Related papers: 3d spectral networks and classical Chern-Simons th…

We study 3d theories containing $\mathcal{N}=3$ Chern-Simons vector multiplets coupled to the $\mathrm{SU}(N)^3$ flavour symmetry of 3d $T_N$ theories with Chern-Simons level $k_1$, $k_2$ and $k_3$. It was formerly pointed out that these…

We consider closed manifolds that admit a metric locally isometric to a product of symmetric planes. For such manifolds, we prove that the Euler characteristic is an obstruction to the existence of flat structures, confirming an old…

The field equations of the Chern-Simons theory quantized in the axial gauge are shown to be completely determined by supersymmetry Ward identities which express the invariance of the theory under the topological supersymmetry of Delduc,…

We study CFT data of 3-dimensional superconformal field theories (SCFTs) arising from wrapped two M5-branes on closed hyperbolic 3-manifolds. Via so-called 3d/3d correspondence, central charges of these SCFTs are related to a $SL(2)$…

We construct and study a new topological field theory in three dimensions. It is a hybrid between Chern-Simons and Rozansky-Witten theory and can be regarded as a topologically-twisted version of the N=4 d=3 supersymmetric gauge theory…

We find further evidence for the conjecture relating large N Chern-Simons theory on S^3 with topological string on the resolved conifold geometry by showing that the Wilson loop observable of a simple knot on S^3 (for any representation)…

We extend the Chern-Simons perturbative invariant of Axelrod and Singer to non-acyclic connections. We construct a solution of the quantum master equation on the space of functions on the cohomology of the connection. We prove that this…

We consider the superspace of D=3, N=5 supersymmetry using SO(5)/U(2) harmonic coordinates. Three analytic N=5 gauge superfields depend on three vector and six harmonic bosonic coordinates and also on six Grassmann coordinates.…

Topological quantum field theories can be used to probe topological properties of low dimensional manifolds. A class of these theories known as Schwarz type theories, comprise of Chern-Simons theories and BF theories. In three dimensions…

We develop a ready-to-use comprehensive theory for (super) 2-vector bundles over smooth manifolds. It is based on the bicategory of (super) algebras, bimodules, and intertwiners as a model for 2-vector spaces. We discuss symmetric monoidal…

Scalar relative invariants play an important role in the theory of group actions on a manifold as their zero sets are invariant hypersurfaces. Relative invariants are central in many applications, where they often are treated locally since…

Suppose $\Gamma$ is a discrete group, and $\alpha\in Z^3(B\Gamma;A)$, with $A$ an abelian group. Given a representation $\rho:\pi_1(M)\to\Gamma$, with $M$ a closed 3-manifold, put $F(M,\rho)=\langle(B\rho)^\ast[\alpha],[M]\rangle$, where…

A Chern-Simons theory in 11 dimensions, which is a piece of the 11 dimensional supergravity action, is considered as a quantum field theory in its own right. We conjecture that it defines a non-perturbative phase of M theory in which the…

We address a number of puzzles relating to the proposed formulae for the degeneracies of dyons in orbifold compactifications of the heterotic string to four dimensions with $N =4$ supersymmetry. The partition function for these dyons is…

We introduce tensor field neural networks, which are locally equivariant to 3D rotations, translations, and permutations of points at every layer. 3D rotation equivariance removes the need for data augmentation to identify features in…

A correspondence between three-dimensional flat connections and constant curvature four-dimensional simplices is used to give a novel quantization of geometry via complex SL(2,C) Chern-Simons theory. The resulting quantum geometrical states…

In this paper we study supersymmetric co-dimension 2 and 4 defects in the compactification of the 6d $(2,0)$ theory of type $A_{N-1}$ on a 3-manifold $M$. The so-called 3d-3d correspondence is a relation between complexified Chern-Simons…

The perturbative expansion of Chern-Simons gauge theory leads to invariants of knots and links, the finite type invariants or Vassiliev invariants. It has been proven that at any order in perturbation theory the resulting expression is an…

We propose a relation between the operator of S-duality (of N=4 super Yang-Mills theory in 3+1D) and a topological theory in one dimension lower. We construct the topological theory by compactifying N=4 super Yang-Mills on a circle with an…

The notion of holonomy $R$-matrices is introduced. It is shown how to define invariants of tangles with flat connections in a principle $G$-bundle of the complement of a tangle using holonomy $R$-matrices.