Related papers: Superconformal Algebras and Mock Theta Functions
We study the elliptic genera of two-dimensional orbifold CFTs, where the orbifolding procedure introduces du Val surface singularities on the target space. The N=4 character decompositions of the elliptic genus contributions from the…
Recently, Mertens, Ono, and the third author studied mock modular analogues of Eisenstein series. Their coefficients are given by small divisor functions, and have shadows given by classical Shimura theta functions. Here, we construct a…
We prove a closed formula for the integrals of the top Segre classes of tautological bundles over the Hilbert schemes of points of a K3 surface X. We derive relations among the Segre classes via equivariant localization of the virtual…
Extended superalgebras of types A,B,C, heterotic and type-I are all derived as solutions to a BPS equation in 14 dimensions with signature ( 11,3). The BPS equation as well as the solutions are covariant under SO( 11,3). This shows how…
We present BPS indices of the supergroup WZW models that live on intersecting M2-M5 brane systems. They can encode data of the stretched M2-branes between M5-branes and count the BPS states. They are generally expressed in terms of mock…
We review the relation between 4n-dimensional quaternion-Kahler metrics with n+1 abelian isometries and superconformal theories of n+1 tensor supermultiplets. As an application we construct the class of eight-dimensional quaternion-Kahler…
We determine multiplication and convolution topological algebras for classes of $\omega$-ultradifferentiable functions of Beurling type. Hypocontinuity and discontinuity of the multiplication and convolution mappings are also investigated.
We present a universal treatment for imposing superconformal constraints on Mellin amplitudes for $\mathrm{SCFT_d}$ with $3\leq d\leq 6$. This leads to a new technique to compute holographic correlators, which is similar but complementary…
We systematically classify all possible poles of superconformal blocks as a function of the scaling dimension of intermediate operators, for all superconformal algebras in dimensions three and higher. This is done by working out the…
We investigate representations of K\"ahler groups $\Gamma = \pi_1(X)$ to a semisimple non-compact Hermitian Lie group $G$ that are deformable to a representation admitting an (anti)-holomorphic equivariant map. Such representations obey a…
We study the ``flat'' directions of non-BPS extremal black hole attractors for N=2, d=4 supergravities whose vector multiplets' scalar manifold is endowed with homogeneous symmetric special Kahler geometry. The non-BPS attractors with…
We examine a sequence of examples of pairs of moduli spaces of sheaves on $\mathbb P^2$ where Le Potier's strange duality is expected to hold. One of the moduli spaces in these pairs is the Hilbert scheme of two points. We compute the…
Mock modular forms, which give the theoretical framework for Ramanujan's enigmatic mock theta functions, play many roles in mathematics. We study their role in the context of modular parameterizations of elliptic curves $E/\mathbb{Q}$. We…
We revisit certain one-parameter families of affine covers arising naturally from Euler's integral representation of hypergeometric functions. We introduce a partial compactification of this family. We show that the zeta function of the…
In this note, we employ indefinite theta functions to regularize canonical partition functions for single-center dyonic BPS black holes. These partition functions count dyonic degeneracies in the Hilbert space of four-dimensional toroidally…
We present the first example of the Selberg type zeta function for noncompact higher rank locally symmetric spaces. We study certain Selberg type zeta functions and Ruelle type zeta functions attached to the Hilbert modular group of a real…
We study certain special tilting and cotilting modules for an algebra with positive dominant dimension, each of which is generated or cogenerated (and usually both) by projective-injectives. These modules have various interesting…
We study the relationship between $n$-cluster tilting modules over $n$ representation finite algebras and the Euler forms. We show that the dimension vectors of cluster-indecomposable modules give the roots of the Euler form. Moreover, we…
This paper investigates first the four branches of BMS transformations, motivated by the classification into elliptic, parabolic, hyperbolic and loxodromic proposed a few years ago in the literature. We first prove that to each normal…
We study a family of Siegel modular forms that are constructed using Jacobi forms that arise in Umbral moonshine. All but one of them arise as the Weyl-Kac-Borcherds denominator formula of some Borcherds-Kac-Moody (BKM) Lie superalgebras.…