Related papers: Elliptic Genera and N=2 Superconformal Field Theor…

First, I construct an isomorphism between the categories of (topological) groups of nilpotency class 2 with 2-divisible center and (topological) Lie rings of nilpotency class 2 with 2-divisible center. That isomorphism allows us to…

We study the elliptic genera of level $N$ at the cusps of $\Gamma_1(N)$ for any complete intersection. These genera are described as the summations of generalized binomial coefficients, where each generalized binomial coefficient is related…

We consider superstring compactifications where both the classical description, in terms of a Calabi-Yau manifold, and also the quantum theory is known in terms of a Landau-Ginzburg orbifold model. In particular, we study (smooth)…

We continue our study of the N=1* supersymmetric gauge theory and its relation to elliptic integrable systems. Upon compactification on a circle, we show that the semi-classical analysis of the massless and massive vacua depends on the…

This paper surveys the authors recent work on two variable elliptic genus of singular varieties. The last section calculates a generating function for the elliptic genera of symmetric products. This generalizes the classical results of…

We analyze properties of field theories dual to extremal black branes in (4+1) dimensions with anisotropic near-horizon geometries. Such gravity solutions were recently shown to fall into nine classes which align with the Bianchi…

The $\mathcal{N}=2$ Landau--Ginzburg description provides a strongly interacting Lagrangian realization of an $\mathcal{N}=2$ superconformal field theory. It is conjectured that one such example is given by the two-dimensional…

The $N=2$ minimal superconformal model can be twisted yielding an example of topological conformal field theory. In this article we investigate a Lie theoretic extension of this process.

We study a topological Landau-Ginzburg model with superpotential W(X)=X^{-1}. This is argued to be equivalent to c=1 string theory compactified at the self-dual radius. We compute the tree-level correlation function of N tachyons in this…

We construct a new invariant of two-dimensional $\mathcal{N}{=}(0,1)$ supersymmetric quantum field theories (SQFTs), under a couple of assumptions on the general properties of such SQFTs motivated by considerations in heterotic string…

We establish theorems on the existence and compactness of solutions to the $\sigma_2$-Nirenberg problem on the standard sphere $\mathbb S^2$. A first significant ingredient, a Liouville type theorem for the associated fully nonlinear…

We introduce the universal complex elliptic genus phi_ell as the ring homomorphism from the complex cobordism ring Omega^U to the polynomial ring C[A,B,C,D] associated to the characteristic power series Q(x)=x/f(x), where f is the solution…

We investigate Landau-Ginzburg string theory with the singular superpotential X^{-1} on arbitrary Riemann surfaces. This theory, which is a topological version of the c=1 string at the self-dual radius, is solved using results from…

We explain the relationship between the sigma orientation and Witten genus on the one hand and the two-variable elliptic genus on the other. We show that if E is an elliptic spectrum, then the Theorem of the Cube implies the existence of…

A compact oriented 4-manifold is defined to be of ``superconformal simple type'' if certain polynomials in the basic classes (constructed using the Seiberg-Witten invariants) vanish identically. We show that all known 4-manifolds of…

Let F be the cubic field of discriminant -23 and O its ring of integers. Let Gamma be the arithmetic group GL_2 (O), and for any ideal n subset O let Gamma_0 (n) be the congruence subgroup of level n. In a previous paper, two of us (PG and…

We consider Seiberg electric-magnetic dualities for 4d $\mathcal{N}=1$ SYM theories with SO(N) gauge group. For all such known theories we construct superconformal indices (SCIs) in terms of elliptic hypergeometric integrals. Equalities of…

Given a Riemann surface and a riemannian manifold M with certain restrictions, we construct a cobordism invariant of M. This invariant is a generalization of the elliptic genus and it shares some similar properties.

We discuss $SL(2,Z)$ subgroups appropriate for the study of $N=2$ Super Yang-Mills with $N_f=2n$ flavors. Hyperelliptic curves describing such theories should have coefficients that are modular forms of these subgroups. In particular,…

We define and compute the dressed elliptic genus of N = 2 heterotic compactifications with torsion that are principal two-torus bundles over a K3 surface. We consider the most general gauge bundle compatible with supersymmetry, a stable…