Related papers: Line Operators in $U(1|1)$ Chern-Simons Theory

We construct monopole operators for 3d Yang-Mills-matter theories and Chern-Simons-matter theories in canonical formalism. In this framework, monopole operators, although as the disorder operators, could be written in terms of the…

Monopole operators in Chern-Simons theories with charged matter have been studied using the state-operator map in CFTs, as states on $\mathbb{R}\times S^2$ with background magnetic flux on $S^2$. Gauge invariance requires a dressing with…

In this note we define Chern-Simons classes of a superconnection $D+L$ on a complex supervector bundle $E$ such that $D$ is flat and preserves the grading, and $L$ is an odd endomorphism of $E$ on a supermanifold. As an application we…

Let $L(-{1/2}(l+1),0)$ be the simple vertex operator algebra associated to an affine Lie algebra of type $A_{l}^{(1)}$ with the lowest admissible half-integer level $-{1/2}(l+1)$, for even l. We study the category of weak modules for that…

Monopole operators in Abelian N=4 Chern-Simons theories described by circular quiver diagrams are investigated. The magnetic charges of non-diagonal U(1) gauge symmetries form the SU(p)xSU(q) root lattice where p and q are numbers of…

Related to a semigroup of operators on a metric measure space, we define and study pseudodifferential operators (including the setting of Riemannian manifold, fractals, graphs ...). Boundedness on $L^p$ for pseudodifferential operators of…

We extend the hermitian three-algebra formulation of ABJM theory to include $U(1)$ factors. With attention payed to extra $U(1)$ factors, we refine the classification of $\N=6$ ABJM theories. We argue that essentially the only allowed gauge…

We formulate an interpretation of the theory of physical superselection sectors in terms of vertex operator algebra language. Using this formulation we give a construction of simple current from a primary semisimple element of weight one.…

The Bol operators are unary differential operators between spaces of weighted densities on the 1-dimensional manifold invariant under projective transformations of the manifold. On the $1|n$-dimensional supermanifold (superstring)…

We generalize our picture in [arXiv:0904.1744], and consider a pure abelian gauge theory on a four-manifold with nonlocal operators of every codimension arbitrarily and simultaneously inserted. We explicitly show that (i) the theory enjoys…

The study of this paper is Wilson line operators in 3-dimensional Chern-Simons theory on a manifold with boundaries. We prove to leading order through a direct calculation of Feynman integrals that the merging of parallel Wilson lines…

In this paper, we will analyze a three dimensional supersymmetric Chern-Simons theory on a manifold with a boundary. The boundary we will consider in this paper will be defined by $n\cdot x=0$, where $n$ is a light-like vector. It will be…

The proper action functional of (4k+3)-dimensional U(1)-Chern-Simons theory including the instanton sectors has a well known description: it is given on the moduli space of fields by the fiber integration of the cup product square of…

Classical and quantum Chern-Simons with gauge group $\text{U}(1)^N$ were classified by Belov and Moore in \cite{belov_moore}. They studied both ordinary topological quantum field theories as well as spin theories. On the other hand a…

We consider several topologically twisted Chern-Simons-matter theories and propose boundary VOAs whose module categories should model the category of line operators of the 3d bulk. Our main examples come from the topological $A$ and $B$…

Let $\mathbb F$ be a finite field. Consider a direct sum $V$ of an infinite number of copies of $\mathbb F$, consider the dual space $V^\diamond$, i.~e., the direct product of an infinite number of copies of $\mathbb F$. Consider the direct…

In this paper, we studied line operators in the Left-Right Symmetric Model. The gauge group of Left-Right Symmetric Electroweak Model is ${G} = SU(3) \times SU(2)_{L} \times SU(2)_{R} \times U(1)_{B - L}$. We derived the spectrum of line…

This article summarises the theory of several bounded functional calculi for unbounded operators that have recently been discovered. The extend the Hille--Phillips calculus for (negative) generators $A$ of certain bounded $C_0$-semigroups,…

Extending previous work that involved D3-branes ending on a fivebrane with $\theta_{\mathrm{YM}}\not=0$, we consider a similar two-sided problem. This construction, in case the fivebrane is of NS type, is associated to the three-dimensional…

We show that if $V$ is a vertex operator algebra such that all the irreducible ordinary $V$-modules are $C_1$-cofinite and all the grading-restricted generalized Verma modules for $V$ are of finite length, then the category of finite length…