The large-N(c) nuclear potential puzzle

An analysis of the baryon-baryon potential from the point of view of large-N(c) QCD is performed. A comparison is made between the N(c)-scaling behavior directly obtained from an analysis at the quark-gluon level to the N(c)-scaling of the potential for a generic hadronic field theory in which it arises via meson exchanges and for which the parameters of the theory are given by their canonical large-N(c) scaling behavior. The purpose of this comparison is to use large-N(c) consistency to test the widespread view that the interaction between nuclei arises from QCD through the exchange of mesons. Although at the one- and two-meson exchange level the scaling rules for the potential derived from the hadronic theory matches the quark-gluon level prediction, at the three- and higher-meson exchange level a generic hadronic theory yields a potential which scales with N(c) faster than that of the quark-gluon theory.Comment: 17 pages, LaTeX, 5 figure

Nucleon-Nucleon Scattering and Large N(c) QCD

Nucleon-nucleon scattering observables are discussed in the context of large Nc QCD. As is well known, the baryon spectrum in the large Nc limit exhibits contracted SU(2Nf) spin-flavor sym- metry. This symmetry can be used to derive model-independent relations between proton-proton and proton-neutron total cross sections. These relations are valid in the kinematic regime in which the relative momentum of two nucleons is of order of Nc. In this semiclassical regime the nucleon-nucleon scattering can be described in the time-dependent mean field approximation. These model-independent results are compared to experimental data for spin-independent and polarized total nucleon-nucleon cross sections.Comment: 9 pages, 3 figures. Invited talk, Xth Quark Confinement and the Hadron Spectrum, October 201

Quantization of orbit bundles in gl∗(n,C)gl^*(n,C)

Let $G$ be the complex general linear group and $g$ its Lie algebra equipped with a factorizable Lie bialgebra structure; let $U_h$ be the corresponding quantum group. We construct explicit $U_h$-equivariant quantization of Poisson orbit bundles $O_\lambda \to O_\mu$ in $gl(n)*$.Comment: 25 page

Long properly colored cycles in edge colored complete graphs

Let $K_{n}^{c}$ denote a complete graph on $n$ vertices whose edges are colored in an arbitrary way. Let $\Delta^{\mathrm{mon}} (K_{n}^{c})$ denote the maximum number of edges of the same color incident with a vertex of $K_{n}^{c}$. A properly colored cycle (path) in $K_{n}^{c}$ is a cycle (path) in which adjacent edges have distinct colors. B. Bollob\'{a}s and P. Erd\"{o}s (1976) proposed the following conjecture: if $\Delta^{\mathrm{mon}} (K_{n}^{c})<\lfloor \frac{n}{2} \rfloor$, then $K_{n}^{c}$ contains a properly colored Hamiltonian cycle. Li, Wang and Zhou proved that if $\Delta^{\mathrm{mon}} (K_{n}^{c})< \lfloor \frac{n}{2} \rfloor$, then $K_{n}^{c}$ contains a properly colored cycle of length at least $\lceil \frac{n+2}{3}\rceil+1$. In this paper, we improve the bound to $\lceil \frac{n}{2}\rceil + 2$.Comment: 8 page

On the hypersurface orbital varieties of sl(N,C)

We study the structure of hypersurface orbital varieties of sl(N,C) (those that are hypersurfaces in the nilradical of some parabolic subalgebra) and how information about this structure is encoded in the standard Young tableau associated to it by the Robinson-Schensted algorithm. We present a conjecture for the exact form of the unique non-linear defining equations of hypersurface orbital varieties and proofs of the conjecture in certain cases.Comment: 17 page

Thread cutting with 3-axis N/C milling machine

TAPDIE, a generalized macro written for the APT numerical control system, cuts threads in stock too big for conventional machines or for which conventional methods are unsuitable. TAPDIE computes the machine tool path necessary and the information is passed on to a post-processor which produces a control tape

Universal low-temperature behavior of two-dimensional lattice scalar chromodynamics

We study the role that global and local non-Abelian symmetries play in two-dimensional (2D) lattice gauge theories with multicomponent scalar fields. We start from a maximally O(M)-symmetric multicomponent scalar model. Its symmetry is partially gauged to obtain an SU(N-c) gauge theory (scalar chromodynamics) with global U(N-f) (for N-c &gt;= 3) or Sp(N-f) symmetry (for N-c = 2), where N-f &gt; 1 is the number of flavors. Correspondingly, the fields belong to the coset SM/SU(N-c) where S-M is the M-dimensional sphere and M = 2N(f) N-c. In agreement with the Mermin-Wagner theorem, the system is always disordered at finite temperature and a critical behavior only develops in the zero-temperature limit. its universal features are investigated by numerical finite-size scaling methods. The results show that the asymptotic low-temperature behavior belongs to the universality class of the 2D CP&gt;N-f-1 field theory for N-c &gt; 2 and to that of the 2D Sp(N-f ) field theory for N-c = 2. These universality classes correspond to 2D statistical field theories associated with symmetric spaces that are invariant under Sp(N-f ) transformations for N-c = 2 and under SU(N-f ) for N-c &gt; 2. These symmetry groups are the same invariance groups of scalar chromodynamics, apart from a U(1) flavor symmetry that is present for N-f &gt;= N-c &gt; 2, which does not play any role in determining the asymptotic behavior of the model