48 research outputs found

    ADHM Construction of Noncommutative Instantons

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    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

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    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 N=2N=2 SU(ss) 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

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    The exact solution of N=2N=2 supersymmetric SU(N)SU(N) 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 Ď„\tau function of the (generalized) Toda lattice hierarchy is also clarified.Comment: 13 pages, LaTe

    Three-Dimensional Extremal Black Holes and the Maldacena Duality

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    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