E8 orbits of IR dualities

Prehomogeneous Spaces Associated with Nilpotent Orbits in E8(c)

New IR Dualities in Supersymmetric Gauge Theory in Three Dimensions

We present nontrivial examples of d = 3 gauge theories with sixteen and eight supercharges which are infrared dual at special points in the moduli space. This duality is distinct from mirror symmetry. To demonstrate duality we construct the gauge theories of interest using D2-branes and orientifolds and then consider their lift to M-theory. We also discuss the strong coupling limit of orientifo...

From Quantum AN (Sutherland) to E8 Trigonometric Model: Space-of-Orbits View

A number of affine-Weyl-invariant integrable and exactly-solvable quantum models with trigonometric potentials is considered in the space of invariants (the space of orbits). These models are completely-integrable and admit extra particular integrals. All of them are characterized by (i) a number of polynomial eigenfunctions and quadratic in quantum numbers eigenvalues for exactly-solvable case...

Regular Two-graphs from the Even Unimodular Lattice E8 + E8

This is a revised version of the rst part of 8]. Each two-graph is in one-to-one correspondence with a set of equiangular lines. This implies that a two-graph is represented by a system of vectors of equal odd norm with mutual inner products

Scaling Dualities

In this paper rst we prove four fundamental theorems of the alternative, called scaling dualities, characterizing exact and approximate solvability of four signi cant conic problems in nite dimensional spaces, de ned as: homogeneous programming (HP), scaling problem (SP), homogeneous scaling problem (HSP), and algebraic scaling problem (ASP). Let be a homogeneous function of degree p > 0, K a p...