Related papers: Embedded graph invariants in Chern-Simons theory
We review quantum field theory approach to the knot theory. Using holomorphic gauge we obtain the Kontsevich integral. It is explained how to calculate Vassiliev invariants and coefficients in Kontsevich integral in a combinatorial way…
We propose methods to construct gauge invariant decompositions of the nucleon spin, particularly gauge invariant descriptions of the gluon polarization. We show that gauge invariant decompositions of the nucleon spin can be derived…
This is a research announcement on an alternative definition of the Casson invariants by means of virtual counting of the moduli space of irreducible representations of the fundamental group into $\SU(2)$. Along the way, by using derived…
We construct a Chern-Simons gauge theory for dg Lie and L-infinity algebras on any one-dimensional manifold and quantize this theory using the Batalin-Vilkovisky formalism and Costello's renormalization techniques. Koszul duality and…
Taking as starting point a perturbative study of the classical equations of motion of the non-Abelian Chern-Simons Theory with non-dynamical sources, we search for analytical expressions for link invarians. In order to present these…
In this brief presentation, we would like to present our attempts of detecting chirality and mutations from Chern-Simons gauge theory. The results show that the generalised knot invariants, obtained from Chern-Simons gauge theory, are more…
We examine the nonperturbative structure of the radiatively induced Chern-Simons term in a Lorentz- and CPT-violating modification of QED. Although the coefficient of the induced Chern-Simons term is in general undetermined, the…
We construct and study a new topological field theory in three dimensions. It is a hybrid between Chern-Simons and Rozansky-Witten theory and can be regarded as a topologically-twisted version of the N=4 d=3 supersymmetric gauge theory…
In this paper we put forward a systematic and unifying approach to construct gauge invariant composite fields out of connections. It relies on the existence in the theory of a group valued field with a prescribed gauge transformation. As an…
We define an invariant of welded virtual knots from each finite crossed module by considering crossed module invariants of ribbon knotted surfaces which are naturally associated with them. We elucidate that the invariants obtained are non…
% A new, formal, non-combinatorial approach to invariants of % three-dimensional manifolds of Reshetikhin, Turaev and % Witten in the framework of non-perturbative topological % quantum Chern-Simons theory, corresponding to an arbitrary %…
Witten introduced classical Chern-Simons theory to topology in 1989, when he defined an invariant for knots in 3-manifolds by an integral over a certain infinite-dimensional space, which up to today have not been entirely understood.…
We apply the intertwiner operator method of arXiv:2411.08865 to topological field theories, including BF theories, Chern-Simons theory, and three-dimensional gravity. We construct the operator on foliated manifolds while preserving…
Cyclically ordered graphs, or cogs, sit between abstract graphs and cellularly embedded graphs. They arise naturally in topological graph theory, knot theory, and mathematical biology. We develop a formal theory of cogs and establish a…
In the late 1980s Witten used the Chern-Simons form of a connection to construct new invariants of 3-manifolds and knots, recovering in particular the Jones invariants. Since then the associated topological quantum field theory (TQFT) has…
Tensor networks prepare states that share many features of states in quantum gravity. However, standard constructions are not diffeomorphism invariant and do not support an algebra of non-commuting area operators. Recently, analogues of…
Various applications of Chern-Simons theory in algebraic topology, in particular knot theory, condensed matter physics and cosmology are reviewed. Special attention is paid to appearances of Chern-Simons actions in the theory of the…
We study field theories defined in regions of the spatial non-commutative (NC) plane with a boundary present delimiting them, concentrating in particular on the U(1) NC Chern-Simons theory on the upper half plane. We find that classical…
Topological gauge theories provide powerful effective descriptions of certain strongly correlated systems, a prime example being the Chern-Simons gauge theory of fractional quantum Hall states. Engineering topological gauge theories in…
Gauss diagram formulas are extensively used to study Vassiliev link invariants. Now we apply this approach to invariants of 3-manifolds, considering manifolds given by surgery on framed links in the 3-sphere. We study the lowest degree case…