Multi-particle structure in the Z_n-chiral Potts models

We calculate the lowest translationally invariant levels of the Z_3- and Z_4-symmetrical chiral Potts quantum chains, using numerical diagonalization of the hamiltonian for N <= 12 and N <= 10 sites, respectively, and extrapolating N to infinity. In the high-temperature massive phase we find that the pattern of the low-lying zero momentum levels can be explained assuming the existence of n-1 particles carrying Z_n-charges Q = 1, ... , n-1 (mass m_Q), and their scattering states. In the superintegrable case the masses of the n-1 particles become proportional to their respective charges: m_Q = Q m_1. Exponential convergence in N is observed for the single particle gaps, while power convergence is seen for the scattering levels. We also verify that qualitatively the same pattern appears for the self-dual and integrable cases. For general Z_n we show that the energy-momentum relations of the particles show a parity non-conservation asymmetry which for very high temperatures is exclusive due to the presence of a macroscopic momentum P_m=(1-2Q/n)/\phi, where \phi is the chiral angle and Q is the Z_n-charge of the respective particle.Comment: 22 pages (LaTeX) plus 5 figures (included as PostScript), BONN-HE-92-3

Evidence for F(uzz) Theory

We show that in the decoupling limit of an F-theory compactification, the internal directions of the seven-branes must wrap a non-commutative four-cycle S. We introduce a general method for obtaining fuzzy geometric spaces via toric geometry, and develop tools for engineering four-dimensional GUT models from this non-commutative setup. We obtain the chiral matter content and Yukawa couplings, and show that the theory has a finite Kaluza-Klein spectrum. The value of 1/alpha_(GUT) is predicted to be equal to the number of fuzzy points on the internal four-cycle S. This relation puts a non-trivial restriction on the space of gauge theories that can arise as a limit of F-theory. By viewing the seven-brane as tiled by D3-branes sitting at the N fuzzy points of the geometry, we argue that this theory admits a holographic dual description in the large N limit. We also entertain the possibility of constructing string models with large fuzzy extra dimensions, but with a high scale for quantum gravity.Comment: v2: 66 pages, 3 figures, references and clarifications adde

Aberrant synthesis of ATP synthase resulting from a novel deletion in mitochondrial DNA in an African patient with progressive external ophthalmoplegia

A young, adult, African male patient presented with progressive proximal muscle weakness, external ophthalmoplegia and ptosis, as well as cardiac conduction abnormalities resembling Kearns-Sayre syndrome (KSS). Magnetic resonance imaging (MRI) of the brain revealed normal basal ganglia but bilateral well-circumscribed lesions in the cerebellar peduncles. Enzyme deficiencies in oxidative phosphorylation (OXPHOS) complexes I, IV and V was measured in muscle tissue. Blue native polyacrylamide gel electrophoresis (BN-PAGE) confirmed decreased protein content and activity of these complexes and revealed the presence of two catalytically active complex V sub-complexes. Upon investigation by molecular genetics, the mitochondrial DNA (mtDNA) copy number was found to be elevated and a novel deletion of 3431 bp was found in 80% of muscle mtDNA between positions 7115 and 10546, flanked by a 5 bp direct repeat sequence. In addition, it could also be concluded that the absence of mtDNA-encoded ATPase6 and ATPase8 genes in this patient clearly resulted in aberrant synthesis of ATP synthase