Related papers: Twisted chiral de Rham complex, generalized geomet…
Twistor forms are a natural generalization of conformal vector fields on Riemannian manifolds. They are defined as sections in the kernel of a conformally invariant first order differential operator. We study twistor forms on compact…
Twisted complex $K$-theory can be defined for a space $X$ equipped with a bundle of complex projective spaces, or, equivalently, with a bundle of C$^*$-algebras. Up to equivalence, the twisting corresponds to an element of $H^3(X;\Z)$. We…
We consider the global aspects of the 6-dimensional $\mathcal{N}=(1, 0)$ theory arising from the coupling of the vector multiplet to the tensor multiplet. We show that the Yang-Mills field and its dual, when both are abelianized, combine to…
We study the classification of D-branes and Ramond-Ramond fields in Type I string theory by developing a geometric description of KO-homology. We define an analytic version of KO-homology using KK-theory of real C*-algebras, and construct…
Adopting the fully quantal triaxial particle rotor model, the candidate chiral doublet bands in odd-$A$ nuclei $^{103}$Rh and $^{105}$Rh with $\pi g_{9/2}^{-1}\otimes\nu h^{2}_{11/2}$ configuration are studied. For the doublet bands in both…
We continue our investigation of a variation of the group ring isomorphism problem for twisted group algebras. Contrary to previous work, we include cohomology classes which do not contain any cocycle of finite order. This allows us to…
We reconsider some older constructions of T-duality, based on automorphisms of the worldsheet operator algebra, in a modern context. It has been long known that at special points in the moduli space of torus compactifications, the target…
We study the superpotential of a certain class of N=1 supersymmetric type II compactifications with fluxes and D-branes. We show that it has an important two-dimensional meaning in terms of a chiral ring of the topologically twisted theory…
We review Lie polynomials as a mathematical framework that underpins the structure of the so-called double copy relationship between gauge and gravity theories (and a network of other theories besides). We explain how Lie polynomials…
We consider the closed string propagating in the weakly curved background which consists of constant metric and Kalb-Ramond field with infinitesimally small coordinate dependent part. We propose the procedure for constructing the T-dual…
We construct the Atiyah-Hirzebruch spectral sequence (AHSS) for twisted differential generalized cohomology theories. This generalizes to the twisted setting the authors' corresponding earlier construction for differential cohomology…
We study $F$-gauges for de Rham cohomology of smooth algebraic varieties in characteristic $p$. Applying to good reductions of Shimura varieties of Hodge type, we recover the Ekedahl-Oort stratifications by constructing universal de Rham…
We investigate T-duality of toroidally compactified Matrix model with arbitrary Ramond-Ramond backgrounds in the framework of noncommutative super Yang-Mills gauge theory.
The spin foam formalism provides transition amplitudes for loop quantum gravity. Important aspects of the dynamics are understood, but many open questions are pressing on. In this paper we address some of them using a twistorial…
Given an equivariant oriented cohomology theory $h$, a split reductive group $G$, a maximal torus $T$ in $G$, and a parabolic subgroup $P$ containing $T$, we explain how the $T$-equivariant oriented cohomology ring $h_T(G/P)$ can be…
Let $K$ be a field of characteristic zero complete with respect to a non-trivial, non-Archimedean valuation. We relate the sheaf $\widehat{\mathcal{D}}$ of infinite order differential operators on smooth rigid $K$-analytic spaces to the…
The topological Hochschild homology of a ring (or ring spectrum) $R$ is an $S^1$-spectrum, and the fixed points of THH($R$) for subgroups $C_n\subset S^1$ have been widely studied due to their use in algebraic K-theory computations.…
The central result here is an explicit computation of the Hochschild and cyclic homologies of a natural smooth subalgebra of stable continuous trace algebras having smooth manifolds X as their spectrum. More precisely, the Hochschild…
We consider a central extension of the sheaf of Lie algebras of maps from a manifold into a finite-dimensional simple Lie algebra, together with the sheaf of vector fields. Using vertex algebra methods we construct sheaves of modules for…
This paper provides a rigorous account on the geometry of forms on supermanifolds, with a focus on its algebraic-geometric aspects. First, we introduce the de Rham complex of differential forms and we compute its cohomology. We then discuss…