Related papers: SL(2,Z) modular forms and Witten genus in odd dime…

The incorporation of Wilson lines leads to an extension of the modular symmetries of string compactification beyond $\mathrm{SL}(2,\mathbb Z)$. In the simplest case with one Wilson line $Z$, K\"ahler modulus $T$ and complex structure…

We present a unified framework demonstrating how the spinor complex Lorentz group SL(2,C)/Z\_2 is realized as a canonical subgroup within a four-dimensional complex Riemannian manifold. Building on the complex, holomorphic metric extension…

We demonstrate how to find modular discrete symmetry groups for $Z_N$ orbifolds. The $Z_7$ orbifold is treated in detail as a non-trivial example of a $(2,2)$ orbifold model. We give the generators of the modular group for this case which,…

We study the geometric structure of Lorentzian spin manifolds, which admit imaginary Killing spinors. The discussion is based on the cone construction and a normal form classification of skew-adjoint operators in signature $(2,n-2)$.…

A geometric construction of Z_2-graded orthogonal modular categories is given. Their 0-graded parts coincide with categories previously obtained by Blanchet and the author from the category of tangles modulo the Kauffman skein relations.…

We define and discuss an extension of the SpinC quantization concept to odd-dimensional manifolds. After that we describe its relation to (the usual) even-dimensional SpinC quantization and how its famous properties like "Quantization…

This is the third part of a series of articles providing a foundation for the theory of Drinfeld modular forms of arbitrary rank. In the present article we construct and study some examples of Drinfeld modular forms. In particular we define…

By studying modular invariance properties of some characteristic forms, we prove some new anomaly cancellation formulas which generalize the Han-Zhang and Han-Liu-Zhang anomaly cancellation formulas

Target space duality symmetries, which acts on K\"ahler and continuous Wilson line moduli, of a ${\bf Z}_N$ ($N\not=2$) 2-dimensional subspace of the moduli space of orbifold compactification are modified to include twisted moduli. These…

The theory of Topological Modular Forms suggests the existence of deformation invariants for two-dimensional supersymmetric field theories that are more refined than the standard elliptic genus. In this note we give a physical definition of…

We prove several dimension formulas for spaces of scalar-valued Siegel modular forms of degree $2$ with respect to certain congruence subgroups of level $4$. In case of cusp forms, all modular forms considered originate from cuspidal…

Some one- and two-parametric deformations of U[sl(2)] and their representations are considered. Interestingly, a newly introduced two-parametric deformation admits a class of infinite - dimensional representations which have no classical…

In this paper, we study Siegel modular forms with extra twists. We provide conditions on the level and genus of the forms that is necessary for the existence of extra twists for Siegel modular forms. We also give explicit examples of Siegel…

We study vector-valued Siegel modular forms of genus 2 and level 2. We describe the structure of certain modules of vector-valued modular forms over rings of scalar-valued modular forms.

We describe here a degeneration of the symplectic desingularization of the moduli spaces of topologically trivial $GL(2,\mathbb{C})$ and $SL(2,\mathbb{C})$-Higgs bundles over a hyperelliptic curve, into O'Grady's ten and six dimensional…

We construct a ring of meromorphic Siegel modular forms of degree 2 and level 5, with singularities supported on an arrangement of Humbert surfaces, which is generated by four singular theta lifts of weights 1, 1, 2, 2 and their Jacobian.…

In this paper, we extend the elliptic genus in [10] by the gauge group E_8 and the gauge group E_8*E_8. Then we prove that the generalized elliptic genus are the weak Jacobi forms. Using these elliptic genus, we obtain some SL_2(Z) modular…

We construct a class of negative spin irreducible representations of the su(2) Lie algebra. These representations are infinite-dimensional and have an indefinite inner product. We analyze the decomposition of arbitrary products of positive…

We extend our previous work arXiv:1012.5721 [hep-th] on the non-compact N=2 SCFT_2 defined as the supersymmetric SL(2,R)/U(1)-gauged WZW model. Starting from path-integral calculations of torus partition functions of both the axial-type…

The values of the Witten invariants, $I_W$, of the lens space $L(p, 1)$ for SU(2) at level $k$ are obtained for arbitrary $p$. A duality relation for $I_W$ when $p$ and $k$ are interchanged, valid for asymptotic $k$, is observed. A method…