Related papers: More on Wilson toroidal networks and torus blocks
We study gapped systems with anomalous time-reversal symmetry and global gravitational anomaly in three and four spacetime dimensions. These systems describe topological order on the boundary of bosonic Symmetry Protected Topological (SPT)…
We construct Virasoro algebra of differential operators for the Jones-Rosso matrix model. These operators generate various relations between Wilson loops. Then we discuss the con- structed operators and corresponding relations in the…
Let $\mathfrak{g}$ be a simple Lie algebra. We study 1/2-BPS Wilson loops of supersymmetric 5d $\mathfrak{g}$-type quiver gauge theories on a circle, in a non-trivial instanton background. The Wilson loops are codimension 4 defects of the…
The Wilson line defect half-indices for 3d $\mathcal{N}=2$ gauge theories with boundary confining phases admit a formulation in terms of the Askey-Wilson type moments. In the dual Landau-Ginzburg description the dual line operators can be…
We consider the Chern-Simons theory with Wilson lines in 3D and in 1D in the BV-BFV formalism of Cattaneo-Mnev-Reshetikhin. In particular, we allow for Wilson lines to end on the boundary of the space-time manifold. In the toy model of 1D…
We discuss the quantization and holographic aspects of a class of conical spaces in 2+1 dimensional pure AdS gravity. These appear as topological solitons in the Chern-Simons formulation of the theory and are closely related to the recently…
We show that an extended $3D$ Schr\"odinger algebra introduced in [1] can be reformulated as a $3D$ Poincar\'e algebra extended with an SO(2) R-symmetry generator and an $SO(2)$ doublet of bosonic spin-1/2 generators whose commutator closes…
We extend recent results on semi-classical conformal blocks in 2d CFT and their relation to 3D gravity via the AdS/CFT correspondence. We consider four-point functions with two heavy and two light external operators, along with the exchange…
In three dimensional ${\cal N}=4$ Chern-Simons-matter theories two independent fermionic Wilson loop operators can be defined, which preserve half of the supersymmetry charges and are cohomologically equivalent at classical level. We…
A finite Hilbert space can be associated to a periodic phase space, that is, a torus. A finite subgroup of operators corresponding to reflections and translations on the torus form respectively the basis for the discrete Weyl…
Many model quantum spin systems have been proposed to realize critical points or phases described by 2+1 dimensional conformal gauge theories. On a torus of size $L$ and modular parameter $\tau$, the energy levels of such gauge theories…
We introduce the description of a Wilson surface as a 2-dimensional topological quantum field theory with a 1-dimensional Hilbert space. On a closed surface, the Wilson surface theory defines a topological invariant of the principal…
We derive new integral identities for AdS propagators and further develop the Wilson network expansion for AdS Feynman diagrams. In particular, we demonstrate that four-point contact and exchange scalar diagrams in two dimensions can be…
We use the Chern-Simons formulation of higher spin theories in three dimensions to study aspects of holographic W-gravity. Concepts which were useful in studies of pure bulk gravity theories, such as the Fefferman-Graham gauge and the…
We find the canonical and Belinfante energy-momentum tensors and their nonzero traces. We note that the dilatation symmetry is broken and the divergence of the dilatation current is proportional to the topological mass of the gauge field.…
This is the second of a series of two papers devoted to the partition function realization of Wilson surfaces in strict higher gauge theory. A higher 2--dimensional counterpart of the topological coadjoint orbit quantum mechanical model…
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…
The critical 2d classical Ising model on the square lattice has two topological conformal defects: the $\mathbb{Z}_2$ symmetry defect $D_{\epsilon}$ and the Kramers-Wannier duality defect $D_{\sigma}$. These two defects implement…
We analyze (2+1)-dimensional gravity with a Chern--Simons term and a negative cosmological constant, primarily at the weak field level. The full theory is expressible as the sum of two higher derivative SL(2,R) "vector" Chern-Simons terms,…
We provide a holographic perspective on correlation functions in Schwarzian quantum mechanics, as boundary-anchored Wilson line correlators in Jackiw-Teitelboim gravity. We first study compact groups and identify the diagrammatic…