Related papers: Invariants from classical field theory
We study the invariants of spin networks embedded in a three-dimensional manifold which are based on the path integral for SU(2) BF-Theory. These invariants appear naturally in Loop Quantum Gravity, and have been defined as spin-foam state…
A power-counting renormalizable model into which massive Yang-Mills theory is embedded is analyzed. The model is invariant under a nilpotent BRST differential s. The physical observables of the embedding theory, defined by the cohomology…
We define some new invariants for 3-manifolds using the space of taut codim-1 foliations along with various techniques from noncommutative geometry. These invariants originate from our attempt to generalise Topological Quantum Field…
We consider the $U(1)$ Chern-Simons gauge theory defined in a general closed oriented 3-manifold $M$; the functional integration is used to compute the normalized partition function and the expectation values of the link holonomies. The…
The Chern-Simons invariants of irreducible U(n)- flat connections on compact hyperbolic 3-manifolds of the form {\Gamma}\H^3 are derived. The explicit formula for the Chern-Simons functional is given in terms of Selberg type zeta functions…
We study field models for which a quantum action (i.e. the action appearing in the generating functional of Green functions) is invariant under supersymmetric transformations. We derive the Ward identity which is direct consequence of this…
It is well known that in a generally covariant gravitational theory the choice of spacetime scalars as coordinates yields phase-space observables (or "invariants"). However their relation to the symmetry group of diffeomorphism…
We give new functions of Legendrian knots derived from Legendrian fronts. These are integer-valued linear functions that are alike the Arnold basic invariant of plane curves. Various generalizations of the Arnold basic invariant have been…
We compute expectation values of Wilson loops in q-deformed 2d Yang-Mills on a Riemann surface and show that they give invariants of knots in 3-manifolds which are circle bundles over the Riemann surface. The areas of the loops play an…
In this paper we construct a multivariable link invariant arising from the quantum group associated to the special linear Lie superalgebra sl(2|1). The usual quantum group invariant of links associated to (generic) representations of…
The purpose of this survey paper is to bring to a large mathematical audience (containing also non-algebraists) some topics of invariant theory both in the classical commutative and the recent noncommutative case. We have included only…
This thesis is concerned with the application of operadic methods, particularly modular operads, to questions arising in the study of moduli spaces of surfaces as well as applications to the study of homotopy algebras and new constructions…
The superconformal invariants in analytic superspace are found. Superconformal invariance is shown to imply that the Green's functions of analytic operators are invariant holomorphic sections of a line bundle on a product of certain…
For the abelian Chern-Simons field theory, we consider the quantum functional integration over the Deligne-Beilinson cohomology classes and present an explicit path-integral non-perturbative computation of the Chern-Simons link invariants…
We consider $SU(N)$ Yang-Mills theories in $(2n+1)$-dimensional Euclidean spacetime, where $N\geq n+1$, coupled to an even flavour number of Dirac fermions. After integration over the fermionic degrees of freedom the wave functional for the…
The transformation properties of a Kalb-Ramond field are those of a gauge potential. However, it is not clear what is the group structure to which these transformations are associated. In this paper, we complete a program started in…
We study modular invariants arising in the four-point functions of the stress tensor multiplet operators of the ${\cal N} = 4$ $SU(N)$ super-Yang-Mills theory, in the limit where $N$ is taken to be large while the complexified Yang-Mills…
We derive formulas for the classical Chern-Simons invariant of irreducible $SU(n)$-flat connections on negatively curved locally symmetric three-manifolds. We determine the condition for which the theory remains consistent (with basic…
We study the regularization and renormalization of the Yang-Mills theory in the framework of the manifestly invariant formalism, which consists of a higher covariant derivative with an infinitely many Pauli-Villars fields. Unphysical…
We use topological quantum field theory to derive an invariant of a three-manifold with boundary. We then show how to use this invariant as an obstruction to embedding one three-manifold in another.