Related papers: Singlet Vector Models on Lens Spaces

In this paper, we apply ideas of Dijkgraaf and Witten on 2+1 dimensional topological quantum field theory to arithmetic curves, that is, the spectra of rings of integers in algebraic number fields. In the first three sections, we define…

We study the supersymmetric partition function on $S^1 \times L(r, 1)$, or the lens space index of four-dimensional $\mathcal{N}=2$ superconformal field theories and their connection to two-dimensional chiral algebras. We primarily focus on…

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…

We prove identities generating higher dimensional vector partitions. We derive theorems for integer lattice points in the 2D first quadrant, then generalize the approach to find 3D and $n$-space lattice point vector region extensions. We…

Employing the random matrix formulation of Chern-Simons theory on Seifert manifolds, we show how the Stieltjes-Wigert orthogonal polynomials are useful in exact computations in Chern-Simons matrix models. We construct a biorthogonal…

We prove various results on the size and structure of subsets of vector spaces over finite fields which, in some sense, have too many mutually orthogonal pairs of vectors. In particular, we obtain sharp finite field variants of a theorem of…

Chern-Simons theory on a U(1) bundle over a Riemann surface \Sigma_g of genus g is dimensionally reduced to BF theory with a mass term, which is equivalent to the two-dimensional Yang-Mills on \Sigma_g. We show that the former is inversely…

Starting with a regular symmetric Dirichlet form on a locally compact separable metric space $X$, our paper studies elements of vector analysis, $L_p$-spaces of vector fields and related Sobolev spaces. These tools are then employed to…

We study the matrix models that result from localization of the partition functions of N=2 Chern-Simons-matter theories on the three-sphere. A large class of such theories are conjectured to be holographically dual to M-theory on…

We present an elementary review of some aspects of Chern-Simons theory with complex gauge group SL(N,C). We discuss some of the challenges in defining the theory as a full-fledged TQFT, as well as some successes inspired by the 3d-3d…

In this paper a class of multi-Chern-Simons field theories which is relevant to the statistical mechanics of polymer systems is investigated. Motivated by the problems which one encounters in the treatment of these theories, a general…

Light-cone coordinates and supersymmetric discrete light-cone quantization are used to analyze the thermodynamics of two-dimensional supersymmetric quantum chromodynamics with a Chern-Simons term in the large-N_c approximation. This…

A {\it vector space partition} is here a collection $\mathcal P$ of subspaces of a finite vector space $V(n,q)$, of dimension $n$ over a finite field with $q$ elements, with the property that every non zero vector is contained in a unique…

We study three dimensional O(N)_k and U(N)_k Chern-Simons theories coupled to a scalar field in the fundamental representation, in the large N limit. For infinite k this is just the singlet sector of the O(N) (U(N)) vector model, which is…

We consider N=3 supersymmetric Chern-Simons (CS) theories that contain product U(N) gauge groups and bifundamental matter fields. Using the matrix model of Kapustin, Willett and Yaakov, we examine the Euclidean partition function of these…

We study finite-coupling effects of QFT on a rigid de Sitter (dS) background taking the $O(N)$ vector model at large $N$ as a solvable example. Extending standard large $N$ techniques to the dS background, we analyze the phase structure and…

We put forward new explicit realisations of dS/CFT that relate ${\cal N}=2$ supersymmetric Euclidean vector models with reversed spin-statistics in three dimensions to specific supersymmetric Vasiliev theories in four-dimensional de Sitter…

We introduce a technique to construct gapped lattice models using defects in topological field theory. We illustrate with 2+1 dimensional models, for example Chern-Simons theories. These models are local, though the state space is not…

We describe the vector-tensor multiplet and derive its Chern-Simons couplings to the N=2 Yang-Mills gauge superfield in harmonic superspace.

We study a class of scalar, linear, non-local Riemann-Hilbert problems (RHP) involving finite subgroups of PSL(2,C). We associate to such problems a (maybe infinite) root system and describe the relevance of the orbits of the Weyl group in…