Related papers: Multivalued Fields on the Complex Plane and Braid …
The braiding of the worldlines of particles restricted to move on a network (graph) is governed by the graph braid group, which can be strikingly different from the standard braid group known from two-dimensional physics. It has been…
The Liouville field theory on Z_N-Riemann surfaces is studied and it is shown that it decomposes into a Liouville field theory on the sphere and N-1 free boson theories. Also, the partition function of the Liouville field theory on the…
In this paper, we study the class of free multiarrangements of hyperplanes. Specifically, we investigate the relations between freeness over a field of finite characteristic and freeness over the rationals.
We show that various holomorphic quantities in supersymmetric gauge theories can be conveniently computed by configurations of D4-branes and D6-branes. These D-branes intersect along a Riemann surface that is described by a holomorphic…
The R-matrix formalism for the construction of integrable systems with infinitely many degrees of freedom is reviewed. Its application to Poisson, noncommutative and loop algebras as well as central extension procedure are presented. The…
In this work, the following conjectures are proven in the case of a Riemann surface with abelian group of symmetry: a) The $b-c$ systems on a Riemann surface $M$ are equivalent to a multivalued field theory on the complex plane if $M$ is…
Non-relativistic anyons in 1D possess generalized exchange statistics in which the exchange of two identical anyons generates a non-local phase that is governed by the spatial ordering of the particles and the statistical parameter…
The method of deforming free fields by using multiplication operators on Fock space, introduced by G. Lechner in [11], is generalized to a charged free field on two- and three-dimensional Minkowski space. In this case the deformation…
We obtain a simple family of solutions to the set-theoretic Yang-Baxter equation, one which depends only on considering special endomorphisms of a finite group. We show how such an endomorphism gives rise to two non-degenerate solutions to…
A general procedure to reveal an Abelian structure of Yang-Mills theories by means of a (nonlocal) change of variables, rather than by gauge fixing, in the space of connections is proposed. The Abelian gauge group is isomorphic to the…
Known and new results on free Boolean topological groups are collected. An account of properties which these groups share with free or free Abelian topological groups and properties specific of free Boolean groups is given. Special emphasis…
Non-relativistic charged particles and strings coupled with abelian gauge fields are quantized in a geometric representation that generalizes the Loop Representation. We consider three models: the string in self-interaction through a…
Braid groups are an important and flexible tool used in several areas of science, such as Knot Theory (Alexander's theorem), Mathematical Physics (Yang-Baxter's equation) and Algebraic Geometry (monodromy invariants). In this note we will…
We present a complex matrix gauge model defined on an arbitrary two-dimensional orientable lattice. We rewrite the model's partition function in terms of a sum over representations of the group U(N). The model solves the general…
We show that non-abelian quantum statistics can be studied using certain topological invariants which are the homology groups of configuration spaces. In particular, we formulate a general framework for describing quantum statistics of…
We study a system of nonabelian anyons in the lowest Landau level of a strong magnetic field. Using diagrammatic techniques, we prove that the virial coefficients do not depend on the statistics parameter. This is true for all…
Anyons exhibit a non-trivial interplay between local exclusion rules and non-local braiding and exchange phases, making a consistent commutation algebra and second-quantized formulation challenging. We develop an algebraic framework for…
Identifying experimental signatures of anyons, which exhibit fractional exchange statistics, remains a central challenge in the study of two-dimensional topologically ordered systems. Previous theoretical work has shown that the threshold…
Seiberg-Witten maps and a recently proposed construction of noncommutative Yang-Mills theories (with matter fields) for arbitrary gauge groups are reformulated so that their existence to all orders is manifest. The ambiguities of the…
Using the construction of D-branes with nonzero $B$ field in the matrix model we give a physical interpretation of the known background independence in gauge theories on a noncommutative space. The background independent variables are…