Related papers: Generalised Mathieu Moonshine
Let $G$ be a countable monoid and let $A$ be an Artinian group (resp. an Artinian module). Let $\Sigma \subset A^G$ be a closed subshift which is also a subgroup (resp. a submodule) of $A^G$. Suppose that $\Gamma$ is a finitely generated…
We give uniform, explicit, and simple face-pairing descriptions of all the branched cyclic covers of the 3-sphere, branched over two-bridge knots. Our method is to use the bi-twisted face-pairing constructions of Cannon, Floyd, and Parry;…
We construct, as hypersurfaces in toric varieties, Calabi-Yau manifolds corresponding to F-theory vacua dual to E8*E8 heterotic strings compactified to six dimensions on K3 surfaces with non-semisimple gauge backgrounds. These vacua were…
We describe a relationship between the representation theory of the Thompson sporadic group and a weakly holomorphic modular form of weight one-half that appears in work of Borcherds and Zagier on Borcherds products and traces of singular…
The Remodeling Conjecture proposed by Bouchard-Klemm-Marino-Pasquetti [arXiv:0709.1453, arXiv:0807.0597] relates all genus open and closed Gromov-Witten invariants of a semi-projective toric Calabi-Yau 3-manifolds/3-orbifolds to the…
Starting with a $\mathbb{C}^*$-valued cocycle on the global quotient orbifold $X // G$, we apply transgression techniques for 2-gerbes, as developed by Lupercio and Uribe, to construct a gerbe on the orbifold loop space $\mathcal{L}(X//G)$.…
We study the fate of discrete gauge groups and discrete charges of gravitational theories under twisted circle compactification. We then apply our results to six-dimensional F-theory vacua with discrete gauge symmetries and relate them to…
We study type one generalized complex and generalized Calabi--Yau manifolds. We introduce a cohomology class that obstructs the existence of a globally defined, closed 2-form which agrees with the symplectic form on the leaves of the…
Recently a conjecture has been proposed which attaches (mock) modular forms to the largest Mathieu group. This may be compared to monstrous moonshine, in which modular functions are attached to elements of the Monster group. One of the most…
We consider the 33 conjugacy classes of genus zero, torsion-free modular subgroups, computing ramification data and Grothendieck's dessins d'enfants. In the particular case of the index 36 subgroups, the corresponding Calabi-Yau threefolds…
For a given complex n-fold M we present an explicit construction of all complex (n+1)-folds which are principal holomorphic T2-fibrations over M. For physical applications we consider the case of M being a Calabi-Yau 2-fold. We show that…
We introduce the notion of generalized orbifold Euler characteristic associated to an arbitrary group, and study its properties. We then calculate generating functions of higher order (p-primary) orbifold Euler characteristic of symmetric…
We revisit the flavored elliptic genus of the N=2 superconformal cigar model and generalize the analysis of the path integral result to the case of real central charge. It gives rise to a non-holomorphic modular covariant function…
Most of the enveloppes of Planetary Nebulae (and other objects like novae) are far from beeing homogeneous: clumps, knots and tails are often observed. We present here the first attempt to build a 3D-photoionization model of a knot and the…
In this paper we relate umbral moonshine to the Niemeier lattices: the 23 even unimodular positive-definite lattices of rank 24 with non-trivial root systems. To each Niemeier lattice we attach a finite group by considering a naturally…
In the first part of this paper, we obtain mirror formulas for twisted genus 0 two-point Gromov-Witten (GW) invariants of projective spaces and for the genus 0 two-point GW-invariants of Fano and Calabi-Yau complete intersections. This…
This is a short version of hep-th/0406137. We show that the supersymmetry transformations for type II string theories on six-manifolds can be written as differential conditions on a pair of pure spinors, the exponentiated Kahler form e^{iJ}…
By the example of sp^3-bonded semiconductors, we illustrate what 3rd-generation muffin-tin orbitals (MTOs) are. We demonstrate that they can be downfolded to smaller and smaller basis sets: sp^3d^10,sp^3, and bond orbitals. For isolated…
We consider four-dimensional supersymmetric compactifications of the E8 x E8 heterotic string on Calabi-Yau manifolds endowed with vector bundles with structure group SU(N) x U(1) and five-branes. After evaluating the Green-Schwarz…
We construct all complete metrics of cohomogeneity one G(2) holonomy with S^3 x S^3 principal orbits from gauged supergravity. Our approach rests on a generalization of the twisting procedure used in this framework. It corresponds to a…