Related papers: On topological solutions to a generalized Chern-Si…
Various results ensure the existence of large complete bipartite graphs in properly colored graphs when some condition related to a topological lower bound on the chromatic number is satisfied. We generalize three theorems of this kind,…
Motivated by some previously known facts from mathematical and physics literature, we explore certain relations between 3-dimensional topological gauge theories with continuous and finite gauge groups, commonly known as Chern-Simons (CS)…
We study observables and deformations of generalized Chern-Simons action and show how to apply these results to maximally supersymmetric gauge theories. We describe a construction of large class of deformations based on some results on the…
We include a Chern-Simons term in a GL(3,R) gauge formulation of gravity with a cosmological contribution in 2+1 dimension and we explore consistence showing that excitations must be causal and standard topological massive gravity is…
We propose a gauge-invariant system of the Chern-Simons-Schrodinger type on a one-dimensional lattice. By using the spatial gauge condition, we prove local and global well-posedness of the initial-value problem in the space of square…
We present a simple criterion for solvability of lattice spin systems on the basis of the graph theory and the simplicial homology. The lattice systems satisfy algebras with graphical representations. It is shown that the null spaces of…
It is a long-standing question to extend the definition of 3-dimensional Chern-Simons theory to one which associates values to 1-manifolds with boundary and to 0-manifolds. We provide a solution in case the gauge group is a torus. We also…
Non-standard overview on the possible formulation towards a unified model on the lattice is presented. It is based on the generalized gauge theory which is formulated by differential forms and thus expected to fit in a simplicial manifold.…
We generalize a real-space Chern number formula for gapped free fermions to higher orders. Using the generalized formula, we prove recent proposals for extracting thermal and electric Hall conductance from the ground state via the…
We consider the mixed topological-holomorphic Chern-Simons theory introduced by Costello, Yamazaki and Witten on a $\mathbb{Z}_2$ orbifold. We use this to construct semi-classical solutions of the boundary Yang-Baxter equation in the…
We analyze the hamiltonian quantization of Chern-Simons theory associated to the universal covering of the Lorentz group SO(3,1). The algebra of observables is generated by finite dimensional spin networks drawn on a punctured topological…
Existence of Maxwell-Chern-Simons-Higgs (MCSH) vortices in a Hermitian line bundle $\L$ over a general compact Riemann surface $\Sigma$ is proved by a continuation method. The solutions are proved to be smooth both spatially and as…
In temporal gauge A_{0}=0 the 3d Chern-Simons theory acquires quadratic action and an ultralocal propagator. This directly implies a 2d R-matrix representation for the correlators of Wilson lines (knot invariants), where only the crossing…
Conventional approaches to lattice gauge theories do not properly consider the topology of spacetime or of its fields. In this paper, we develop a formulation which tries to remedy this defect. It starts from a cubical decomposition of the…
Chern-Simons Theories with gauge super-groups appear naturally in string theory and they possess interesting applications in mathematics, e.g. for the construction of knot and link invariants. This paper is the first in a series where we…
The Abelian Chern-Simons gauge theory is constructed on the three-dimensional spacetime lattice. This proposal introduces both lattice and dual lattice, and the gauge field on the dual lattice is expressed in terms of the gauge field on the…
A direct relation between two types of topological field theories, Chern-Simons theory and BF theory, is presented by using ``Generalized Differential Calculus'', which extends an ordinary p-form to an ordered pair of p and (p+1)-form. We…
We investigate the existence of non-topological solutions $(u_1,u_2)$ satisfying $$u_{i}(x)=-2\beta_i\ln|x|+O(1),\quad\text{as }|x|\rightarrow +\infty,$$ such that $\beta_i>1$ and $$(\beta_1-1)(\beta_2-1)>(N_1+1)(N_2+1),$$ for a…
Let $G=(V, E)$ be a finite connected graph, where $V$ denotes the set of vertices and $E$ denotes the set of edges. We revisit the following Chern-Simons Higgs model, \begin{equation*} \Delta u=\lambda…
We construct parity and time reversal invariant Maxwell-Chern-Simons gauge theory coupled to fermions with adding the parity partner to the matter and the gauge fields, which can give nontopological vortex solutions depending on the sign of…