Related papers: String Homology and Lie Algebra Structures (Ph.D. …

New loop equations for all genera in $c = \frac{1}{2}$ non-critical string theory are constructed. Our loop equations include two types of loops, loops with all Ising spins up (+ loops) and those with all spins down ( $-$ loops). The loop…

In this article, we first briefly introduce the history of the Weil-\'etale cohomology theory of arithmetic schemes and review some important results established by Lichtenbaum, Flach and Morin. Next we generalize the Weil-etale cohomology…

We study the application of IBL-infinity-algebras to string topology and explicitly compute the case of spheres. This involves finding a Green kernel and computing integrals associated to trivalent ribbon graphs, which are similar to…

For any simplicial complex $X$ with a total ordering of its vertices, one can construct a chain complex $\mathbb{L}_\bullet(X)$ generated by necklaces of simplices in $X$, which computes the homology of the free loop space of the geometric…

After recalling the construction of a graded Lie bracket on the space of cyclic multilinear forms on a vector space V, due to Georges Pinczon and Rosane Ushirobira, we prove this construction gives a structure of quadratic associative…

For every $n \ge 3$, we construct 2-component links in $S^{n+1}$ that are a split by an integer homology $n$-sphere, but not by $S^n$. In the special case $n=3$, i.e. that of 2-links in $S^4$, we produce an infinite family of links $L_\ell$…

We construct and study an algebraic analogue of the loop coproduct in string topology, also known as the Goresky-Hingston coproduct. Our algebraic setup, which under this analogy takes the place of the complex of chains on the free loop…

Homogeneous gravitational wave backgrounds arise as infinite momentum limits of many geometries with a well-understood holographic description. General global aspects of these geometries are discussed. Using exact CFT techniques, strings in…

The cell-attachment problem, perhaps first studied by J.H.C. Whitehead around 1940, asks one to describe the effect of attaching one or more cells, on the algebraic invariants of a topological space. This thesis studies the effect of cell…

For a spectrum $X$ represented by a special $\Gamma$-space $Y$ via the Segal machine, we give an elementary formula computing the homology groups of $X$ in terms of $Y$. Both the result and the method of proof are essentially due to T.…

We demonstrate that string consistency in four spacetime dimensions leads to a spectrum of string states which satisfies the supertrace constraints Str(M^0)=0 and Str(M^2)=\Lambda at tree level, where \Lambda is the one-loop string…

The homology of the free and the based loop space of a compact globally symmetric space can be studied through explicit cycles. We use cycles constructed by Bott and Samelson and by Ziller to study the string topology coproduct and the…

We construct $\mathbb{Z}_N$ orbifolds of the ten-dimensional heterotic string theories appropriate for implementing the stringy replica method for the calculation of quantum entanglement entropy. A novel feature for the heterotic string is…

This paper studies in great detail a family of supersymmetric Wilson loop operators in N=4 supersymmetric Yang-Mills theory we have recently found. For a generic curve on an S^3 in space-time the loops preserve two supercharges but we will…

We construct a model for the string group as an infinite-dimensional Lie group. In a second step we extend this model by a contractible Lie group to a Lie 2-group model. To this end we need to establish some facts on the homotopy theory of…

Using results on topological line defects of 4D Chern-Simons theory and the algebra/cycle homology correspondence in complex surfaces $\mathcal{S}$ with ADE singularities, we study the graded properties of the $sl(m|n)$ chain and its…

Hess and Shipley defined an invariant of coalgebra spectra called topological coHochschild homology, and Bohmann-Gerhardt-H{\o}genhaven-Shipley-Ziegenhagen developed a coB\"okstedt spectral sequence to compute the homology of coTHH for…

The purpose of this article is to embed the string topology bracket developed by Chas-Sullivan and Menichi on negative cyclic cohomology groups as well as the dual bracket found by de Thanhoffer de Voelcsey-Van den Bergh on negative cyclic…

Chas and Sullivan showed that the homology of the free loop space LM of an oriented closed smooth finite dimensional manifold M admits the structure of a Batalin-Vilkovisky (BV) algebra equipped with an associative product called the loop…

The loop variable approach is a proposal for a gauge invariant generalization of the sigma-model renormalization group method of obtaining equations of motion in string theory. The basic guiding principle is space-time gauge invariance…