Related papers: Duality and cohomology in M-theory with boundary
We study the partition function associated with the democratic formulation of M-theory, focusing on its global definition and quantum properties. Using a path-integral representation that makes manifest the underlying cohomological…
This paper gives an introduction and overview about recent developments on the interaction of the theories of characteristic classes and mixed Hodge theory for singular spaces in the complex algebraic context. It uses M. Saito's deep theory…
In the quest for mathematical foundations of M-theory, the "Hypothesis H" that fluxes are quantized in Cohomotopy theory, implies, on flat but possibly singular spacetimes, that M-brane charges locally organize into equivariant homotopy…
The generalized Miller-Morita-Mumford classes of a manifold bundle with fiber $M$ depend only on the underlying $\tau_M$-fibration, meaning the family of vector bundles formed by the tangent bundles of the fibers. This motivates a closer…
We formulate differential cohomology and Chern-Weil theory -- the theory of connections on fiber bundles and of gauge fields -- abstractly in the context of a certain class of higher toposes that we call "cohesive". Cocycles in this…
We show that the vector bundle on the moduli stack $M_\mathrm{ell}$ of elliptic curves associated to the $2$-cell complex $C\nu$ is isomorphic to the de Rham cohomology sheaf $\mathrm{H}^1_\mathrm{dR}(\mathcal{E}/M_\mathrm{ell})$ of the…
Given an effective Cartier divisor D with simple normal crossing support on a smooth and proper scheme X over a perfect field of positive characteristic p, there is a natural notion of de Rham-Witt sheaves on X with zeros along D. We show…
Free Maxwell theory on general four-manifolds may, under certain conditions on the background geometry, exhibit holomorphic factorization in its partition function. We show that when this occurs, new discrete symmetries emerge at orbifold…
This chapter sets out preliminaries for the duality theory in later chapters. An underlying idea is that local cohomology functors are higher derived functors of colocalizations (a.k.a.~coreflections). Predominantly well-known facts about…
We introduce new boundary conditions for differential forms on symplectic manifolds with boundary. These boundary conditions, dependent on the symplectic structure, allows us to write down elliptic boundary value problems for both…
Let M be a closed enlargeable spin manifold. We show non-triviality of the universal index obstruction in the K-theory of the maximal $C^*$-algebra of the fundamental group of M. Our proof is independent from the injectivity of the…
Holomorphic principal G-bundles over a complex manifold M can be studied using non-abelian cohomology groups H^1(M,G). On the other hand, if M=\Sigma is a closed Riemann surface, there is a correspondence between holomorphic principal…
Theorem. Let M be a compact, connected, oriented smooth Riemannian n-manifold with non-empty boundary. Then the cohomology of the complex (Harm*(M),d) of harmonic forms on M is given by the direct sum H^p(Harm*(M),d) = H^p(M;R) +…
We describe a duality relation between configurations of M5-branes in M-theory and type IIB theory on Taub-NUT geometries with NSNS and RR 3-form field strength fluxes. The flux parameters are controlled by the angles between the M5-brane…
Neumann boundary condition plays an important role in the initial proposal of holographic dual of boundary conformal field theory, which has yield many interesting results and passed several non-trivial tests. In this paper, we show that…
In this paper we continue the study started in part I (posted). We consider a planar, bounded, $m$-connected region $\Omega$, and let $\bord\Omega$ be its boundary. Let $\mathcal{T}$ be a cellular decomposition of $\Omega\cup\bord\Omega$,…
The compactification from the 11-dimensional Horava-Witten orbifold to 5-dimensional heterotic M-theory on a Schoen Calabi-Yau threefold is reviewed, as is the specific $SU(4)$ vector bundle leading to the "heterotic standard model" in the…
It is shown that many of the conjectured dualities involving orbifold compactification of M-theory follow from the known dualities involving M-theory and string theory in ten dimensions, and the ansatz that orbifolding procedure commutes…
A new global approach in the study of duality transformations is introduced. The geometrical structure of complex line bundles is generalized to higher order U(1) bundles which are classified by quantized charges and duality maps are…
If M is a smooth compact oriented Riemannian manifold of dimension n=4k+2, with or without boundary, and F is a vector bundle on M with an inner product and a flat connection, we construct a modification of the Hodge star operator on the…