Related papers: Mathieu twining characters for K3

A CHL model is the quotient of $\mathrm{K3} \times E$ by an order $N$ automorphism which acts symplectically on the K3 surface and acts by shifting by an $N$-torsion point on the elliptic curve $E$. We conjecture that the primitive…

We show how special forms of an $N=2$ Landau-Ginzburg potential directly imply the presence of an $N=2$ super-$W$ algebra. If the Landau-Ginzburg model has a super-$W$ algebra, we show how the elliptic genus can be refined so as to give…

We investigate a Gepner-like superstring model described by a combination of multiple minimal models and an N=2 Liouville theory. This model is thought to be equivalent to the superstring theory on a singular noncompact Calabi-Yau manifold.…

We extend the investigation of special toroidal compactifications of heterotic string theory for which the half-BPS states provide representations of subgroups of the Conway group. We also explore dual descriptions of these theories and…

The duality between $E_8\times E_8$ heteritic string on manifold $K3\times T^2$ and Type IIA string compactified on a Calabi-Yau manifold induces a correspondence between vector bundles on $K3\times T^2$ and Calabi-Yau manifolds. Vector…

Given a $K3$ surface, a supersymmetric non-linear K3 sigma model is the internal superconformal field theory (SCFT) in a six dimensional compactification of type IIA superstring on $\mathbb{R}^{1,5} \times K3$. These models have attracted…

We propose a moonshine for the sporadic Mathieu group M_12 that relates its conjugacy classes to various modular forms and Borcherds Kac-Moody Lie superalgebras.

Umbral moonshine connects the symmetry groups of the 23 Niemeier lattices with 23 sets of distinguished mock modular forms. The 23 cases of umbral moonshine have a uniform relation to symmetries of $K3$ string theories. Moreover, a…

In characteristic $0$, symplectic automorphisms of K3 surfaces (i.e.\ automorphisms preserving the global $2$-form) and non-symplectic ones behave differently. In this paper we consider the actions of the group schemes $\mu_{n}$ on K3…

The conformal field theoretic elliptic genus, an invariant for N=(2,2) superconformal field theories, counts the BPS states in any such theory with signs, according to their bosonic or fermionic nature. For K3 theories, this invariant is…

We consider type II superstring theory on $K3 \times S^1 \times \mathbb{R}^{1,4}$ and study perturbative BPS states in the near-horizon background of two Neveu-Schwarz fivebranes whose world-volume wraps the $K3 \times S^1$ factor. These…

We study the symplectic action of the group (Z/2Z)^2 on a K3 surface X: we describe its action on H^2(X,Z) and the maps induced in cohomology by the rational quotient maps; we give a lattice-theoretic characterization of the resolution of…

We compute the Kauffman skein module of the complement of torus knots in S^3. Precisely, we show that these modules are isomorphic to the algebra of Sl(2,C)-characters tensored with the ring of Laurent polynomials.

We introduce a sequence of families of lattice polarized $K3$ surfaces. This sequence is closely related to complex reflection groups of exceptional type. Namely, we obtain modular forms coming from the inverse correspondences of the period…

A definition is offered of the factorial characters of the general linear group, the symplectic group and the orthogonal group in an odd dimensional space. It is shown that these characters satisfy certain flagged Jacobi-Trudi identities.…

We consider the natural action of a finite group on the moduli space of polarized K3 surfaces which induces a duality defined by Mukai for surfaces of this type. We show that the group permutes polarized Fourier-Mukai partners of polarized…

Nikulin has classified all finite abelian groups acting symplectically on a K3 surface and he has shown that the induced action on the K3 lattice $U^3\oplus E_8(-1)^2$ depends only on the group but not on the K3 surface. For all the groups…

Let $f:X\to C$ be a family of semistable K3 surfaces with non-empty set $S$ of singular fibres having infinite local monodromy. Then, when the so called Arakelov-Yau inequality reaches equality, we prove that $C\setminus S$ is a modular…

In this paper we study compactifications of the ${\cal N}=2$ heterotic $E_8\times E_8$ string on $(K3\times T^2)/\mathbb{Z}_3$ with various gauge backgrounds and calculate the topological couplings in the effective supergravity action that…

Elliptic modular graph functions and forms (eMGFs) are defined for arbitrary graphs as natural generalizations of modular graph functions and forms obtained by including the character of an Abelian group in their Kronecker--Eisenstein…