Related papers: SL(2,Z) Modular Forms and Anomaly Cancellation For…
The main result of this article is a Llarull-type rigidity statement for scalar curvature on Riemannian spin manifolds with cone-like singularities in odd dimensions. The even dimensional analog was proven in an earlier work together with…
We investigate using Clifford algebra methods the theory of algebraic dotted and undotted spinor fields over a Lorentzian spacetime and their realizations as matrix spinor fields, which are the usual dotted and undotted two component spinor…
We prove an index formula for the Dirac operator acting on two-valued spinors on a $3$-manifold $M$ which branch along a smoothly embedded graph $\Sigma \subset M$, and with respect to a boundary condition along $\Sigma$ inspired by an…
The SL(2,Z) duality transformations of type IIB supergravity are shown to be anomalous in generic F-theory backgrounds due to the anomalous transformation of the phase of the chiral fermion determinant. The anomaly is partially cancelled…
The modular transformation properties of admissible characters of the affine superalgebra sl(2|1;C) at fractional level k=1/u-1, u=2,3,... are presented. All modular invariants for u=2 and u=3 are calculated explicitly and an A-series and…
Suppose $M$ is a closed $n$-dimensional spin$^c$ manifold with spin$^c$ structure $\sigma$ and associated spin$^c$ line bundle $L$. If one fixes a Riemannian metric $g$ on $M$ and a connection $\nabla_L$ on $L$, the generalized scalar…
The finite symplectic group Sp(2g) over the field of two elements has a natural representation on the vector space of Siegel modular forms of given weight for the principal congruence subgroup of level two. In this paper we decompose this…
We give an index formula for a class of Dirac operators coupled with unbounded potentials. More precisely, we study operators of the form P := D+ V, where D is a Dirac operators and V is an unbounded potential at infinity on a possibly…
We study $T^2/Z_N$ orbifold models with magnetic fluxes. We propose a systematic way to analyze the number of zero-modes and their wavefunctions by use of modular transformation. Our results are consistent with the previous results, and our…
In this paper we show that both of the Green-Schwarz anomaly factorization formula for the gauge group $E_8\times E_8$ and the Ho\v{r}ava-Witten anomaly factorization formula for the gauge group $E_8$ can be derived through modular forms of…
For any congruence subgroup $\Gamma$, we study the vertex operator algebra $\Omega^{ch}(\mathbb H,\Gamma)$ constructed from the $\Gamma$-invariant global sections of the chiral de Rham complex on the upper half plane, which are holomorphic…
In this present communication we provide a new derivation of the Dirac dual structure by employing a different approach from the originally proposed. Following a general and rigorous mathematical process to compute the dual structure, we…
Let $\Gamma$ be the Fuchsian group of the first kind. For an even integer $m\ge 4$, we study $m/2$-holomorphic differentials in terms of space of (holomorphic) cuspidal modular forms $S_m(\Gamma)$. We also give in depth study of Wronskians…
We will give the graded ring of Siegel modular forms of degree two with respect to a non-split symplectic group explicitly.
We consider some infinitesmal and global deformations of G_2 structures on 7-manifolds. We discover a canonical way to deform a G_2 structure by a vector field in which the associated metric gets "twisted" in some way by the vector cross…
We determine the ring structure of Siegel modular forms of degree g modulo a prime p, extending Nagaoka's result in the case of degree g=2. We characterize U(p) congruences of Jacobi forms and Siegel modular forms, and surprisingly find…
To every $k$-dimensional modular invariant vector space we associate a modular form on $SL(2,\mathbb{Z})$ of weight $2k$. We explore number theoretic properties of this form and find a sufficient condition for its vanishing which yields…
On a complex symplectic manifold, we construct the stack of quantization-deformation modules, that is, (twisted) modules of microdifferential operators with an extra central parameter, a substitute to the lack of homogeneity. We also…
We study configurations consisting of a gravitating spinor field $\psi$ with a nonlinearity of the type $\lambda\left(\bar\psi\psi\right)^2$. To ensure spherical symmetry of the configurations, we use two spin-$\frac{1}{2}$ fields forming a…
We show that it is possible to remove two differential operators from the standard collection of $m$ of them used to embed the space of Jacobi forms of \textit{odd} weight $k$ and index $m$ into several pieces of elliptic modular forms.…