arXiv research

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

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 $\rm{PSL}(2,\mathbb{C})$.

Researchers compute knot invariants in Seifert manifolds using Wilson loops.

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

Level-rank duality relates the observables of two different Chern-Simons theories in which the roles of the Chern-Simons level and the rank of the gauge group are exchanged. In this note, we explore the consequences of this duality in the realm of topological string theory. We show that this duality induces a number of…

Abstract summarizes level-rank duality in knot and link invariants.

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

We develop the theory of Chern-Simons bundle 2-gerbes and multiplicative bundle gerbes associated to any principal $G$-bundle with connection and a class in $H^4(BG, \ZZ)$ for a compact semi-simple Lie group $G$. The Chern-Simons bundle 2-gerbe realises differential geometrically the Cheeger-Simons invariant. We apply …

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…

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

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…

Analyzes string topology operations using Chen's integrals and homotopy transfer.

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

We use the 3d-3d correspondence together with the DGG construction of theories $T_n[M]$ labelled by 3-manifolds M to define a non-perturbative state-integral model for SL(n,C) Chern-Simons theory at any level k, based on ideal triangulations. The resulting partition functions generalize a widely studied k=1 state-integ…

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

The abstract discusses constructing 3d N=2 gauge theories using surgeries and M5-branes.

Computing Chern-Simons action for perturbed Dirac triples

We introduce certain relative differential characters which we call Cheeger-Chern-Simons characters. These combine the well-known Cheeger-Simons characters with Chern-Simons forms. In the same way as the Cheeger-Simons characters generalize Chern-Simons invariants of oriented closed manifolds, the Cheeger-Chern-Simons …

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

Geometrically constructs dilogarithm from Chern-Simons theory.

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

We consider Chern-Simons theory on 3-manifold $M$ that is the total space of a circle bundle over a 2d base $Σ$. We show that this theory is equivalent to a new 2d TQFT on the base, which we call Caloron BF theory, that can be obtained by an appropriate type of push-forward. This is a gauge theory on a bundle with stru…

The abstract discusses conjectures about Chern-Simons invariants of 3-manifolds.

We calculate the asymptotic behavior of hyperbolic volume and Chern-Simons invariant.

New $L_\infty$ liftings derived from Chern-Simons classes for coherent sheaves.

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

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

We study the asymptotic behaviour of the quantum representations of the modular group in the large level limit. We prove that each element of the modular group acts as a Fourier integral operator. This provides a link between the classical and quantum Chern-Simons theories for the torus. From this result we deduce the …

We calculate the Chern-Simons invariants of the hyperbolic double twist knot orbifolds using the Schläfli formula for the generalized Chern-Simons function on the family of cone-manifold structures of double twist knots.

We give an efficient simplicial formula for the volume and Chern-Simons invariant of a boundary-parabolic PSL(2,C)-representation of a tame 3-manifold. If the representation is the geometric representation of a hyperbolic 3-manifold, our formula computes the volume and Chern-Simons invariant directly from an ideal tria…

Chern-Simons theory on a closed contact three-manifold is studied when the Lie group for gauge transformations is compact, connected and abelian. A rigorous definition of an abelian Chern-Simons partition function is derived using the Faddeev-Popov gauge fixing method. A symplectic abelian Chern-Simons partition functi…

New invariant from non-acyclic flat connections.

The Chern-Simons forms for R-linear connections on Lie algebroids are considered. A generalized Chern-Simons formula for such R-linear connections is obtained. We it apply to define Chern character and secondary characteristic classes for R-linear connections of Lie algebroids.

The Quantum Modularity Conjecture of Zagier predicts the existence of a formal power series with arithmetically interesting coefficients that appears in the asymptotics of the Kashaev invariant at each root of unity. Our goal is to construct a power series from a Neumann-Zagier datum (i.e., an ideal triangulation of th…

Classifies extended Abelian Chern-Simons theories using quadratic modules.

Develops method to compute Chern-Simons potentials from higher-dimensional Pontryagin densities.

Two non-Morse-Bott Chern-Simons functions on homology 3-spheres.

We perform a resurgence analysis of the $SU(2)$ Chern-Simons partition function on a Brieksorn homology sphere $Σ(2,5,7)$. Starting from an exact Chern-Simons partition function, we study the Borel resummation of its perturbative expansion.

We compute the Chern-Simons transgressed forms of some modularly invariant characteristic forms, which are related to the elliptic genera. We study the modularity properties of these secondary characteristic forms and the relations among them. We also compute the Chern-Simons forms of some vector bundles over free loop…

We extend finite dimensional Chern-Simons theory to certain infinite dimensional principal bundles with connections, in particular to the frame bundle $FLM\to LM$ over the loop space of a Riemannian manifold $M$. Chern-Simons forms are defined roughly as in finite dimensions with the invariant polynomials replaced by a…

We define an extended Bloch group and show it is naturally isomorphic to H_3(PSL(2,C)^δ;Z). Using the Rogers dilogarithm function this leads to an exact simplicial formula for the universal Cheeger-Chern-Simons class on this homology group. It also leads to an independent proof of the analytic relationship between volu…

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

We exhibit the Chern-Simons forms of some characteristic classes in the simplicial de Rham complex.

We calculate the Chern-Simons invariants of the hyperbolic orbifolds of the knot with Conway's notation $C(2n, 3)$ using the Schläfli formula for the generalized Chern-Simons function on the family of $C(2n,3)$ cone-manifold structures. We present the concrete and explicit formula of them. We apply the general instruct…

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,…

The contribution of reducible connections to the U(N) Chern-Simons invariant of a Seifert manifold $M$ can be expressed in some cases in terms of matrix integrals. We show that the U(N) evaluation of the LMO invariant of any rational homology sphere admits a matrix model representation which agrees with the Chern-Simon…

We consider the Witten-Reshetikhin-Turaev invariants or Chern-Simons partition function at or around roots of unity $q=e^{2πi \frac{1}{K}}$ with rational level $K=\frac{r}{s}$ where $r$ and $s$ are coprime integers. From the exact expression for the $G=SU(2)$ Witten-Reshetikhin-Turaev invariants of Seifert manifolds at…

Categorifies Stokes coefficients in Chern-Simons theory models.