We construct supergravity solutions for Dp-branes at orbifold points. The solutions are written in terms of a single function, which is the solution to a nonlinear differential equation. The near horizon limits of these solutions are dual, in the AdS/CFT sense, to super-Yang-Mills theories with 8 supercharges in various dimensions. In particular, we present a dual to N = 2 SU(N) SYM theory in 3...

The electrogravity transformation is defined by an interchange of the “active” and “passive” electric parts of the Riemann tensor. Such a transformation has been used to find new solutions that are “dual” to the Kerr family of black hole spacetimes in general relativity. In such a case, the dual solution is a similar black hole spacetime endowed with a global monopole charge. Here, we extend th...

Ellipsoids that contain all optimal primal solutions, those that contain all optimal dual slack solutions, and primal– dual ellipsoids are derived. They are independent of the algorithm used and have a smaller size than the Choi–Goldfarb ellipsoids [J. Optim. Theory Appl. 80 (1994) 161–173]. c © 2000 Elsevier Science B.V. All rights reserved.

This paper characterizes the asymptotic convergence properties of the primal-dual dynamics to the solutions of a constrained concave optimization problem using classical notions from stability analysis. We motivate our study by providing an example which rules out the possibility of employing the invariance principle for hybrid automata to analyze the asymptotic convergence. We understand the s...

A multiobjective nonlinear programming problem is considered. Sufficiency theorems are derived for efficient and properly efficient solutions under generalized (F, ρ)-convexity assumptions. Weak, strong and strict converse duality theorems are established for a general Mond–Weir type dual relating properly efficient solutions of the primal and dual problems.

We consider solutions to low energy string theory which have a horizon and a spacelike symmetry. Each of these solutions has a geometrically different dual description. We show that the dual solution has a horizon with exactly the same Hawking temperature (surface gravity) and entropy (area) as the original solution.

We use the double affine Hecke algebra of type GLN to construct an explicit consistent system of q-difference equations, which we call the bispectral quantum Knizhnik-Zamolodchikov (BqKZ) equations. BqKZ includes, besides Cherednik’s quantum affine KZ equations associated to principal series representations of the underlying affine Hecke algebra, a compatible system of q-difference equations ac...

We investigate the integrable structures in an N = 2 superconformal Sp(N) Yang-Mills theory with matter, which is dual to an open+closed string system. We restrict ourselves to the BMN operators that correspond to free string states. In the closed string sector, an integrable structure is inherited from its parent theory, N = 4 SYM. For the open string sector, the planar one-loop mixing matrix ...

Self-dual gauge fields play an important role in four-dimensional Riemannian geometry. In this essay we review some of the basic ideas surrounding these gauge fields. In particular we review the Atiyah-Hitchin-Singer theorem on the dimension of the moduli space of such solutions. We also review the role of self-dual gauge fields in the geometry of Euclidean Yang-Mills theory where these solutio...

We apply algebraic and vertex operator techniques to solve two dimensional reduced vacuum Einstein's equations. This leads to explicit expressions for the coefficients of metrics solutions of the vacuum equations as ratios of determinants. No quadratures are left. These formulas rely on the identification of dual pairs of vertex operators corresponding to dual metrics related by the Kramer-Neug...