We study excited baryon decay widths in large Nc QCD. It was suggested previously that some spin-flavor mixed-symmetric baryon states have strong couplings of O(N −1/2 c ) to nucleons [implying narrow widths of O(1/Nc)], as opposed to the generic expectation based on Witten's counting rules of an O(N 0 c ) coupling. The calculation obtaining these narrow widths was performed in the context of a simple quark-shell model. This paper addresses the question of whether the existence of such narrow states is a general property of large Nc QCD. We show that a general large Nc QCD analysis does not predict such narrow states; rather they are a consequence of the extreme simplicity of the quark model.

We derive expressions for pion photoproduction amplitudes in the 1/N c expansion of QCD, and obtain linear relations directly from this expansion that relate electromagnetic multipole amplitudes at all energies. The leading-order relations in 1/N c compare favorably with available data, while the next-to-leading order relations seem to provide only a small improvement. However, when resonance parameters are compared directly, the agreement at O(1/N c ) or O(1/N 2 c ) is impressive.

Motivated by the possibility of creating non-Abelian fields using cold atoms in optical lattices, we explore the richness and complexity of non-interacting two-dimensional electron gases (2DEGs) in a lattice, subjected to such fields. In the continuum limit, a non-Abelian system characterized by a two-component "magnetic flux" describes a harmonic oscillator existing in two different charge states (mimicking a particle-hole pair) where the coupling between the states is determined by the non-Abelian parameter, namely the difference between the two components of the "magnetic flux". A key feature of the non-Abelian system is a splitting of the Landau energy levels, which broaden into bands, as the spectrum depends explicitly on the transverse momentum. These Landau bands result in a coarse-grained "moth", a continuum version of the generalized Hofstadter butterfly. Furthermore, the bands overlap, leading to effective relativistic effects. Importantly, similar features also characterize the corresponding two-dimensional lattice problem when at least one of the components of the magnetic flux is an irrational number. The lattice system with two competing "magnetic fluxes" penetrating the unit cell provides a rich environment in which to study localization phenomena. Some unique aspects of the transport properties of the non-Abelian system are the possibility of inducing localization by varying the quasimomentum, and the absence of localization of certain zero-energy states exhibiting a linear energy-momentum relation. Furthermore, non-Abelian systems provide an interesting localization scenario where the localization transition is accompanied by a transition from relativistic to non-relativistic theory.

We obtain relations between partial-wave amplitudes for πN → πN and πN → π∆ directly from large Nc QCD. While linear relations among certain amplitudes holding at leading order (LO) in 1/Nc were derived in the context of chiral soliton models two decades ago, the present work employs a fully model-independent framework based on consistency with the large Nc expansion. At LO in 1/Nc we reproduce the soliton model results; however, this method allows for systematic corrections. At next-to-leading order (NLO), most relations require additional unknown functions beyond those appearing at LO and thus have little additional predictive power. However, three NLO relations for the πN → π∆ reaction are independent of unknown functions and make predictions accurate at this order. The amplitudes relevant to two of these relations were previously extracted from experiment. These relations describe experiment dramatically better than their LO counterparts.