Related papers: Measuring Chern-Simons level $k$ by braiding $SU(2…
Correlations of partitioned particles carry essential information about their quantumness. Partitioning full beams of charged particles leads to current fluctuations, with their autocorrelation (namely, shot noise) revealing the particle'…
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…
Non-abelian Chern-Simons theories coupled to fermions are known to provide an interesting class of non-supersymmetric conformal fixed points \cite{Giombi:2011kc}. These theories, particularly those based on bifundamental matter, are…
We propose a framework for topological quantum computation using newly discovered non-semisimple analogs of topological quantum field theories in 2+1 dimensions. These enhanced theories offer more powerful models for quantum computation.…
We study field theories defined in regions of the spatial non-commutative (NC) plane with a boundary present delimiting them, concentrating in particular on the U(1) NC Chern-Simons theory on the upper half plane. We find that classical…
We have studied ${\rm SU}(2)_k$ anyon models, assessing their prospects for topological quantum computation. In particular, we have compared the Ising ($k=2$) anyon and Fibonacci ($k=3$) anyon models, motivated by their potential for future…
We study topological properties of quasi-particle states in the non-Abelian quantum Hall states. We apply a skein-theoretic method to the Read--Rezayi state whose effective theory is the SU(2)_K Chern--Simons theory. As a generalization of…
There are two natural Chern-Simons theories associated with the embedding of a three-dimensional surface in Euclidean space; one is constructed using the induced metric connection -- it involves only the intrinsic geometry, the other is…
Geometric quantization of 2+1 dimensional pure Yang-Mills theory is studied with focusing on finite large scales. It is previously shown that (Yildirim, 2015, Int. J. Mod. Phys A, 30(7), 1550034), topologically massive Yang-Mills theory…
The Chern-Simons axion coupling of a bulk insulator is only defined modulo a quantum of e^2/h. The quantized part of the coupling is uniquely defined for a bounded insulating sample, but it depends on the specific surface termination.…
We study SU(N) level k Chern-Simons theories coupling to a fundamental fermion with chemical potential for U(1) flavor symmetry. We solve this system exactly in the 't Hooft limit, N,k\to\infty with \lambda = N/k fixed. The solution exists…
We present a rigorous analysis of the Schr\"{o}dinger picture quantization for the $SU(2)$ Chern-Simons theory on 3-manifold torus$\times$line, with insertions of Wilson lines. The quantum states, defined as gauge covariant holomorphic…
We calculate perturbatively the pressure of a dilute gas of anyons through second order in the anyon coupling constant, as described by Chern-Simons field theory. Near Bose statistics , the divergences in the perturbative expansion are…
It is shown, using level-rank duality that a universal topological quantum computer based on Chern-Simons theory for SU(2)$_3$ also implies an analogous universal quantum computer based on SU(3)$_2$. Suggestions are made for the possible…
We provide a comprehensive systematic method for the numerical computation of elementary braid operations in topological quantum computation (TQC). This {procedure} is systematically applicable to all anyon models, including $SU(2)_k$.…
In this paper, the decomposition of SU(2) gauge potential in terms of Pauli spinors is studied. Using this decomposition, the spinor strutures of the Chern-Simons form and the Chern density are obtained. Furthermore, by these spinor…
We reinterpret U(N) Chern-Simons-Witten theory quantized on a torus as a free fermion system. Its Hilbert space and some observables are simply related to those of group quantum mechanics, even at finite N and k. Its large N limit can be…
We study ${\cal N}=2$ Chern-Simons-matter theories with gauge group $U_{k_1}(1)\times U_{k_2}(1)$. We find that, when $k_1+k_2=0$, the partition function computed by localization dramatically simplifies and collapses to a single term. We…
The purpose of this paper is to describe the basics of a dictionary between Chern-Simons levels in three-dimensional gauged linear sigma models (GLSMs) and the (coincidentally-named) Ruan-Zhang levels for twisted quantum K-theory in…
Anyon models are algebraic structures that model universal topological properties in topological phases of matter and can be regarded as mathematical characterization of topological order in two spacial dimensions. It is conjectured that…