Related papers: SL(2,Z) modular forms and anomaly cancellation for…

By some SL(2, Z) modular forms introduced in [4] and [9], we construct some {\Gamma}^0(2) and {\Gamma}_0(2) modular forms and obtain some new cancellation formulas for spin manifolds and spin^c manifolds respectively. As corollaries, we get…

By some SL(2, Z) modular forms introduced in [4] and [10], we construct some modular forms over SL2(Z) and some modular forms over {\Gamma}^0(2) and {\Gamma}_0(2) in odd dimensions. In parallel, we obtain some new cancellation formulas for…

In \cite{HLZ2} and \cite{HHLZ}, using $E_8$ bundles, some modular forms over $SL(2,{\bf Z})$ were constructed on $12$-dimensional manifolds and the Witten-Freed-Hopkins anomaly cancellation formula was derived by these $SL(2,Z)$ modular…

In [5], [6] and [8], the authors gave some modular forms over $\Gamma^0(2)$. In this note, we proceed with the study of cancellation formulas relating to the modular forms.

By studying modular invariance properties of some characteristic forms, we get some new anomaly cancellation formulas on $(4r-1)$ dimensional manifolds. As an application, we derive some results on divisibilities of the index of Toeplitz…

Using $E_8$ bundles, we construct some modular forms over $SL(2,{\bf Z})$, $\Gamma^0(2)$ and $\Gamma_0(2)$. By these modular forms, we get some new anomaly cancellation formulas of characteristic forms.

This paper aims to derive new anomaly cancellation formulas by combining modular forms with E8 and E8*E8 bundles. To this end, we systematically twist and generalize known SL(2,Z) modular forms to define new modular forms associated with…

Using $E_8$ bundles, we construct some new modular forms over $SL(2,{\bf Z})$, $\Gamma^0(2)$ and $\Gamma_0(2)$ and get some new anomaly cancellation formulas of characteristic forms which generalize some anomaly cancellation formulas in…

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

By the family index theory, we generalize some well-known $SL(2,Z)$ modular forms to the family case and obtain some new anomaly cancellation formulas for the determinant line bundle and index gerbes, and certain results about eta…

In [7], Liu and Wang generalized the Han-Liu-Zhang cancellation formulas to the (a, b) type cancellation formulas. In this note, we prove some another (a, b) type cancellation formulas for even-dimensional Riemannian manifolds. And by…

We compute the transgressed forms of some modularly invariant characteristic forms,which are related to the twisted elliptic genera. We study the modularity properties of these secondary characteristic forms and relations among them. We…

In this paper, we define a generalized elliptic genus of an almost complex manifold with an extra complex bundle which generalize the elliptic genus in [10]. This generalized elliptic genus is a generalized Jacobi form. By this generalized…

By studying modular invariance properties of some characteristic forms, we obtain twisted anomaly cancellation formulas. We apply these twisted cancellation formulas to study divisibilities on spin manifolds and congruences on spin$^c$…

In [5] and [19], the authors gave anomaly cancellation formulas for the gauge groups E8,E8*E8. In this paper, we mainly deal with the case of gauge group E8*E8*E8. Using the E8*E8*E8 bundle, we construct some modular forms over SL2(Z). By…

For even dimensional manifolds, we prove some twisted anomaly cancellation formulas which generalize some well-known cancellation formulas. For odd dimensional manifolds, we obtain some modularly invariant characteristic forms by the…

Examples of SL(2, Z) actions on differential graded categories are defined and explored.

In this paper, we generalize the anomaly cancellation formulas in \cite{AW, Liu1, HZ2} to the cases that an auxiliary bundle $W$ as well as a complex line bundle $\xi$ are involved with no conditions on the first Pontryagin forms being…

We show that a general miraculous cancellation formula, the divisibility of certain characteristic numbers and some other topologiclal results are con- sequences of the modular invariance of elliptic operators on loop spaces. Previously we…

We study the instanton partition functions of two well-known superconformal field theories with mass deformations. Two types of anomaly equations, namely, the modular anomaly and holomorphic anomaly, have been discovered in the literature.…