相关论文: Elliptic genera of ALE and ALF manifolds from gaug…

Recently Witten proposed to consider elliptic genus in $N=2$ superconformal field theory to understand the relation between $N=2$ minimal models and Landau-Ginzburg theories. In this paper we first discuss the basic properties satisfied by…

We use annular foam TQFTs introduced by the first two authors to define equivariant $SL(2)$ and $SL(3)$ web algebras in the annulus. To a diagram of a tangle in the thickened annulus we assign a complex of bimodules over these algebras…

In this note we calculate elliptic genus in various examples of twisted chiral de Rham complex on two dimensional toric compact manifolds and Calabi-Yau hypersurfaces in toric manifolds. At first the elliptic genus is calculated for the…

Let M be a manifold carrying the action of a Lie group G, and A a Lie algebroid on M equipped with a compatible infinitesimal G-action. Out of these data we construct an equivariant Lie algebroid cohomology and prove for compact G a related…

We consider multiply periodic functions, sometimes called Abelian functions, defined with respect to the period matrices associated with classes of algebraic curves. We realise them as generalisations of the Weierstras P-function using two…

The elliptic genera of two-dimensional N=2 superconformal field theories can be twisted by the action of the integral Heisenberg group if their U(1) charges are fractional. The basic properties of the resulting twisted elliptic genera and…

We show that the genus 34 Seiberg-Witten curve underlying $N=2$ Yang-Mills theory with gauge group $E_6$ yields physically equivalent results to the manifold obtained by fibration of the $E_6$ ALE singularity. This reconciles a puzzle…

In this paper, we show the equivalence between two seemingly distinct 2d TQFTs: one comes from the "Coulomb branch index" of the class S theory $T[\Sigma,G]$ on $L(k,1) \times S^1$, the other is the $^LG$ "equivariant Verlinde formula", or…

Let $E$ be an ordinary elliptic curve over a finite field and $g$ be a positive integer. Under some technical assumptions, we give an algorithm to span the isomorphism classes of principally polarized abelian varieties in the isogeny class…

In this work we study the phase structure of skew symplectic sigma models, which are a certain class of two-dimensional N = (2,2) non-Abelian gauged linear sigma models. At low energies some of them flow to non-linear sigma models with…

We present affine Lie algebras generated by the supercovariant derivatives and the supersymmetry generators for the left and right moving modes in the doubled space. Chirality is manifest in our doubled space as well as the T-duality…

The elliptic genus for arbitrary two dimensional $N=2$ Landau-Ginzburg orbifolds is computed. This is used to search for possible mirror pairs of such models. An important aspect of this work is that there is no restriction to theories for…

We will discuss the equivariant cohomology of a manifold endowed with the action of a Lie group. Localization formulae for equivariant integrals are explained by a vanishing theorem for equivariant cohomology with generalized coefficients.…

We construct a class of companion elliptic functions associated with the even Dirichlet characters. Using the well-known properties of the classical Weierstrass elliptic function $\wp(z|\tau)$ as the blueprint, we will derive their…

I show how elliptic genera for various Calabi-Yau threefolds may be understood from supergravity localization using the quantization of the phase space of certain multi-center configurations. I present a simple procedure that allows for the…

Let $p, q$ be twin prime numbers with $q-p=2$ . Consider the elliptic curves E=E_\sigma: y^2 = x (x+\sigma p)(x+\sigma q) . (\sigma =\pm 1). E=E_\sigma is also denoted as E_+ or E_- when \sigma = +1or $-1.Here the Mordell-Weil group and the…

We construct {\it Topological Elliptic Genera}, homotopy-theoretic refinements of the elliptic genera for $SU$-manifolds and variants including the Witten-Landweber-Ochanine genus. The codomains are genuinely $G$-equivariant Topological…

We construct the moduli spaces associated to the solutions of equations of motion (modulo gauge transformations) of the Poisson sigma model with target being an integrable Poisson manifold. The construction can be easily extended to a case…

We build representations of the elliptic braid group from the data of a quantum D-module M over a ribbon Hopf algebra U. The construction is modelled on, and generalizes, similar constructions by Lyubashenko and Majid, and also certain…

We compute equivariant fundamental classes of orbits in GL(2)-representations. As applications, we find degrees of the orbit closures corresponding to elliptic fibrations and self-maps of the projective line.