Related papers: $\Gamma^{0}(2)$ modular forms and anomaly cancella…
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.
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
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…
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…
By some SL(2, Z) modular forms introduced in [11] and [4] , we get some interesting anomaly cancellation formulas. As corollaries, we get some divisibility results of index of twisted Dirac operators.
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…
We give a direct proof of a cancellation formula raised in [7] on the level of differential forms. We also obtain more cancellation formulas for even dimensional Riemannian manifolds with a complex line bundle involved. Relations among…
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…
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…
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…
In this paper, by combining modular forms and characteristic forms, we obtain general anomaly cancellation formulas of any dimension. For $4k+2$ dimensional manifolds, our results include the gravitational anomaly cancellation formulas of…
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 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…
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$^c$…
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…
We state conjectures that relate Hermitian modular forms of degree two and algebraic modular forms for the compact group $SO(6)$. We provide evidence for these conjectures in the form of dimension formulas and explicit computations of…
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 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 give explicit structure of the graded ring of modular forms with respect to Gamma(N) (N=1,2,3,4,5,6,7,8,9,10,12,16,18) and for some other congruence groups. We also study the modular forms of half-integer weight for certain groups.