Related papers: A Little Large N Group Theory
The construction of generators of the Clifford group and of stabilizer states from Chern-Simons theory is presented for the Kac-Moody algebras SU(2)1, U(N)N,N(K+N) with N = 2 and K = 1, and SU(N)1 extending results of Salton, et. al.
We show that a remarkable compatibility exists between the results of a potential model with constituent quarks and the 1/Nc expansion mass formula for strange and nonstrange baryon resonances. Such compatibility brings support to the basic…
We describe a supersymmetric Grand Unified Theory based on the gauge group $\SU(5)^3$, or $\SO(10)^3$, invariant under the interchange of any~SU(5), or~SO(10), with each family multiplet transforming non trivially under one different…
We study the U(M/N) supergroup keeping in mind its connection with electronic Hamiltonians. It is explicitly shown that the generators of the supergroup U(N/N) can be expressed by Clifford operators or Fermi operators. A multi-band…
We use deformation quantization to construct the large N limits of Bosonic vector models as classical dynamical systems on the Siegel disc and study the relation of this formulation to standard results of collective field theory. Special…
We give a finite presentation by generators and relations for the group O_n(Z[1/2]) of n-dimensional orthogonal matrices with entries in Z[1/2]. We then obtain a similar presentation for the group of n-dimensional orthogonal matrices of the…
$\mathcal{N} = 1$ supersymmetric Yang-Mills theory describes gluons interacting with gluinos, which are spin-$\frac{1}{2}$ Majorana particles in the adjoint representation of the gauge group. In addition to glueballs and mesonic bound…
Consider any sequence of finite groups $A^t$, where $t$ takes values in an integer index set $\mathbf{Z}$. A group system $A$ is a set of sequences with components in $A^t$ that forms a group under componentwise addition in $A^t$, for each…
We show how to use quantum mechanics on the group manifold U(N) as a tool for problems in U(N) representation theory. The quantum mechanics reduces to free fermions on the circle, which in the large N limit become relativistic. The theory…
At large number of colors, N_c quarks in baryons are in a mean field of definite space and flavor symmetry. We write down the general Lorentz and flavor structure of the mean field, and derive the Dirac equation for quarks in that field.…
We discuss theoretical issues pertaining to baryonic matter in the combined heavy-quark and large $N_c$ limits of QCD. Witten's classic argument that baryons and interacting systems of baryons can be described in a mean-field approximation…
We solve two-dimensional large-N QCD in the presence of a nonzero baryon number B, and for arbitrary quark mass m and volume L. We fully treat the dynamics of the gluonic zero modes and check how this affects results from previous studies…
Wilson loops in large N gauge theory exhibit a weak to strong coupling transition as the loop is dilated. A multiplicative matrix model captures the universal behavior associated with this transition. A universal scaling function is…
The spectrum of baryons containing heavy quarks of one flavor is described in terms of representations of the group SU(2) X SU(6), where the two factor groups refer to spin rotations of the heavy quarks and spin-flavor rotations of the…
This paper is a significant contribution to a general programme aimed to classify all projective irreducible representations of finite simple groups over an algebraically closed field, in which the image of at least one element is…
We consider a simple model of large-Nc QCD defined by a spectrum consisting of an infinite set of equally spaced zero-width vector resonances. This model is an excellent theoretical laboratory for investigating certain approximation schemes…
QCD_{AS}, a variant of large N_c QCD in which quarks transform under the color two-index antisymmetric representation, reduces to standard QCD at N_c = 3 and provides an alternative to the usual large N_c extrapolation that uses fundamental…
We consider a class of matrix integrals over the unitary group $U(N)$ with an infinite set of couplings characterized by a series $f(q)=\sum_{n \ge 1} a_n q^n$, with $a_n \in \mathbb{Z}$. Such integrals arise in physics as the partition…
We present a model-independent analysis of the mass spectrum of nonstrange L=1 baryons in large N_c QCD. The 1/N_c expansion is used to select and order a basis of effective operators that spans the nine observables (seven masses and two…
We give a criterion of classicality for mixed states in terms of expectation values of a quantum observable. Using group representation theory we identify all cases when the criterion can be computed exactly in terms of the spectrum of a…