A Generalization of Cachazo-Douglas-Seiberg-Witten Conjecture for Symmetric Spaces

On the Cachazo-douglas-seiberg-witten Conjecture for Simple Lie Algebras

On Cachazo–Douglas–Seiberg–Witten Conjecture for Simple Lie Algebras

Let g be a finite dimensional simple Lie algebra over the complex numbers C. Consider the exterior algebra R := ∧ (g⊕ g) on two copies of g. Then, the algebra R is bigraded under R = ∧p(g)⊗∧q(g). The diagonal adjoint action of g gives rise to a g-algebra structure on R compatible with the bigrading. There are three ‘standard’ copies of the adjoint representation g in R. Let J be the (bigraded) ...

Torsion, TQFT, and Seiberg–Witten invariants of 3–manifolds

We prove a conjecture of Hutchings and Lee relating the Seiberg–Witten invariants of a closed 3–manifold X with b1 ≥ 1 to an invariant that “counts” gradient flow lines—including closed orbits—of a circle-valued Morse function on the manifold. The proof is based on a method described by Donaldson for computing the Seiberg–Witten invariants of 3–manifolds by making use of a “topological quantum ...

On the quantum cohomology of a symmetric product of an algebraic curve

Quantum cohomology is a novel multiplication on the cohomology of a smooth complex projective variety, or even a compact symplectic manifold. It can be regarded as a deformation of the ordinary cup product, defined in terms of the Gromov-Witten invariants of the manifold. Since its introduction in 1991, there has been enormous interest in computing quantum cohomology for various target spaces. ...

Seiberg-witten Prepotential from Instanton Counting

Direct evaluation of the Seiberg-Witten prepotential is accomplished following the localization programme suggested in [1]. Our results agree with all low-instanton calculations available in the literature. We present a two-parameter generalization of the Seiberg-Witten prepotential, which is rather natural from the M-theory/five dimensional perspective, and conjecture its relation to the tau-f...