arXiv research

We study complex Chern-Simons theory on a Seifert manifold $M_3$ by embedding it into string theory. We show that complex Chern-Simons theory on $M_3$ is equivalent to a topologically twisted supersymmetric theory and its partition function can be naturally regularized by turning on a mass parameter. We find that the d…

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…

We test the 3d-3d correspondence for theories that are labelled by Lens spaces. We find a full agreement between the index of the 3d ${\cal N}=2$ "Lens space theory" $T[L(p,1)]$ and the partition function of complex Chern-Simons theory on $L(p,1)$. In particular, for $p=1$, we show how the familiar $S^3$ partition func…

Constructs BPS complexes and Chern--Simons theories from G-structures.

Study wave functions in complex Chern-Simons theory, finding integrality and rational points.

We develop several methods that allow us to compute all-loop partition functions in perturbative Chern-Simons theory with complex gauge group G_C, sometimes in multiple ways. In the background of a non-abelian irreducible flat connection, perturbative G_C invariants turn out to be interesting topological invariants, wh…

In this manuscript we review the construction of the Teichmüller TQFT in [AK1], upgrading it to a theory dependent on an extra odd integer $N$ using results developed in [AK3]. We also describe how this theory is related with quantum Chern--Simons Theory at level $N$ with gauge group $\rm{PSL}(2,\mathbb{C})$.

Complex Chern-Simons theory reveals peacock patterns in perturbative series.

Develops Hamiltonian quantization for complex Chern-Simons theory at even level k.

We clarify and refine the relation between the asymptotic behavior of the colored Jones polynomial and Chern-Simons gauge theory with complex gauge group SL(2,C). The precise comparison requires a careful understanding of some delicate issues, such as normalization of the colored Jones polynomial and the choice of pola…

Deformed holomorphic Chern-Simons theory yields new instantons.

Study on Chern-Simons theory at generic levels, revealing universal resurgent structure.

Novel mathematical approach using resurgent analysis reveals new structures in complex Chern-Simons theory.

We consider Chern-Simons theory with complex gauge group and present a complete non-perturbative evaluation of the path integral (the partition function and certain expectation values of Wilson loops) on Seifert fibred 3-Manifolds. We use the method of Abelianisation. In certain cases the path integral can be seen to f…

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…

New method calculates Chern-Simons volume for 3-manifolds with surgery diagrams.

Graphs with given k vertices generate an (acyclic) simplicial complex. We describe the homology of its quotient complex, formed by all connected graphs, and demonstrate its applications to the topology of braid groups, knot theory, combinatorics, and singularity theory. The multidimensional analogues of this complex ar…

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

We study resurgence properties of partition function of SU(2) Chern-Simons theory (WRT invariant) on closed three-manifolds. We check explicitly that in various examples Borel transforms of asymptotic expansions posses expected analytic properties. In examples that we study we observe that contribution of irreducible f…

Researchers define new quantum representations for a Lorentz algebra and study their Clebsch-Gordan decomposition.

Introduces modular $q$-holonomic modules to solve $q$-difference equations.

Lecture notes on Lie groups and Chern-Simons theory for grad students.

Arithmetic Dijkgraaf-Witten theory constructs analogues in Chern-Simons TQFT.

This paper introduces complex Chern-Simons bundles in families setting and proves their crystalline nature.

This paper analyzes $Δ_a$ invariants in non-perturbative complex Chern-Simons theory.

We give a direct calculation of the curvature of the Hitchin connection, in geometric quantization on a symplectic manifold, using only differential geometric techniques. In particular, we establish that the curvature acts as a first-order operator on the quantum spaces. Projective flatness follows if the Kähler struct…

Classifies extended Abelian Chern-Simons theories using quadratic modules.

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

New theory connects string theory to swampland distance conjecture.

We consider finite deformations of the Hull--Strominger system. Starting from the heterotic superpotential, we identify complex coordinates on the off-shell parameter space. Expanding the superpotential around a supersymmetric vacuum leads to a third-order Maurer--Cartan equation that controls the moduli. The resulting…

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 are hence represented by the 3d blocks of analytically continued Chern-Simons t…

We propose an extension of the recently-proposed volume conjecture for closed hyperbolic 3-manifolds, to all orders in perturbative expansion. We first derive formulas for the perturbative expansion of the partition function of complex Chern-Simons theory around a hyperbolic flat connection, which produces infinitely-m…

We study S-dualities in analytically continued SL(2) Chern-Simons theory on a 3-manifold M. By realizing Chern-Simons theory via a compactification of a 6d five-brane theory on M, various objects and symmetries in Chern-Simons theory become related to objects and operations in dual 2d, 3d, and 4d theories. For example,…

This paper approximates SU(2) Chern-Simons theory using finite group gauge theories.

Quantizes Chern-Simons invariant for tangle exteriors.

Categorifies Stokes coefficients in Chern-Simons theory models.

We show that Chern-Simons gauge theory with appropriate cutoffs is equivalent, term by term in perturbation theory, to a Fermionic theory with a nonlocal interaction term. When an additional cutoff is placed on the Fermi fields, this Fermionic theory gives rise to a convergent perturbation expansion. This leads us to c…

Chern-Simons and Reshetikhin-Turaev theories are shown equivalent for U(1) gauge group.

The paper connects Chern-Simons invariants to mixed Tate motives in hyperbolic 3-manifolds.

Study of $U(1)$ gauge theories on $G_2$ manifolds, including instantons and Chern-Simons.

We give a construction of the abelian Chern-Simons gauge theory from the point of view of a 2+1 dimensional topological quantum field theory. The definition of the quantum theory relies on geometric quantization ideas which have been previously explored in connection to the nonabelian Chern-Simons theory [JW,ADW]. We f…

In a previous paper we constructed classical spin Chern-Simons for any compact Lie group $G$: a gauge theory whose action depends on the spin structure of the 3-manifold. Here we apply geometric quantization to the classical Hamiltonian theory and investigate the formal properties of the partition function in the Lagra…

Diagrammatic method calculates knot invariant related to Chern-Simons theory.

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 served as a key example in understanding the structure of TQFTs in general. We su…

Non-trivial obstructions found for topological solitons in Yang-Mills-Chern-Simons theories.

The Habiro ring of a number field uses power series to study algebraic K-theory.

Chern-Simons and Reshetikhin-Turaev theories are shown equivalent.

We study refined topological string theory in the presence of orientifolds by counting second-quantized BPS states in M-theory. This leads us to propose a new integrality condition for both refined and unrefined topological strings when orientifolds are present. We define the SO(2N) refined Chern-Simons theory which co…