Related papers: Instantons, Hilbert Schemes and Integrability
We study U(1) and U(2) noncommutative instantons on R^2_{NC} x R^2_C based on the ADHM construction. It is shown that a mild singularity in the instanton solutions for both self-dual and anti-self-dual gauge fields always disappears in…
We describe explicitly how certain standard opens of the Hilbert scheme of points are embedded into Grassmannians. The standard opens of the Hilbert scheme that we consider are given as the intersection of a corresponding basic open affine…
A formulation of U(1) - symmetric classical membrane motions (preserving one rotational symmetry) is given, and reductions to systems of ODE's, as well as some ideas concerning singularities and integrability.
The Hilbert scheme $S^{[n]}$ of points on an algebraic surface $S$ is a simple example of a moduli space and also a nice (crepant) resolution of singularities of the symmetric power $S^{(n)}$. For many phenomena expected for moduli spaces…
Three kinds of integrable Kondo problems in one-dimensional extended Hubbard models are studied by means of the boundary graded quantum inverse scattering method. The boundary K matrices depending on the local moments of the impurities are…
The Drinfeld-Manin construction of U(N) instanton is reformulated in the ADHM formulism, which gives explicit general solutions of the ADHM constraints for U(N) (N>=2k-1) k-instantons. For the N<2k-1 case, implicit results are given…
We consider aspects of instanton dynamics in the large-N limit using the AdS/CFT duality for D0/D4 bound states. In the supergravity picture of wrapped D0-brane world-lines on D4-branes, we find the single-instanton measure and discuss its…
Numerical and anaytical studies of the instanton liquid model have allowed the determination of many hadronic parameters during the last 13 years. Most part of this thesis is devoted to the extension of the analytical methods. The meson…
Numerical and anaytical studies of the instanton liquid model have allowed the determination of many hadronic parameters during the last 13 years. Most part of this thesis is devoted to the extension of the analytical methods. The meson…
We define and compute the $L^2$ metric on the framed moduli space of circle invariant 1-instantons on the 4-sphere. This moduli space is four dimensional and our metric is $SO(3) \times U(1)$ symmetric. We study the behaviour of generic…
We discuss various aspects of multi-instanton configurations in generic multi-cut matrix models. Explicit formulae are presented in the two-cut case and, in particular, we obtain general formulae for multi-instanton amplitudes in the…
There have been two distinct schemes studied in the literature for instanton counting in A_{p-1} asymptotically locally Euclidean (ALE) spaces. We point out that the two schemes---namely the counting of orbifolded instantons and instanton…
The SU(4)-instanton equations are natural BPS equations for instantons on 8-manifolds. We study these equations on nearly Kaehler and Calabi-Yau torsion manifolds of the form M x G/H, with G/H a coset space and M a product of a torus with…
Various algebraic structures have recently appeared in a parallel way in the framework of Hilbert schemes of points on a surface and respectively in the framework of equivariant K-theory [N1,Gr,S2,W], but direct connections are yet to be…
Calculations of the number of curves on a Calabi-Yau manifold via an instanton expansion do not always agree with what one would expect naively. It is explained how to account for continuous families of instantons via deformation theory and…
We show that the one dimensional unitary matrix model with potential of the form $a U + b U^2 + h.c.$ is integrable. By reduction to the dynamics of the eigenvalues, we establish the integrability of a system of particles in one space…
We discuss some physical issues related to the K-theoretic classification of D-brane charges, putting an emphasis on the role of D-brane instantons. The relation to D-instantons provides a physical interpretation to the mathematical…
We apply the methods recently developed for computation of type IIA disk instantons using mirror symmetry to a large class of D-branes wrapped over Lagrangian cycles of non-compact Calabi-Yau 3-folds. Along the way we clarify the notion of…
An instanton $(E, D)$ on a (pseudo-)hyperk\"ahler manifold $M$ is a vector bundle $E$ associated to a principal $G$-bundle with a connection $D$ whose curvature is pointwise invariant under the quaternionic structures of $T_x M, \ x\in M$,…
We discuss two-dimensional sigma models on moduli spaces of instantons on K3 surfaces. These N=(4,4) superconformal field theories describe the near-horizon dynamics of the D1-D5-brane system and are dual to string theory on AdS_3. We…