopic formulas for the partition functions of black holes made out of
D4-D2-D0 bound states wrapping four-dimensional toric varieties inside a
Calabi-Yau. The partition function gets contributions from regular and
fractional instantons. Regular instantons are described in terms of symmetric
products of the four-dimensional variety. Fractional instantons are built out
of elementary self-dual connections with no moduli carrying non-trivial fluxes
along the exceptional cycles of the variety. The fractional instanton
contribution agrees with recent results based on 2d SYM analysis. The partition
function, in the large charge limit, reproduces the supergravity macroscopic
formulae for the D4-D2-D0 black hole entropy.Comment: 29 pages, 3 fig Section 5 is improved by the inclusion of a detailed
comparison between the instanton partition function and the D4-D2-D0 black
hole entropy formula coming from supergravit