Related papers: Secondary products in supersymmetric field theory
We establish a direct connection between two fundamental topics: one in probability theory and one in quantum field theory. The first topic is the problem of pointwise multiplication of random Schwartz distributions which has been the…
The symmetrized product for quantum mechanical observables is defined. It is seen as consisting of the ordinary multiplication and the application of the superoperator that orders the operators of coordinate and momentum. This superoperator…
We analyze geometry of the second order differential operators, having in mind applications to Batalin--Vilkovisky formalism in quantum field theory. As we show, an exhaustive picture can be obtained by considering pencils of differential…
We describe the topological $A$ and $B$ twists of 3d $\mathcal{N}=4$ theories of hypermultiplets gauged by $\mathcal{N}=4$ vector multiplets as certain deformations of the holomorphic-topological ($HT$) twist of those theories, utilizing…
We consider the geometry of second order linear operators acting on the commutative algebra of densities on a (super)manifold introduced in our previous work. In the conventional language, operators on the algebra of densities correspond to…
In many quantum field theories (such as higher-dimensional holomorphic field theories or raviolo theories), operator product expansions of local operators can have as coefficients not only ordinary functions but also 'derived' functions…
In our previous works, we introduced, for each (super)manifold, a commutative algebra of densities. It is endowed with a natural invariant scalar product. In this paper, we study geometry of differential operators of second order on this…
The string theory on symmetric product describes the second-quantized string theory. The development for the bosonic open string was discussed in the previous work. In this paper, we consider the open superstring theory on the symmetric…
We consider a recursive scheme for defining the coefficients in the operator product expansion (OPE) of an arbitrary number of composite operators in the context of perturbative, Euclidean quantum field theory in four dimensions. Our…
In this paper we discuss the relationship between noninvertible topological operators, one-form symmetries, and decomposition of two-dimensional quantum field theories, focusing on two-dimensional orbifolds with and without discrete…
Local superlinear convergence of the semismooth Newton method usually necessitates assumptions on the uniform invertibility of the utilized, generalized Jacobian matrices, such as, e.g., BD- or CD-regularity. For certain composite-type…
We present an approach to cohomological dimension theory based on infinite symmetric products and on the general theory of dimension called the extension dimension. The notion of the extension dimension $\ExD(X)$ was introduced by…
We construct a class of extended operators in the cohomology of a pair of twisted Schur supercharges of 4d N=2 SCFTs. The extended operators are constructed from the local operators in this cohomology -- the Schur operators -- by a version…
We incorporate gauge-invariant local composite operators into the twistor-space formulation of $\mathcal{N}=4$ Super Yang-Mills theory. In this formulation, the interactions of the elementary fields are reorganized into infinitely many…
It has been common wisdom among mathematicians that Extended Topological Field Theory in dimensions higher than two is naturally formulated in terms of n-categories with n> 1. Recently the physical meaning of these higher categorical…
Quantization of coordinates leads to the non-commutative product of deformation quantization, but is also at the roots of string theory, for which space-time coordinates become the dynamical fields of a two-dimensional conformal quantum…
We construct a mathematical framework for twisted N=2 supersymmetric topological quantum field theory on a 4-manifold. Supersymmetry in flat space is defined and the twist homomorphism is constructed, giving us a supermanifold that is the…
In this paper we study various convolution-type algebras associated with a locally compact quantum group from cohomological and geometrical points of view. The quantum group duality endows the space of trace class operators over a locally…
In 4D renormalisable theories, integrating out massive states generates in the low energy effective action higher dimensional operators (derivative or otherwise). Using a superfield language it is shown that a 4D N=1 supersymmetric theory…
We study the noncommutative superspace of arbitrary dimensions in a systematic way. Superfield theories on a noncommutative superspace can be formulated in two folds, through the star product formalism and in terms of the supermatrices. We…