arXiv research

3D dual field theories for Virasoro minimal models constructed using Seifert fiber spaces.

Study 3d N=1 vacua from M-theory compactification on Spin(7) space.

Defines a map connecting 3d-index and skein module.

Paper connects 3D gravity averages to 2D CFT correlators.

Overview of 3D TQFTs and 3-manifold invariants.

New approach connects 3D Chern-Simons theory to spectral networks.

We show that 3D gravity, in its pure connection formulation, admits a natural 6D interpretation. The 3D field equations for the connection are equivalent to 6D Hitchin equations for the Chern-Simons 3-form in the total space of the principal bundle over the 3-dimensional base. Turning this construction around one gets …

We present a string inspired 3D Euclidean field theory as the starting point for a modified Ricci flow analysis of the Thurston conjecture. In addition to the metric, the theory contains a dilaton, an antisymmetric tensor field and a Maxwell-Chern Simons field. For constant dilaton, the theory appears to obey a Birkhof…

Summarizes quantum field theories with discrete symmetry, classifying representations and anomalies.

We consider topological field theories that compute the Reidemeister-Milnor-Turaev torsion in three dimensions. These are the psl(1|1) and the U(1|1) Chern-Simons theories, coupled to a background complex flat gauge field. We use the 3d mirror symmetry to derive the Meng-Taubes theorem, which relates the torsion and th…

Study of IR phases in 3D class R theories linked to non-hyperbolic 3-manifolds.

Extends string-net theory to 3D TQFT via surface graphs and surgery.

Recent work extends Turaev's modular categories to non-semisimple settings.

We consider several diffeomorphism invariant field theories of 2- and 3-forms in six dimensions. They all share the same kinetic term $BdC$, but differ in the potential term that is added. The theory $BdC$ with no potential term is topological - it describes no propagating degrees of freedom. We show that the theory co…

To formulate the universal constraints of quantum statistics data of generic long-range entangled quantum systems, we introduce the geometric-topology surgery theory on spacetime manifolds where quantum systems reside, cutting and gluing the associated quantum amplitudes, specifically in 2+1 and 3+1 spacetime dimension…

New algorithm constructs characters of rational VOAs from knot complements.

Constructs 3D topological field theories from a specific quantum group, linking to physics invariants.

We introduce and study the Wilson loops in a general 3D topological field theories (TFTs), and show that the expectation value of Wilson loops also gives knot invariants as in Chern-Simons theory. We study the TFTs within the Batalin-Vilkovisky (BV) and Alexandrov-Kontsevich-Schwarz-Zaboronsky (AKSZ) framework, and the…

EuLearn creates diverse 3D topological datasets for machine learning.

A modular functor is constructed from non-semisimple 3d TFTs.

New method describes entanglement of straight lines in 3D space.

New framework for 3D spatial topology enumeration and identification.

There is a remarkable and canonical problem in 3D geometry and topology: To understand existing models of 3D fluid motion or to create new ones that may be useful. We discuss from an algebraic viewpoint the PDE called Euler's equation for incompressible frictionless fluid motion. In part I we define a "finite dimension…

Topology-GS improves 3D GS for better structural and feature integrity.

We propose a method to assign non-unitary TQFTs to certain SCFTs, deriving bounds and examples.

The paper explores the connection between 3d gravity and Chern-Simons theory using affine group connections.

Study reveals failure of uniqueness in dynamical invariants for 3D volume-preserving diffeomorphisms.

We construct a new family of exact quantum field theories modeled on hyperbolic geometry, called {\it quantum hyperbolic field theories} (QHFTs). The QHFTs are defined for a $(2+1)$-bordism category based on the set of compact oriented 3-manifolds $Y$, equipped with properly embedded framed links $L_\Ff$ and with flat …

Study fermionic theories, their anomalies, and modular transformations.

We identify a large class R of three-dimensional N=2 superconformal field theories. This class includes the effective theories T_M of M5-branes wrapped on 3-manifolds M, discussed in previous work by the authors, and more generally comprises theories that admit a UV description as abelian Chern-Simons-matter theories w…

3D HQFTs constructed using graded monoidal categories.

Lectures on topological field theories and differential cohomology.

A 3D almost-Riemannian manifold is a generalized Riemannian manifold defined locally by 3 vector fields that play the role of an orthonormal frame, but could become collinear on some set $\Zz$ called the singular set. Under the Hormander condition, a 3D almost-Riemannian structure still has a metric space structure, wh…

Teichmüller TQFT is a unitary 3d topological theory whose Hilbert spaces are spanned by Liouville conformal blocks. It is related but not identical to PSL(2,R) Chern-Simons theory. To physicists, it is known in particular in the context of 3d-3d correspondence and also in the holographic description of Virasoro conform…

Dimofte, Gaiotto and Gukov introduced a powerful invariant, the 3D-index, associated to a suitable ideal triangulation of a 3-manifold with torus boundary components. The 3D-index is a collection of formal power series in $q^{1/2}$ with integer coefficients. Our goal is to explain how the 3D-index is a generating serie…

New method uses resurgent analysis to determine growth rate of quantum field theory coefficients.

The paper connects quivers to knot complements and studies their BPS states and 3d N=2 theories.

We describe a family of 3d topological B-models whose target spaces are Hilbert schemes of points in $\mathbb{C}^2$. The interfaces separating theories with different numbers of points correspond to braid strands. The Hilbert space of the picture of a closed braid is the HOMFLY-PT homology of the corresponding link.

This paper explores a particular statistical model on 6-valent graphs with special properties which turns out to be invariant with respect to certain Roseman moves if the graph is the singular point graph of a diagram of a 2-knot. The approach uses the technic of the tetrahedral complex cohomology. We emphasize that th…

Study classifies moduli spaces of spin connections on 3D homogeneous spaces.

We find and propose an explanation for a large variety of modularity-related symmetries in problems of 3-manifold topology and physics of 3d $\mathcal{N}=2$ theories where such structures a priori are not manifest. These modular structures include: mock modular forms, $SL(2,\mathbb{Z})$ Weil representations, quantum mo…

We study the Chern-Simons topological quantum field theory with an inhomogeneous gauge group, a non-semi-simple group obtained from a semi-simple one by taking its semi-direct product with its Lie algebra. We find that the standard knot observables (i.e. traces of holonomies along knots) essentially vanish, but yet, th…

The paper proves UV finiteness and vanishing anomalies for hybrid topological-holomorphic field theories.

Paper presents a consistent discretization for Hodge decomposition on volumetric meshes.

Proves helicity is the only regular Casimir for 3D hydrodynamics.

Unified Higgs bundle vacua from M-theory on Spin(7) spaces.

The paper quantizes hybrid topological-holomorphic field theories on $\mathbb{R}^m imes \mathbb{C}^n$.

Develops method to construct Lie algebra weight system kernel using Vogel algebra.