Fei Han, Xiaoling Huang
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 these cancellation formulas are discussed.
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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 Chern-Simons transgression and we also get some twisted anomaly cancellation formulas.
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$^c$ manifolds. Especially, we get twisted Rokhlin congruences for $8k+4$ dimensional spin$^c$ 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.
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
E8 bundles and some new anomaly cancellation formulas
本文通过E8丛构造新的模形式，并推广了特征形式的异常抵消公式。
SL(2,Z) modular forms and anomaly cancellation formulas
本研究利用已有文献中的SL(2,Z)模形式推导出反常抵消公式，并进一步得到扭曲Dirac算子指标的可除性推论，丰富了模形式与微分几何交叉领域的结果。
Anomaly cancellation formulas and E8 bundles
该研究利用E8丛构造特殊群上的模形式，进而得到新的特征形式反常抵消公式，为微分几何领域相关研究提供了新的公式结果。
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。
Several new $SL(2,Z)$ modular forms and anomaly cancellation formulas
本文构造了任意维流形上的SL(2,Z)模形式，并给出了新的异常抵消公式及其应用。
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 Alvarez-Gaumé and Witten in dimensions 2, 6 and 10 (\cite{AW}) as special cases. In dimension $4k+1$, we derive anomaly cancellation formulas for index gerbes. In dimension $4k+3$, we obtain certain results about eta invariants, which are interesting in spectral geometry.
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。
$Γ^{0}(2)$ modular forms and anomaly cancellation formulas
本文基于文献中$Γ^0(2)$上的模形式，继续研究与之相关的消去公式。
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 $ξ$ are involved with no conditions on the first Pontryagin forms being assumed.
Anomaly cancellation formulas and E_8 bundles for almost complex manifolds
本文用E_8及E_8×E_8推广椭圆亏格，证明其为弱Jacobi形式，进而导出SL_2(Z)模形式，得到近复流形的新反常消去公式。
We consider the hypothesis that the C-field 4-flux and 7-flux forms in M-theory are in the image of the non-abelian Chern character map from the non-abelian generalized cohomology theory called J-twisted Cohomotopy theory. We prove for M2-brane backgrounds in M-theory on 8-manifolds that such charge quantization of the C-field in Cohomotopy theory implies a list of expected anomaly cancellation conditions, including: shifted C-field flux quantization and C-field tadpole cancellation, but also the DMW anomaly cancellation and the C-field's integral equation of motion.
Motivated by the cubic forms and anomaly cancellation formulas of Witten-Freed-Hopkins, we give some new cubic forms on spin, spin$^c$, spin$^{w_2}$ and orientable 12-manifolds respectively. We relate them to $η$-invariants when the manifolds are with boundary, and mod 2 indices on 10 dimensional characteristic submanifolds when the manifolds are spin$^c$ or spin$^{w_2}$. Our method of producing these cubic forms is a combination of (generalized) Witten classes and the character of the basic representation of affine $E_8$.
SL(2,Z) modular forms and anomaly cancellation formulas for almost complex manifolds
本文通过定义带额外复向量丛的近复流形的广义椭圆亏格，构造SL(2,Z)模形式，进而得到反常消除公式及全纯Euler示性数的整除性结果。
SL(2,Z) Modular Forms and Anomaly Cancellation Formulas II
本文利用已知SL(2,Z)模形式构造Γ^0(2)与Γ_0(2)模形式，建立spin及spin^c流形的新反常抵消公式，并推出扭曲Dirac算子指标的整除性结论。
We show that the heterotic supersymmetry (Killing spinor equations) and the anomaly cancellation imply the heterotic equations of motion in dimensions five, six, seven, eight if and only if the connection on the tangent bundle is an instanton. For heterotic compactifications in dimension six this reduces the choice of that connection to the unique SU(3) instanton on a manifold with stable tangent bundle of degree zero.
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 operators on $(4r-1)$ dimensional spin manifolds and some congruent formulas on characteristic number for $(4r-1)$ dimensional spin$^c$ manifolds.
We highlight what seems to be a remaining subtlety in the argument for the cancellation of the total anomaly associated with the M5-brane in M-theory. Then we prove that this subtlety is resolved under the hypothesis that the C-field flux is charge-quantized in the generalized cohomology theory called J-twisted Cohomotopy.
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.
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 …
We survey the Hirzebruch signature theorem as a special case of the Atiyah-Singer index theorem. The family version of the Atiyah-Singer index theorem in the form of the Riemann-Roch-Grothendieck-Quillen (RRGQ) formula is then applied to the complexified signature operators varying along the universal family of elliptic curves. The RRGQ formula allows us to determine a generalized cohomology class on the base of the elliptic fibration that is known in physics as (a measure of) the local and global anomaly. Combining several anomalous operators allows us to cancel the local anomaly on a Jacobia…
We characterize the integral cohomology and the rational homotopy type of the maximal Borel-equivariantization of the combined Hopf/twistor fibration, and find that subtle relations satisfied by the cohomology generators are just those that govern Horava-Witten's proposal for the extension of the Green-Schwarz mechanism from heterotic string theory to heterotic M-theory. We discuss how this squares with the Hypothesis H that the elusive mathematical foundation of M-theory is based on charge quantization in J-twisted Cohomotopy theory.
Holomorphic supergravity in ten dimensions and anomaly cancellation
本文提出一种十维全纯超引力理论，通过量子化二次涨落并消除奇异性，揭示其与$SU(5)$扭曲超引力及I型Kodaira-Spencer理论的关系。
Elliptic genera and E8 Bundles in odd dimensions
本文通过结合模形式与E8和E8*E8束，推导出新的异常抵消公式。
Elliptic genera and $SL(2,Z)$ modular forms for fibre bundles
本文通过族索引理论推广$SL(2,Z)$模形式，获得行列式线丛和索引丛的奇点抵消公式及eta不变量结果，并探讨高次残差陈形式的奇点抵消公式。
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