String Spectrum of 1+1-Dimensional Large N QCD with Adjoint Matter

We propose gauging matrix models of string theory to eliminate unwanted non-singlet states. To this end we perform a discretised light-cone quantisation of large N gauge theory in 1+1 dimensions, with scalar or fermionic matter fields transforming in the adjoint representation of SU(N). The entire spectrum consists of bosonic and fermionic closed-string excitations, which are free as N tends to infinity. We analyze the general features of such bound states as a function of the cut-off and the gauge coupling, obtaining good convergence for the case of adjoint fermions. We discuss possible extensions of the model and the search for new non-critical string theories.Comment: 20 pages (7 figures available from authors as postscipt files), PUPT-134

A derivation of Regge trajectories in large-N transverse lattice QCD

Large-N QCD is analysed in light-front coordinates with a transverse lattice at strong coupling. The general formalism can be looked up on as a d+n expansion with a stack of d-dimensional hyperplanes uniformly spaced in n transverse dimensions. It can arise by application of the renormalisation group transformations only in the transverse directions. At leading order in strong coupling, the gauge field dynamics reduces to the constraint that only colour singlet states can jump between the hyperplanes. With d=2, n=2 and large-N, the leading order strong coupling results are simple renormalisations of those for the 't Hooft model. The meson spectrum lies on a set of parallel trajectories labeled by spin. This is the first derivation of the widely anticipated Regge trajectories in a regulated systematic expansion in QCD.Comment: Lattice 2000 (spectrum), 5 pages, to appear in the proceeding

Transverse Lattice Approach to Light-Front Hamiltonian QCD

We describe a non-perturbative procedure for solving from first principles the light-front Hamiltonian problem of SU(N) pure gauge theory in D spacetime dimensions (D>2), based on enforcing Lorentz covariance of observables. A transverse lattice regulator and colour-dielectric link fields are employed, together with an associated effective potential. We argue that the light-front vacuum is necessarily trivial for large enough lattice spacing, and clarify why this leads to an Eguchi-Kawai dimensional reduction of observables to 1+1-dimensions in the infinite N limit. The procedure is then tested by explicit calculations for 2+1-dimensional SU(infinity) gauge theory, within a first approximation to the lattice effective potential. We identify a scaling trajectory which produces Lorentz covariant behaviour for the lightest glueballs. The predicted masses, in units of the measured string tension, are in agreement with recent results from conventional Euclidean lattice simulations. In addition, we obtain the potential between heavy sources and the structure of the glueballs from their light-front wavefunctions. Finally, we briefly discuss the extension of these calculations to 3+1-dimensions.Comment: 55 pages, uses macro boxedeps.tex, minor corrections in revised versio

On the Spectrum of QCD(1+1) with SU(N_c) Currents

Extending previous work, we calculate in this note the fermionic spectrum of two-dimensional QCD (QCD_2) in the formulation with SU(N_c) currents. Together with the results in the bosonic sector this allows to address the as yet unresolved task of finding the single-particle states of this theory as a function of the ratio of the numbers of flavors and colors, \lambda=N_f/N_c, anew. We construct the Hamiltonian matrix in DLCQ formulation as an algebraic function of the harmonic resolution K and the continuous parameter \lambda. Amongst the more surprising findings in the fermionic sector chiefly considered here is that the fermion momentum is a function of \lambda. This dependence is necessary in order to reproduce the well-known 't Hooft and large N_f spectra. Remarkably, those spectra have the same single-particle content as the ones in the bosonic sectors. The twist here is the dramatically different sizes of the Fock bases in the two sectors, which makes it possible to interpret in principle all states of the discrete approach. The hope is that some of this insight carries over into the continuum. We also present some new findings concerning the single-particle spectrum of the adjoint theory.Comment: 21 pp., 13 figures, version published in PR

In search of predictive endophenotypes in addiction: insights from preclinical research.

Drug addiction is widely recognized to afflict some but not all individuals by virtue of underlying risk markers and traits involving multifaceted interactions between polygenic and external factors. Remarkably, only a small proportion of individuals exposed to licit and illicit drugs develop compulsive drug-seeking behavior, maintained in the face of adverse consequences and associated detrimental patterns of drug intake involving extended and repeated bouts of binge intoxication, withdrawal and relapse. As a consequence, research has increasingly endeavored to identify distinctive neurobehavioral mechanisms and endophenotypes that predispose individuals to compulsive drug use. However, research in active drug users is hampered by the difficulty in categorizing putatively causal behavioral traits prior to the initiation of drug use. By contrast, research in experimental animals is often hindered by the validity of approaches used to investigate the neural and psychological mechanisms of compulsive drug-seeking habits in humans. Herein, we survey and discuss the principal findings emanating from preclinical animal research on addiction and highlight how specific behavioral endophenotypes of presumed genetic origin (e.g. trait anxiety, novelty preference and impulsivity) differentially contribute to compulsive forms of drug seeking and taking and, in particular, how these differentiate between different classes of stimulant and non-stimulant drugs of abuse.The authors acknowledge funding support from the UK Medical Research Council (grants G9536855; G0701500; G0802729), the Newton-Cambridge Trust and the Wellcome Trust (grant WT109738MA). The Behavioural and Clinical Neuroscience Institute at Cambridge University is supported by a core award from the Medical Research Council (G1000183) and Wellcome Trust (093875/Z/10/Z).This is the author accepted manuscript. The final version is available from Wiley via http://dx.doi.org/10.1111/gbb.1226

Mesons on a transverse lattice

The meson eigenstates of the light-cone Hamiltonian in a coarse transverse lattice gauge theory are investigated. Building upon previous work in pure gauge theory, the Hamiltonian and its Fock space are expanded in powers of dynamical fields. In the leading approximation, the couplings appearing in the Hamiltonian are renormalised by demanding restoration of space-time symmetries broken by the cut-off. Additional requirements from chiral symmetry are discussed and difficulties in imposing them from first principles in the leading approximation are noted. A phenomenological calculation is then performed, in which chiral symmetry in spontaneously broken form is modelled by imposing the physical pion-rho mass splitting as a constraint. The light-cone wavefunctions of the resulting Hamiltonian are used to compute decay constants, form factors and quark momentum and spin distributions for the pion and rho mesons. Extensions beyond leading order, and the implications for first principles calculations, are briefly discussed.Comment: 31 pages, 7 figure

Depopulation of dense α-synuclein aggregates is associated with rescue of dopamine neuron dysfunction and death in a new Parkinson's disease model.

Parkinson's disease (PD) is characterized by the presence of α-synuclein aggregates known as Lewy bodies and Lewy neurites, whose formation is linked to disease development. The causal relation between α-synuclein aggregates and PD is not well understood. We generated a new transgenic mouse line (MI2) expressing human, aggregation-prone truncated 1-120 α-synuclein under the control of the tyrosine hydroxylase promoter. MI2 mice exhibit progressive aggregation of α-synuclein in dopaminergic neurons of the substantia nigra pars compacta and their striatal terminals. This is associated with a progressive reduction of striatal dopamine release, reduced striatal innervation and significant nigral dopaminergic nerve cell death starting from 6 and 12 months of age, respectively. In the MI2 mice, alterations in gait impairment can be detected by the DigiGait test from 9 months of age, while gross motor deficit was detected by rotarod test at 20 months of age when 50% of dopaminergic neurons in the substantia nigra pars compacta are lost. These changes were associated with an increase in the number and density of 20-500 nm α-synuclein species as shown by dSTORM. Treatment with the oligomer modulator anle138b, from 9 to 12 months of age, restored striatal dopamine release, prevented dopaminergic cell death and gait impairment. These effects were associated with a reduction of the inner density of large α-synuclein aggregates and an increase in dispersed small α-synuclein species as revealed by dSTORM. The MI2 mouse model recapitulates the progressive dopaminergic deficit observed in PD, showing that early synaptic dysfunction is associated to fine behavioral motor alterations, precedes dopaminergic axonal loss and neuronal death that become associated with a more consistent motor deficit upon reaching a certain threshold. Our data also provide new mechanistic insight for the effect of anle138b's function in vivo supporting that targeting α-synuclein aggregation is a promising therapeutic approach for PD

Colour-Dielectric Gauge Theory on a Transverse Lattice

We investigate in some detail consequences of the effective colour-dielectric formulation of lattice gauge theory using the light-cone Hamiltonian formalism with a transverse lattice. As a quantitative test of this approach, we have performed extensive analytic and numerical calculations for 2+1-dimensional pure gauge theory in the large N limit. Because of Eguchi-Kawai reduction, one effectively studies a 1+1-dimensional gauge theory coupled to matter in the adjoint representation. We study the structure of coupling constant space for our effective potential by comparing with the physical results available from conventional Euclidean lattice Monte Carlo simulations of this system. In particular, we calculate and measure the scaling behaviour of the entire low-lying glueball spectrum, glueball wavefunctions, string tension, asymptotic density of states, and deconfining temperature. We employ a new hybrid DLCQ/wavefunction basis in our calculations of the light-cone Hamiltonian matrix elements, along with extrapolation in Tamm-Dancoff truncation, significantly reducing numerical errors. Finally we discuss, in light of our results, what further measurements and calculations could be made in order to systematically remove lattice spacing dependence from our effective potential a priori.Comment: 48 pages, Latex, uses macro boxedeps.tex, minor errors corrected in revised versio

On the spectrum of QCD(1+1) with large numbers of flavours N_F and colours N_C near N_F/N_C = 0

QCD(1+1) in the limit of a large number of flavours N_F and a large number of colours N_C is examined in the small N_F/N_C regime. Using perturbation theory in N_F/N_C, stringent results for the leading behaviour of the spectrum departing from N_F/N_C = 0 are obtained. These results provide benchmarks in the light of which previous truncated treatments of QCD(1+1) at large N_F and N_C are critically reconsidered.Comment: 6 revtex page

A Review of Symmetry Algebras of Quantum Matrix Models in the Large-N Limit

This is a review article in which we will introduce, in a unifying fashion and with more intermediate steps in some difficult calculations, two infinite-dimensional Lie algebras of quantum matrix models, one for the open string sector and one for the closed string sector. Physical observables of quantum matrix models in the large-N limit can be expressed as elements of these Lie algebras. We will see that both algebras arise as quotient algebras of a larger Lie algebra. We will also discuss some properties of these Lie algebras not published elsewhere yet, and briefly review their relationship with well-known algebras like the Cuntz algebra, the Witt algebra and the Virasoro algebra. We will also review how Yang--Mills theory, various low energy effective models of string theory, quantum gravity, string-bit models, and quantum spin chain models can be formulated as quantum matrix models. Studying these algebras thus help us understand the common symmetry of these physical systems.Comment: 77 pages, 21 eps figures, 1 table, LaTeX2.09; an invited review articl