Cubic forms, anomaly cancellation and modularity

Anomaly Cancellation and Modularity

It has been shown that the Alvarez-Gaum$\mathrm{\acute{e}}$-Witten miraculous anomaly cancellation formula in type IIB superstring theory and its various generalizations can be derived from modularity of certain characteristic forms. In this paper, we show that the Green-Schwarz formula and the Schwarz-Witten formula in type I superstring theory can also be derived from the modularity of those characteristic forms and thus unify the Alvarez-Gaum$\mathrm{\acute{e}}$-Witten formula, the Green-Schwarz formula as well as the Schwarz-Witten formula in the same framework. Various generalizations of …

Anomaly Cancellation and Modularity. II: $E_8\times E_8$ case

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 Hořava-Witten anomaly factorization formula for the gauge group $E_8$ can be derived through modular forms of weight 14. This answers a question of J. H. Schwarz. We also establish generalizations of these factorization formulas and obtain a new Hořava-Witten type factorization formula.

反常消除与模性：E8*E8*E8 情形

Anomaly cancellation and modularity: E8*E8*E8 case

本文将反常消除公式从 E8 和 E8*E8 推广到 E8*E8*E8 规范群，通过构造 SL2(Z) 上的模形式，得到了新的特征形式反常消除公式。

Transgression and twisted anomaly cancellation formulas on odd dimensional manifolds

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 also get some twisted anomaly cancellation formulas on some odd dimensional manifolds.

关于模形式与广义反常消去公式2的注记

A note on modular forms and generalized anomaly cancellation formulas 2

本文推广了(a,b)型消去公式至偶数维黎曼流形，并通过超渡得到奇数维流形上具有模性的特征形式。

Consistency of M-Theory on nonorientable manifolds

We prove that there is no parity anomaly in M-theory in the low-energy field theory approximation. Our approach is computational. We determine generators for the 12-dimensional bordism group of pin manifolds with a w_1-twisted integer lift of w_4; these are the manifolds on which Wick-rotated M-theory exists. The anomaly cancellation comes down to computing a specific eta-invariant and cubic form on these manifolds. Of interest beyond this specific problem are our expositions of: computational techniques for eta-invariants, the algebraic theory of cubic forms, Adams spectral sequence technique…