Related papers: Lax Operator and superspin chains from 4D CS gauge…
Recent studies of the topological properties of a general class of lattice Dirac operators are reported. This is based on a specific algebraic realization of the Ginsparg-Wilson relation in the form…
We propose an SL(2,R) Chern-Simons description of Liouville field theory (LFT), whose correlation function duals to partition function of N=2 SU(2) gauge theories. We give the dual expressions for conformal blocks, fusion rules, and Wilson…
We study a sector of the 5d maximally supersymmetric Yang-Mills theory on $S^5$ consisting of $1/8$-BPS Wilson loop operators contained within a great $S^3$ inside $S^5$. We conjecture that these observables are described by a 3d Chern…
We consider the planar limit of Chern-Simons theories coupled to a scalar $\phi$ in the fundamental representation of a $U(N)_k$ gauge group, at both the regular and Wilson-Fisher conformal points. These theories have one single-trace…
The families index theory for the overlap lattice Dirac operator is applied to derive topological features of the space of SU(N) lattice gauge fields on the 4-torus: The topological sectors, specified by the fermionic topological charge,…
The $4$-dimensional semi-holomorphic Chern-Simons theory of Costello and Yamazaki provides a gauge-theoretic origin for the Lax connection of $2$-dimensional integrable field theories. The purpose of this paper is to extend this framework…
We study Wilson loops in the three-dimensional N=6 supersymmetric Chern-Simons theory recently constructed by Aharony, Bergman, Jafferis and Maldacena, that is conjectured to be dual to type IIA string theory on AdS_4 x CP^3. We construct…
We study supersymmetric structure of the self-isospectral crystalline chains formed by N copies of the mutually displaced one-gap Lame systems. It is generated by the N(N-1) integrals of motion which are the first order matrix differential…
We gauge the abelian hierarchy of tensor fields in 4D by a Lie algebra. The resulting non-abelian tensor hierarchy can be interpreted via an equivariant chain complex. We lift this structure to N=1 superspace by constructing superfield…
We study the Schur line defect correlation functions in $\mathcal{N}=4$ and $\mathcal{N}=2^*$ $U(N)$ super Yang-Mills (SYM) theory. We find exact closed-form formulae of the correlation functions of the Wilson line operators in the…
We calculate the superconformal index for N=6 Chern-Simons-matter theory with gauge group U(N) X U(N) at arbitrary allowed value of the Chern-Simons level k. The calculation is based on localization of the path integral for the index. Our…
In this paper we study Open Wilson Lines (OWL's) in the context of two Supersymmetric Yang Mills theories. First we consider four dimensional N=2 Supersymmetric Yang Mills Theory with hypermultiplets transforming in the fundamental…
We derive, within the Hamiltonian formalism, the classical exchange algebra of a lambda deformed string sigma model in a symmetric space directly from a 4d holomorphic Chern-Simons theory. The explicit forms of the extended Lax connection…
We study the gauge invariant 't Hooft operator in canonical formalism for Yang-Mills theory as well as the $\mathcal{N} =4 $ super-Yang-Mills theory with the gauge group $ U(N) $. It is shown that the spectrum of the 't Hooft operator…
We study how the symmetry operator of the axial $U(1)$ non-invertible symmetry acts on the 't~Hooft line operator in the $U(1)$ gauge theory by employing the modified Villain-type lattice formulation. We model the axial anomaly by a compact…
Representations of quantum superalgebras provide a natural framework in which to model supersymmetric quantum systems. Each quantum superalgebra, belonging to the class of quasi-triangular Hopf superalgebras, contains a universal R-matrix…
This is the first of a series of two papers in which we study the one-dimensional defect CFT defined by insertions of local operators along a $\tfrac{1}{2}$-BPS Wilson line in $\mathcal{N}=4$ super Yang-Mills. In this first paper we focus…
We discuss U(1) lattice gauge theory models based on a modified Villain formulation of the gauge action, which allows coupling to bosonic electric and magnetic matter. The formulation enjoys a duality which maps electric and magnetic…
We point out that the N=4 supersymmetric KdV hierarchy, when written through the prepotentials of the bosonic chiral and antichiral N=2 supercurrents, exhibits a freedom related to the possibility to choose different gauges for the…
We study operator mixing, due to planar one-loop corrections, for composite operators in D=4 supersymmetric theories. We present some N=1,2 Yang-Mills and Wess-Zumino models, in which the planar one-loop anomalous dimension matrix in the…