Related papers: On the Whitham hierarchy: dressing scheme, string …

We study N=2 super Yang-Mills theory with gauge group SU(N) from the point of view of the Whitham hierarchy. We develop a new recursive method to compute the whole instanton expansion of the prepotential using the theta function associated…

In this paper, we consider a generalization of the Stirling number sequence of both kinds by using a specialization of a new family of symmetric functions. We give combinatorial interpretations for this symmetric functions by means of…

The study of the generalized Hamming weight of linear codes is a significant research topic in coding theory as it conveys the structural information of the codes and determines their performance in various applications. However,…

A Nikishin-Maurey characterization is given for bounded subsets of weak-type Lebesgue spaces. New factorizations for linear and multilinear operators are shown to follow.

Factorization of string amplitudes is one way of constructing string interaction vertices. We show that correlation functions in string theory can be conveniently factorized using loop variables representing delta functionals. We illustrate…

In a quantum many-body system that possesses an additive conserved quantity, the entanglement entropy of a subsystem can be resolved into a sum of contributions from different sectors of the subsystem's reduced density matrix, each sector…

We present a generalization of first-order unification to a term algebra where variable indexing is part of the object language. We exploit variable indexing by associating some sequences of variables ($X_0,\ X_1,\ X_2,\dots$) with a…

It is becoming increasingly clear that the supercharacter theory of the finite group of unipotent upper-triangular matrices has a rich combinatorial structure built on set-partitions that is analogous to the partition combinatorics of the…

A brief review of the status of duality symmetries in string theory is presented. The evidence is accumulating rapidly that an enormous group of duality symmetries, including perturbative T dualities and non-perturbative S-dualities,…

In this paper we shall describe some correlation function computations in perturbative heterotic strings that, for example, in certain circumstances can lend themselves to a heterotic generalization of quantum cohomology calculations.…

We present a framework to systematically investigate higher categorical symmetries in two-dimensional spin systems. Though exotic, such generalised symmetries have been shown to naturally arise as dual symmetries upon gauging invertible…

These lectures present some topics of string phenomenology and contain two parts. In the first part, I review the possibility of lowering the string scale in the TeV region, that provides a theoretical framework for solving the mass…

The theory of distributions provides generalized solutions for problems which do not have a classical solution. However, there are problems which do not have solutions, not even in the space of distributions. As model problem you may think…

In this paper we develop a dressing method for constructing and solving some classes of matrix quasi-linear Partial Differential Equations (PDEs) in arbitrary dimensions. This method is based on a homogeneous integral equation with a…

The characterization of systems of differential equations admitting a superposition function allowing us to write the general solution in terms of any fundamental set of particular solutions is discussed. These systems are shown to be…

A classical result of Littlewood gives a factorisation for the Schur function at a set of variables "twisted" by a primitive $t$-th root of unity, characterised by the core and quotient of the indexing partition. While somewhat neglected,…

In this work, we prove the new factorization pattern for tree-level Yang-Mills (YM) amplitudes proposed in a companion paper. This pattern reveals a decomposition of amplitudes into a sum of gluings of lower-point amplitudes under specific…

For a family of Poisson algebras, parametrized by by an integer number r, and an associated Lie algebraic splitting, we consider the factorization of given canonical transformations. In this context we rederive the recently found r-th…

What do applications like semantic optimization, data exchange and integration, answering queries under dependencies, query reformulation with constraints, and data cleaning have in common? All these applications can be processed by the…

Models with large extra dimensions offer the possibility of the Planck scale being of order the electroweak scale, thus alleviating the gauge hierarchy problem. We show that these models suffer from a breakdown of unitarity at around three…