Related papers: Coleff-Herrera currents, duality, and Noetherian o…
We construct an infinite set of conserved tensor currents of rank $2n$, $n=1,2,\dots$, in the two-dimensional theory of free massive fermions, which are bilinear in the fermionic fields. The one-point functions of these currents on the…
We find the conserved current associated to invariance under generalised diffeomorphisms in double field theory. This can be used to define a generalised Komar integral. We comment on its applications to solutions, in particular to the…
A decade ago, a Lagrangian density has been proposed by the author where only the local symmetries of the Lorentz subgroup of (A)ds group is retained. This formalism has been found to produce some results encompassing that of standard…
We consider a (3+1)-dimensional local field theory defined on the sphere. The model possesses exact soliton solutions with non trivial Hopf topological charges, and infinite number of local conserved currents. We show that the Poisson…
In this paper, we introduce the theory of local cohomology and local duality to Notherian connected cochain DG algebras. We show that the notion of local cohomology functor can be used to detect the Gorensteinness of a homologically smooth…
Using methods from the conformal bootstrap, we study the properties of Noether currents in the critical $O(n)$ loop model. We confirm that they do not give rise to a Kac-Moody algebra (for $n\neq 2$), a result expected from the underlying…
Let U be a pseudoconvex open set in a complex manifold M. When is U a Stein manifold? There are classical counter examples due to Grauert, even when U has real-analytic boundary or has strictly pseudoconvex points. We give new criteria for…
A gauged bi-differential calculus over an associative (and not necessarily commutative) algebra A is an N-graded left A-module with two covariant derivatives acting on it which, as a consequence of certain (e.g., nonlinear differential)…
The maximal algebra of symmetries of the free single-particle Schroedinger equation is determined and its relevance for the holographic duality in non-relativistic Fermi systems is investigated. This algebra of symmetries is an infinite…
The purpose of this paper is twofold. The first purpose is to review a systematic construction of Noether currents for supersymmetric theories, especially effective supersymmetric theories. The second purpose is to use these currents to…
Following arXiv:1310.2027 and arXiv:0801.0762, we consider a non-supersymmetric Seiberg duality between electric and magnetic "orientifold field theories". These theories live on brane configurations of type 0' string theory. In the…
We review recent results for heterotic moduli and the Hull--Strominger system. In particular, we discuss mathematical properties of the recently derived deformation operator $\bar D$ associated to the deformation complex of heterotic…
Previously we have established that the second Hamiltonian structure of the KP hierarchy is a nonlinear deformation, called $\hat{W}_{\infty}$, of the linear, centerless $W_{\infty}$ algebra. In this letter we present a free-field…
In the dimer model, a configuration consists of a perfect matching of a fixed graph. If the underlying graph is planar and bipartite, such a configuration is associated to a height function. For appropriate "critical" (weighted) graphs,…
For a smooth quasi-projective surface S over complex numbers we consider the Borel-Moore homology of the stack of coherent sheaves on S with compact support and make this space into an associative algebra by a version of the Hall…
Given a free resolution of an ideal $J$ of holomorphic functions, one can construct a vector valued residue current $R$, whose annihilator is precisely $J$. In this paper we compute $R$ in case $J$ is a monomial ideal and the resolution is…
Let $E$and $F$ be Hermitian vector bundles over a complex manifold $X$ and let $g\colon E\to F$ be a holomorphic morphism. We prove a Poincar\'e-Lelong type formula with a residue term $M^g$. The currents $M^g$ so obtained have an expected…
We present new models of non-linear electromagnetism which satisfy the Noether-Gaillard-Zumino current conservation and are, therefore, self-dual. The new models differ from the Born-Infeld-type models in that they deform the Maxwell theory…
Let X be the toric scheme over a ring R associated with a fan Sigma. It is shown that there are a group B, a B-graded R-algebra S and a graded ideal I of S such that there is an essentially surjective, exact functor ~ from the category of…
Let R be a commutative Noetherian ring. We introduce the notion of colocalization functors with supports in arbitrary subsets of Spec R, which is a natural generalization of right derived functors of section functors with supports in…