When we discuss knot invariants in terms of Chern-Simons theory [1–6] and the relationship between Chern-Simons field theory and conformal field theory , an important relation is Gauss law constraint in presence of Wilson line, which was first given in ref. [1]. This relation plays an important role in proving that states of Chern-Simons theory satisfy the Knizhnik-Zamolodchikov equation [9–13]...

We investigate the development of winding number and Chern-Simons number in a tachyonic transition in the SU(2) Higgs model, motivated by the scenario of cold electroweak baryogenesis. We find that localized configurations with approximately halfinteger winding number, dubbed half-knots, play an important role in this process. When the Chern-Simons number adjusts locally to the winding number, ...

The dimensional reduction of the three-dimensional model (related to Hopf maps) of Adam et el. is shown to be equivalent to (i) either the static, fixed–chirality sector of the non-relativistic spinor-Chern-Simons model in 2 + 1 dimensions, (ii) or a particular Heisenberg ferromagnet in the plane. 1. Scalar Chern-Simons vortices and Hopf instantons In the non-relativistic Chern-Simons model of ...

We introduce Chern-Simons interaction into the three dimensional fourfermi theory, and suggest a possible line of non-Gaussian infrared stable fixed points of the four-fermi operator, which is characterized by the Chern-Simons coupling. 0∗ [email protected]

Garg et al. [FOCS 2013] showed how to construct indistinguishability obfuscation (iO) from a restriction of cryptographic multilinear maps called Multilinear Jigsaw Puzzles. Since then, a number of other works have shown constructions and security analyses for iO from different abstractions of multilinear maps. However, the converse question — whether some form of multilinear maps follows from ...

We reconsider Chern-Simons gauge theory on a Seifert manifold M (the total space of a nontrivial circle bundle over a Riemann surface Σ). When M is a Seifert manifold, Lawrence and Rozansky have shown from the exact solution of Chern-Simons theory that the partition function has a remarkably simple structure and can be rewritten entirely as a sum of local contributions from the flat connections...

An algebraic restriction of the nonabelian self-dual Chern-Simons-Higgs systems leads to coupled-abelian self-dual models with intricate mass spectra. The vacua are characterized by embeddings of SU (2) into the gauge algebra; and in the broken phases, the gauge and real scalar masses are related to the exponents of the gauge algebra. In this paper we compute the gauge-gauge-Higgs couplings in ...