New anomaly formulas from E8 bundles.
problem Anomaly cancellation in characteristic forms.
method Constructing modular forms using E8 bundles.
result New anomaly cancellation formulas.
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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
New anomaly formulas derived from bundles.
problem Anomaly cancellation in characteristic forms.
method Constructing modular forms over specific groups using bundles.
result Derived new anomaly cancellation formulas.
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.
SL(2,Z) forms lead to new anomaly formulas.
problem Anomaly cancellation in physics.
method SL(2,Z) modular forms.
result New anomaly cancellation formulas derived.
Mathematical formulas for elliptic curve integrals solve anomaly equations.
problem Mathematical formulation of contact term singularities on elliptic curves.
method Residue formulas and holomorphic anomaly equations.
result Regularized integrals on elliptic curves satisfy holomorphic anomaly equations.
New modular forms for anomaly cancellation formulas on any dimensional manifolds.
problem Constructing new modular forms for anomaly cancellation formulas.
method Using bundles, constructing modular forms on any dimensional manifolds.
result Derived new anomaly cancellation formulas and applications.
Study modular forms over Γ^0(2) and anomaly cancellation formulas.
problem Anomaly cancellation formulas for modular forms over Γ^0(2).
method Study and analysis of modular forms over Γ^0(2).
result Anomaly cancellation formulas derived for modular forms over Γ^0(2).
New formulas derived for anomaly cancellation on odd-dimensional manifolds.
problem Anomaly cancellation on dimensional manifolds.
method Study of modular invariance properties of characteristic forms.
result Derive new anomaly cancellation formulas and congruent formulas on characteristic numbers.
New anomaly cancellation formulas for E8*E8*E8 gauge group.
problem Anomaly cancellation for E8*E8*E8 gauge group.
method Constructed modular forms over SL2(Z) to get new anomaly cancellation formulas.
result New anomaly cancellation formulas for characteristic forms.
In this paper, by combining modular forms and characteristic forms, we obtain general anomaly cancellation formulas of any dimension. For 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. …
New formulas derived for anomaly cancellation using modular forms and E8 bundles.
problem Anomaly cancellation in odd dimensions.
method Systematic twisting and generalization of SL(2,Z) modular forms to define new forms associated with E8 and E8*E8 bundles.
result Derivation of a new series of anomaly cancellation formulas.
In this paper we show that both of the Green-Schwarz anomaly factorization formula for the gauge group and the Hořava-Witten anomaly factorization formula for the gauge group can be derived through modular forms of weight 14. This answers a question of J. H. Schwarz. We also establish generalizati…
We present an explicit expression of the anomaly formula for the Cappell-Miller holomorphic torsion for Kähler manifolds.
Abstract: Generalizes modular forms to family case and finds new anomaly cancellation formulas.
problem Finding anomaly cancellation formulas for determinant line bundles and index gerbes.
method Family index theory applied to modular forms.
result Obtains new anomaly cancellation formulas for determinant line bundles and index gerbes.
The paper extends elliptic genus and proves anomaly cancellation formulas for almost complex manifolds.
problem Anomaly cancellation formulas for almost complex manifolds.
method Extended elliptic genus, proved weak Jacobi forms, derived SL_2(Z) modular forms.
result New anomaly cancellation formulas of characteristic forms for almost complex manifolds.
Note on new cancellation formulas for manifolds.
problem Generalizing anomaly cancellation formulas to manifolds.
method Proving new (a, b) type cancellation formulas and using transgression.
result Obtained characteristic forms with modularity properties.
The paper defines new modular forms from almost complex manifolds and derives anomaly cancellation formulas.
problem Anomaly cancellation in almost complex manifolds.
method Defined a generalized elliptic genus and derived SL(2,Z) modular forms.
result Derived anomaly cancellation formulas and divisibility results for holomorphic Euler characteristic.
Surveying the signature theorem, researchers cancel anomalies on elliptic surfaces.
problem Anomaly cancellation in elliptic surface physics.
method Application of the Riemann-Roch-Grothendieck-Quillen formula to elliptic curves.
result Local and global anomalies can be canceled on Jacobian elliptic surfaces.
In this paper, we generalize the anomaly cancellation formulas in \cite{AW, Liu1, HZ2} to the cases that an auxiliary bundle as well as a complex line bundle are involved with no conditions on the first Pontryagin forms being assumed.
It has been shown that the Alvarez-Gaum-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 i…
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 manifolds. Especially, we get twisted Rokhlin congruences for dimensional spi…
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 manifol…
New formulas derived from modular forms for manifold indices.
problem Calculating indices of twisted Dirac operators on manifolds.
method SL(2, Z) modular forms and Γ^0(2), Γ_0(2) forms.
result New anomaly cancellation formulas for spin and spin^c manifolds.
Anomaly formula derived for CR manifolds with S^1 action.
problem Analyzing the Quillen metric on CR manifolds with S^1 action.
method Introduced Quillen metric on Fourier components of Kohn-Rossi cohomology.
result Anomaly formula for Quillen metric on CR manifolds.
We extend the complex-valued analytic torsion, introduced by Burghelea and Haller on closed manifolds, to compact Riemannian bordisms. We do so by considering a flat complex vector bundle over a compact Riemannian manifold, endowed with a fiberwise nondegenerate symmetric bilinear form. The Riemmanian metric and the bi…
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.
Mathematical derivation of chiral anomaly in curved spacetime.
problem Chiral anomaly in curved spacetime.
method Application of index theorem for Lorentzian Dirac operator.
result Derivation of total charge generated by gravitational and gauge fields.
Paper proves anomaly formula and functoriality for equivariant eta forms.
problem Anomaly formula and functoriality of equivariant eta forms for compact Lie group actions.
method Extended spectral section properties, introduced higher spectral flow, constructed new analytic model of equivariant differential K-theory.
result Well-definedness of push-forward map for equivariant differential K-theory on compact orbifolds.
Analytic torsion defined for rank 2 distributions on 5-manifolds.
problem Defining and analyzing analytic torsion for rank 2 distributions.
method Proposed an analytic torsion for Rumin complex associated with rank 2 distributions on 5-manifolds, established anomaly formulas, and showed coincidence with Ray-Singer torsion.
result The proposed torsion coincides with Ray-Singer torsion for certain nilmanifolds.
We argue that the AdS/CFT calculational prescription for double-trace deformations leads to a holographic derivation of the conformal anomaly, and its conformal primitive, associated to the whole family of conformally covariant powers of the Laplacian (GJMS operators) at the conformal boundary. The bulk side involves a…
We derive a formula for the global gravitational anomaly of the self-dual field theory on an arbitrary compact oriented Riemannian manifold. Along the way, we uncover interesting links between the theory of determinant line bundles of Dirac operators, Siegel theta functions and a functor constructed by Hopkins and Sing…
Renormalized Volumehep-th
Develops a new calculus for volumes of singular metrics.
problem Calculating anomalies and divergences for volumes of singular metrics.
method Distributional calculus and boundary calculus for conformally compact manifolds.
result Explicit formulae for divergences and anomaly of regulated volumes.
New cubic forms linked to η-invariants and mod 2 indices.
problem Anomaly cancellation and modularity in 12-manifolds.
method Combination of Witten classes and affine character.
result Relates cubic forms to η-invariants and mod 2 indices.
Advances geometric approach to invariant forms on G-equivariant bundles.
problem Understanding invariant geometric structures on G-equivariant bundles.
method Differential geometric approach to convert equivariant to nonequivariant forms.
result Determinant line moment map derived from G-equivariant Dirac operator.
The holographic description in the presence of gravitational Chern-Simons term is studied. The modified gravitational equations are integrated by using the Fefferman-Graham expansion and the holographic stress-energy tensor is identified. The stress-energy tensor has both conformal anomaly and gravitational or, if re-f…
Anomaly cancellation condition for M5-brane action is proven using twisted Cohomotopy.
problem Anomaly in the 6d Wess-Zumino term of M5-brane action.
method Twisted Cohomotopy theory and a twisted/parametrized Hopf invariant.
result Anomaly cancellation condition is implied by charge quantization in twisted Cohomotopy.
New elliptic genera defined for spin manifolds.
problem Defining new elliptic genera for spin manifolds.
method Defined new two-variable elliptic genera using Jacobi forms and modular forms.
result Anomaly cancellation formulas derived from modular forms.
We study eta-invariants on odd dimensional manifolds with boundary. The dependence on boundary conditions is best summarized by viewing the (exponentiated) eta-invariant as an element of the (inverse) determinant line of the boundary. We prove a gluing law and a variation formula for this invariant. This yields a new, …
In the spirit of Ray and Singer we define a complex valued analytic torsion using non-selfadjoint Laplacians. We establish an anomaly formula which permits to turn this into a topological invariant. Conjecturally this analytically defined invariant computes the complex valued Reidemeister torsion, including its phase. …
We study the geometry of determinant line bundles associated to Dirac operators on compact odd dimensional manifolds. Physically, these arise as (local) vacuum line bundles in quantum gauge theory. We give a simplified derivation of the commutator anomaly formula using a construction based on noncyclic trace extensions…
A recent anomaly computation of Horava and Witten is proved and generalized in the form of two index theorems in odd dimensions. Theorem A is a fixed point formula for orientation-reversing involutions. Theorem B is an index theorem for manifolds with boundary using local boundary conditions. Both hold for families of …
For a strictly pseudoconvex domain in a complex manifold we define a renormalized volume with respect to the approximately Einstein complete Kähler metric of Fefferman. We compute the conformal anomaly in complex dimension two and apply the result to derive a renormalized Chern--Gauss--Bonnet formula. Relations between…
Analytic torsion defined for surfaces with cusps, linking to non-cusped surfaces.
problem Defining and analyzing analytic torsion for surfaces with cusps.
method Defining analytic torsion for surfaces with cusps and proving anomaly formula.
result Analytic torsion for surfaces with cusps related to non-cusped surfaces.
The coefficient of the logarithmic term in the entropy on even spheres is re-computed by the local technique of integrating the finite temperature energy density up to the horizon on static d--dimensional de Sitter space and thence finding the entropy by thermodynamics. Numeric evaluation yields the known answer i.e. (…
Study quantum aspects of 1-form symmetries using BV-BRST cohomology.
problem Quantum aspects of gauging continuous 1-form global symmetries.
method BV-BRST quantization of a U(1) 2-form gauge field, Lie 2-algebroid construction, Čech-de Rham bicomplex.
result Anomaly descent for U(1) 1-form symmetries is naturally set up in the Čech-de Rham bicomplex.
Study quantum aspects of 1-form symmetries using BV-BRST cohomology and gerbes.
problem Quantum aspects of gauging continuous 1-form global symmetries.
method BV-BRST quantization of a U(1) 2-form gauge field, Lie 2-algebroid construction, Čech-de Rham bicomplex.
result Anomaly descent for U(1) 1-form symmetries is naturally set up in the Čech-de Rham bicomplex.
The zeta and eta-functions associated with massless and massive Dirac operators, in a D-dimensional (D odd or even) manifold without boundary, are rigorously constructed. Several mathematical subtleties involved in this process are stressed, as the intrisic ambiguity present in the definition of the associated fermion …