48 research outputs found
ADHM Construction of Noncommutative Instantons
We discuss the Atiyah-Drinfeld-Hitchin-Manin (ADHM) construction of U(N)
instantons in noncommutative (NC) space and prove the one-to-one correspondence
between moduli spaces of the noncommutative instantons and the ADHM data,
together with an origin of the instanton number for U(1). We also give a
derivation of the ADHM construction from the viewpoint of the Nahm
transformation of instantons on four-tori. This article is a composite version
of [23] and [24].Comment: 23pages, 3 figures, LaTeX; A composite version of proceedings of the
20th International Colloquium on Integrable Systems and Quantum Symmetries
(ISQS20), 17-23 June 2012, Prague, Czech Republic and the 10th International
Conference on Symmetries and Integrability of Difference Equations (SIDE10),
11-15 June 2012, Ningbo, Chin
Isomonodromic deformations and supersymmetric gauge theories
Seiberg-Witten solutions of four-dimensional supersymmetric gauge theories
possess rich but involved integrable structures. The goal of this paper is to
show that an isomonodromy problem provides a unified framework for
understanding those various features of integrability. The Seiberg-Witten
solution itself can be interpreted as a WKB limit of this isomonodromy problem.
The origin of underlying Whitham dynamics (adiabatic deformation of an
isospectral problem), too, can be similarly explained by a more refined
asymptotic method (multiscale analysis). The case of SU()
supersymmetric Yang-Mills theory without matter is considered in detail for
illustration. The isomonodromy problem in this case is closely related to the
third Painlev\'e equation and its multicomponent analogues. An implicit
relation to t\tbar fusion of topological sigma models is thereby expected.Comment: Several typos are corrected, and a few sentenses are altered. 19 pp +
a list of corrections (page 20), LaTe
Whitham-Toda hierarchy and N = 2 supersymmetric Yang-Mills theory
The exact solution of supersymmetric Yang-Mills theory is
studied in the framework of the Whitham hierarchies. The solution is identified
with a homogeneous solution of a Whitham hierarchy. This integrable hierarchy
(Whitham-Toda hierarchy) describes modulation of a quasi-periodic solution of
the (generalized) Toda lattice hierarchy associated with the hyperelliptic
curves over the quantum moduli space. The relation between the holomorphic
pre-potential of the low energy effective action and the function of the
(generalized) Toda lattice hierarchy is also clarified.Comment: 13 pages, LaTe
Three-Dimensional Extremal Black Holes and the Maldacena Duality
We discuss the microscopic states of the extremal BTZ black holes. Degeneracy
of the primary states corresponding to the extremal BTZ black holes in the
boundary N=(4,4) SCFT is obtained by utilizing the elliptic genus and the
unitary representation theory of N=4 SCA. The degeneracy is consistent with the
Bekenstein-Hawking entropy.Comment: 25 pages, Latex file, no figure, minor changes in section 2.2 and
several typos are correcte