Related papers: A Smooth Model for the String Group
Recently the strings and the string number of self-maps were used in the computation of the algebraic entropy of special group endomorphisms. We introduce two special kinds of strings, and their relative string numbers. We show that a…
We propose a string theory model which explains several features of two dimensional YM theory. Folds are suppressed. This in turn leads to the empty theory in flat target spaces. The Nambu-Goto action appears in the usual way. The model…
In this note we expose some surprising connections between string theory and statistical inference. We consider a large collective of agents sweeping out a family of nearby statistical models for an M-dimensional manifold of statistical…
It is known that a single mapping defined on one term of a differential graded vector space extends to a strongly homotopy Lie algebra structure on the graded space when that mapping satisfies two conditions. This strongly homotopy Lie…
We prove the decomposition theorem for the loop homotopy algebra of quantum closed string field theory and use it to show that closed string field theory is unique up to gauge transformations on a given string background and given S-matrix.…
We study the group of homotopy classes of self maps of compact Lie groups which induce the trivial homomorphism on homotopy groups. We completely determine the groups for SU(3) and Sp(2). We investigate these groups for simple Lie groups in…
Employing the nonabelian duality transformation, I derive the Gauge String form of certain D>=3 lattice Yang-Mills (YM_{D}) theories in the strong coupling (SC) phase. With the judicious choice of the actions, in D>=3 our construction…
This paper explores the properties of multiplicative Lie algebra structures on a nilpotent group of class $2$. We also present a method for determining a multiplicative Lie algebra structure on a group that serves as an extension of one Lie…
Motivated by the problem of constructing explicit geometric string structures, we give a rigid model for bundle 2-gerbes, and define connective structures thereon. This model is designed to make explicit calculations easier in applications…
We propose a string theory realization of three-dimensional $\mathcal{N}=4$ quiver gauge theories with special unitary gauge groups. This is most easily understood in type IIA string theory with D4-branes wrapped on holomorphic curves in…
As we said in our previous work [4], the main idea of our research is to introduce a class of Lie groupoids by means of co-adjoint representation of a Lie groupoid on its isotropy Lie algebroid, which we called coadjoint Lie groupoids. In…
The aim of this paper is to explain how to get a complex of smooth representations out of the dual vector space to a smooth representation of a p-adic Lie group, in natural characteristic. The construction does not depend on any…
The role of integrable systems in string theory is discussed. We remind old examples of the correspondence between stringy partition functions or effective actions and integrable equations, based on effective application of the matrix model…
N=2 heterotic strings may provide a window into the physics of M-theory radically different than that found via the other supersymmetric string theories. In addition to their supersymmetric structure, these strings carry a four-dimensional…
In this article we investigate a monoid of smooth mappings on the space of arrows of a Lie groupoid and its group of units. The group of units turns out to be an infinite-dimensional Lie group which is regular in the sense of Milnor.…
In this paper we study contact structure on 2-step nilpotent, Heisenberg type Lie groups. We decompose this Lie groups to center and orthogonal complement, then investigate properties of both orthogonal Lie subgroups. Finally, we provide a…
This is a preliminary version of a book on infinite-dimensional Lie groups. It covers the basics of calculus and manifolds in the context of locally convex spaces, based on Bastiani's notion of a smooth map. Starting from this concept, we…
Let $X$ be a simply connected closed oriented manifold of rationally elliptic homotopy type. We prove that the string topology bracket on the $S^1$-equivariant homology $\overline{H}_{\ast}^{S^1}(\mathcal{L}X,\mathbb{Q}) $ of the free loop…
We present a simple physical representation for states of the two-dimensional string theory. In order to incorporate a fundamental cutoff of the order 1/g we use a picture consisting of q-oscillators at the first-quantized level. In this…
In this paper we develop combinatorial techniques for the case of string algebras with the aim to give a characterization of string complexes with infinite minimal projective resolution. These complexes will be called \textit{periodic…