Related papers: Loop groups and string topology
The article covers developments in the representation theory of finite group schemes over the last fifteen years. We start with the finite generation of cohomology of a finite group scheme and proceed to discuss various consequences and…
Notes of the lectures delivered in Les Houches during the Summer School on Complex Systems (July 2006).
These lectures give an introduction to thermal perturbation theory, hard thermal loops, and their use in a nonperturbative, approximately self-consistent resummation of the thermodynamical potentials of quantum chromodynamics.
In which is developed a new form of superselection sectors of topological origin. By that it is meant a new investigation that includes several extensions of the traditional framework of Doplicher, Haag and Roberts in local quantum…
This paper is a self contained review of the Loop Variable approach to string theory. The Exact Renormalization Group is applied to a world sheet theory describing string propagation in a general background involving both massless and…
These are notes from an informal mini-course on factorization homology, infinity-categories, and topological field theories. The target audience was imagined to be graduate students who are not homotopy theorists.
We survey some important results concerning the finite--dimensional representations of the loop algebra of a simple complex Lie algebra, and their twisted loop subalgebras. In particular, we review the parametrization and description of the…
We study the complex irreducible representations of special linear, symplectic, orthogonal and unitary groups over principal ideal local rings of length two. We construct a canonical correspondence between the irreducible representations of…
We study the structure of abelian extensions of the group $L_qG$ of $q$-differentiable loops (in the Sobolev sense), generalizing from the case of central extension of the smooth loop group. This is motivated by the aim of understanding the…
I review several old/new approaches to the string/gauge correspondence for the cusped/lightcone Wilson loops. The main attention is payed to SYM perturbation theory calculations at two loops and beyond and to the cusped loop equation. These…
This paper surveys, and in some cases generalises, many of the recent results on homomorphisms and the higher Ext groups for q-Schur algebras and for the Hecke algebra of type A. We review various results giving isomorphisms between Ext…
The topology of center vortices is studied. For this purpose it is sufficient to consider mathematically idealised vortices, defined in a gauge invariant way as closed (infinitely thin) flux surfaces (in D=4 dimensions) which contribute the…
We investigate one-loop four-point scattering of non-abelian gauge bosons in heterotic string theory and identify new connections with the corresponding open-string amplitude. In the low-energy expansion of the heterotic-string amplitude,…
Building upon the Jones-Wassermann program of studying Conformal Field Theory using operator algebraic tools, and the work of A. Wassermann on the loop group of LSU(n) (Invent. Math. 133 (1998), 467-538), we give a solution to the problem…
This article consists of six lectures on the categorification of the Burau representation and on link homology groups which categorify the Jones and the HOMFLY-PT polynomial. The notes are based on the lecture course at the PCMI 2006 summer…
These are lecture notes for a 4h mini-course held in Toulouse, May 9-12th, at the thematic school on "Quantum topology and geometry". The goal of these lectures is to (a) explain some incarnations, in the last ten years, of the idea of…
Group field theories are particular quantum field theories defined on D copies of a group which reproduce spin foam amplitudes on a space-time of dimension D. In these lecture notes, we present the general construction of group field…
These lecture notes review the structure of anomalies and present some of their applications in field theory, string theory and M theory. They expand on material presented at the TASI 2003 summer school and the 2005 International Spring…
This is an edited write-up of lecture notes of the 7-th Appalachian set theory workshop of the same title led by the first named author at the Cornell University on November 22, 2008. A draft version of the notes was prepared by the second…
This survey is based on a series of five lectures, given May 3--7, 2010, at the Centre de Recerca Matematica, Barcelona. The goal of the lectures was to present aspects of the theory of foliation dynamical systems which have particular…