Related papers: Nekrasov's Partition Function and Refined Donaldso…

Donaldson-Thomas theory on a Calabi-Yau can be described in terms of a certain six-dimensional cohomological gauge theory. We introduce a certain class of defects in this gauge theory which generalize surface defects in four dimensions.…

Let $A$ be an abelian variety. We introduce $A$-equivariant Grothendieck rings and $A$-equivariant motivic Hall algebras, and endow them with natural integration maps to the ring of dual numbers. The construction allows a systematic…

Using Arakelov geometry, we compute the partition function of the noncompact free boson at genus two. We begin by compiling a list of modular invariants which appear in the Arakelov theory of Riemann surfaces. Using these quantities, we…

A theorem of Dubrovin establishes the relationship between the GUE partition function and the partition function of Gromov-Witten invariants of the complex projective line. Based on this theorem we derive loop equations for the Gaussian…

I consider the partition function of the inhomogeneous 6-vertex model defined on the $n$ by $n$ square lattice. This function depends on 2n spectral parameters $x_i$ and $y_i$ attached to the horizontal and vertical lines respectively. In…

In the large rank limit, for any nonexceptional affine algebra, the graded branching multiplicities known as one-dimensional sums, are conjectured to have a simple relationship with those of type A, which are known as generalized Kostka…

For any subgroup of $\mathrm{SL}(3,\mathbb{R})\ltimes\mathbb{R}^3$ obtained by adding a translation part to a subgroup of $\mathrm{SL}(3,\mathbb{R})$ which is the fundamental group of a finite-volume convex projective surface, we first show…

The generating functions of the Severi degrees for sufficiently ample line bundles on algebraic surfaces are multiplicative in the topological invariants of the surface and the line bundle. Recently new proofs of this fact were given for…

Using the Ocneanu quantum geometry of ADE diagrams (and of other diagrams belonging to higher Coxeter-Dynkin systems), we discuss the classification of twisted partition functions for affine and minimal models in conformal field theory and…

A deformation of the N=2 topological string partition function is analyzed by considering higher dimensional F-terms of the type W^{2g}*Upsilon^n, where W is the chiral Weyl superfield and each Upsilon factor stands for the chiral…

We propose a new prescription for computing the Nekrasov partition functions of five-dimensional theories with eight supercharges realized by gauging non-perturbative flavor symmetries of three five-dimensional superconformal field…

We consider a pure U(1) quantum gauge field theory on a general Riemannian compact four manifold. We compute the partition function with Abelian Wilson loop insertions. We find its duality covariance properties and derive topological…

In analogy to Nekrasov's theory of gauge origami on intersecting branes, we introduce the gauge origami moduli space on broken lines. We realize this moduli space as a Quot scheme parametrising zero-dimensional quotients of a torsion sheaf…

We prove that affine invariant manifolds in strata of flat surfaces are algebraic varieties. The result is deduced from a generalization of a theorem of M\"oller. Namely, we prove that the image of a certain twisted Abel-Jacobi map lands in…

We compute the partition function of five-dimensional abelian gauge theory on a five-torus T5 with a general flat metric using the Dirac method of quantizing with constraints. We compare this with the partition function of a single…

J. Lepowsky and R. L. Wilson initiated the approach to combinatorial Rogers-Ramanujan type identities via the vertex operator constructions of representations of affine Lie algebras. In a joint work with Arne Meurman this approach is…

We calculate gauge instanton corrections to a class of higher derivative string effective couplings introduced in [1]. We work in Type I string theory compactified on K3xT2 and realise gauge instantons in terms of D5-branes wrapping the…

We study the low energy effective action of the $\Omega$-deformed $\mathcal N =2^{*}$ $SU(2) $ gauge theory. It depends on the deformation parameters $\epsilon_{1},\epsilon_{2}$, the scalar field expectation value $a$, and the…

The orbifold generalization of the partition function, which would describe the gauge theory on the ALE space, is investigated from the combinatorial perspective. It is shown that the root of unity limit of the q-deformed partition function…

We study the interaction between two structures on the group of polynomial automorphisms of the affine plane: its structure as an amalgamated free product and as an infinite-dimensional algebraic variety. We introduce a new conjecture, and…