Related papers: Q-operators are 't Hooft lines
We study 't Hooft lines and the associated $\mathcal{L}$- operators in topological 4D Chern-Simons theory with gauge symmetry given by the exceptional groups E$_{6}$ and E$_{7}$. We give their oscillator realisations and propose topological…
We investigate 4D Chern-Simons theory with ADE gauge symmetries in the presence of interacting Wilson and 't Hooft line defects. We analyse the intrinsic properties of these lines' coupling and explicate the building of oscillator-type Lax…
We establish a correspondence between a class of Wilson-'t Hooft lines in four-dimensional $\mathcal{N} = 2$ supersymmetric gauge theories described by circular quivers and transfer matrices constructed from dynamical L-operators for…
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…
We consider the defect CFT defined by a 't Hooft line embedded in N=4 super Yang-Mills theory. By explicitly quantizing around the given background we exactly reproduce a prediction from S-duality for the correlators between the 't Hooft…
We set up a perturbative framework for the 't Hooft line in the N=4 super-Yang-Mills theory, and apply it to correlators thereof with Wilson loops and local operators. Using this formalism we obtain a number of perturbative and…
We introduce the notion of modular $q$-holonomic modules whose fundamental matrices define a cocycle with improved analyticity properties and show that the generalised $q$-hypergeometric equation, as well as three key $q$-holonomic modules…
We obtain the Baxter Q-operators in the $U_q(\hat{sl}_2)$ invariant integrable models as a special limits of the quantum transfer matrices corresponding to different spins in the auxiliary space both from the functional relations and from…
Topological quantum field theory (TQFT) is a powerful tool to describe homologies, which normally involve complexes and a variety of maps/morphisms, what makes a functional integration approach with a sum over a single kind of maps…
We construct a family of 3d quantum field theories $\mathcal T_{n,k}^A$ that conjecturally provide a physical realization -- and derived generalization -- of non-semisimple mathematical TQFT's based on the modules for the quantum group…
We provide a quantum path integral definition of an 't Hooft loop operator, which inserts a pointlike monopole in a four dimensional gauge theory. We explicitly compute the expectation value of the circular 't Hooft operators in N=4 super…
We construct Q-operators for the open spin-1/2 XXX Heisenberg spin chain with diagonal boundary matrices. The Q-operators are defined as traces over an infinite-dimensional auxiliary space involving novel types of reflection operators…
We develop Yang-Baxter integrability structures connected with the quantum affine superalgebra Uq(\hat sl(2|1)). Baxter's Q-operators are explicitly constructed as supertraces of certain monodromy matrices associated with (q-deformed)…
We study supersymmetric 't Hooft loop operators in N=4 super Yang-Mills, generalizing the well-known circular 1/2 BPS case and investigating their S-duality properties. We derive the BPS condition for a generic line operator describing…
We study Chern-Simons theories at large $N$ with either bosonic or fermionic matter in the fundamental representation. The most fundamental operators in these theories are mesonic line operators, the simplest example being Wilson lines…
We study intersecting surface operators in 6d holomorphic field theories with the aim of unraveling associated quantum integrable structures. We first study the intersections of surface operators in 6d holomorphic Chern-Simons theory on…
We consider a topologically twisted maximally supersymmetric Yang-Mills theory on a four-manifold of the form $V = W \times {\mathbb R}_+$. 't Hooft disorder operators localized in the boundary component at finite distance of $V$ are…
We revisit the role of loop and surface operators as order parameters for gapped phases of four-dimensional gauge theories. We show that in some cases surface operators are confined, and that this fact can be used to distinguish phases…
In this paper, we construct a Q-operator as a trace of a representation of the universal R-matrix of $U_q(\hat{sl}_2)$ over an infinite-dimensional auxiliary space. This auxiliary space is a four-parameter generalization of the q-oscillator…
We construct the explicit $Q$-operator incorporated with the $sl_2$-loop-algebra symmetry of the six-vertex model at roots of unity. The functional relations involving the $Q$-operator, the six-vertex transfer matrix and fusion matrices are…