Related papers: Partition function of Chern-Simons theory as renor…
We compute partition functions of Chern-Simons type theories for cylindrical spacetimes $I \times \Sigma$, with $I$ an interval and $\dim \Sigma = 4l+2$, in the BV-BFV formalism (a refinement of the Batalin-Vilkovisky formalism adapted to…
We show that the fundamental property of preservation of relations, underlying resurgent analysis, provides a new perspective on crossing a natural boundary, an important general problem in theoretical and mathematical physics. This reveals…
We use recent progress on Chern-Simons gauge theory in three dimensions [18] to give explicit, closed form formulas for the star product on some functions on the affine space ${\mathcal A}(\Sigma)$ of (smooth) connections on the trivialized…
We study the partition function of the ABJ theory, which is the N=6 superconformal Chern-Simons matter theory with gauge group U(N)xU(N+M) and Chern-Simons levels (k,-k). We exactly compute the ABJ partition function on a three sphere for…
We study three-dimensional Chern-Simons theory with complex gauge group SL(2,C), which has many interesting connections with three-dimensional quantum gravity and geometry of hyperbolic 3-manifolds. We show that, in the presence of a single…
We study four-point functions in Chern-Simons vector models in the large $N$ limit. We compute the four-point function of the scalar primary to all orders in the `t Hooft coupling $\lambda=N/k$ in $U(N)_k$ Chern-Simons theory coupled to a…
We analyze some features of the perturbative quantization of Chern-Simons theory (CST) in the Landau gauge. In this gauge the theory is known to be perturbatively finite. We consider the renormalization scheme in which the renormalized…
Since the grand partition function $Z_q$ for the so-called $q$-particles (i.e.,\ quons), $q\in(-1,1)$, cannot be computed by using the standard 2nd quantisation technique involving the full Fock space construction for $q=0$, and its…
We consider different large ${\cal N}$ limits of the one-dimensional Chern-Simons action $i\int dt~ \Tr (\del_0 +A_0)$ where $A_0$ is an ${\cal N}\times{\cal N}$ antihermitian matrix. The Hilbert space on which $A_0$ acts as a linear…
We show that matrix models in Chern-Simons theory admit an interpretation as 1D exactly solvable models, paralleling the relationship between the Gaussian matrix model and the Calogero model. We compute the corresponding Hamiltonians,…
The $q$-calculus for generic $q$ is developed and related to the deformed oscillator of parameter $q^{1/2}$. By passing with care to the limit in which $q$ is a root of unity, one uncovers the full algebraic structure of ${{\cal…
We consider the conformal field theory of N complex massless scalars in 2+1 dimensions, coupled to a U(N) Chern-Simons theory at level k. This theory has a 't Hooft large N limit, keeping fixed \lambda = N/k. We compute some correlation…
An extension of the method and results of A. Schwarz for evaluating the partition function of a quadratic functional is presented. This enables the partition functions to be evaluated for a wide class of quadratic functionals of interest in…
We extend the Fermi gas approach to a class of ABJM-like necklace quiver theories without parity invariance. The resulting partition function on $S^3$ retains the form of an Airy function, but now includes a phase that scales as $Nk$ in the…
We study Chern-Simons Gauge Theory in axial gauge on ${\mathbb R}^3.$ This theory has a quadratic Lagrangian and therefore expectations can be computed nonperturbatively by explicit formulas, giving an (unbounded) linear functional on a…
We conjecture, and show in a plethora of examples, that the sphere partition function of 3d $\mathcal{N}=4$ Chern-Simons-matter theories equals a sum of twisted traces on tensor products of Verma modules over the quantization of the moduli…
I argue that the complete partition function of 3D quantum gravity is given by a path integral over gauge-inequivalent manifolds times the Chern-Simons partition function. In a discrete version, it gives a sum over simplicial complexes…
Let $G_q$ be the $q$-deformation of a simply connected simple compact Lie group $G$ of type $A$, $C$ or $D$ and $\mathcal{O}_q(G)$ be the algebra of regular functions on $G_q$. In this article, we prove that the Gelfand-Kirillov dimension…
We determine the unitary and anti-unitary Lagrangian and quantum symmetries of arbitrary abelian Chern-Simons theories. The symmetries depend sensitively on the arithmetic properties (e.g. prime factorization) of the matrix of Chern-Simons…
For a unitary representation of the fundamental group of a compact smooth manifold, Atiyah, Patodi, Singer defined the so called alpha-invariant of the representation using Chern-Simons invariants. In this article using traces on…