Glueball masses in the large N limit

The lowest-lying glueball masses are computed in SU($N$) gauge theory on a spacetime lattice for constant value of the lattice spacing $a$ and for $N$ ranging from 3 to 8. The lattice spacing is fixed using the deconfinement temperature at temporal extension of the lattice $N_T = 6$. The calculation is conducted employing in each channel a variational ansatz performed on a large basis of operators that includes also torelon and (for the lightest states) scattering trial functions. This basis is constructed using an automatic algorithm that allows us to build operators of any size and shape in any irreducible representation of the cubic group. A good signal is extracted for the ground state and the first excitation in several symmetry channels. It is shown that all the observed states are well described by their large $N$ values, with modest ${\cal O}(1/N^2)$ corrections. In addition spurious states are identified that couple to torelon and scattering operators. As a byproduct of our calculation, the critical couplings for the deconfinement phase transition for N=5 and N=7 and temporal extension of the lattice $N_T=6$ are determined.Comment: 1+36 pages, 22 tables, 21 figures. Typos corrected, conclusions unchanged, matches the published versio

Chronic fatigue syndrome: A hypothesis focusing on the autonomic nervous system

Chronic fatigue syndrome is a debilitating illness of unknown aetiology, with estimated levels of prevalence of up to about 8.7/100,000 in the U.S.A. Like pain fatigue it is a personal, emotionally rich experience, which may originate from peripheral or central sites (or both). The nature of the symptoms is complex and reflects the interaction of the patient with the environment and cultural milieu. Accordingly the common use of the same terminology for different types of fatigue may be misleading. Autonomic activation is a key component of both real and simulated physical exercise. Alterations in autonomic nervous system activity are a key component of several physiopathological conditions. In chronic fatigue syndrome disturbances in autonomic activity, and in other homoeostatic mechanisms, such as the hormonal and immune systems, have been reported recently. In this review we followed the hypothesis that in chronic fatigue syndrome the paradoxical condition of disturbing somatic symptoms in the absence of organic evidence of disease might be addressed by focusing on attending functional correlates. In particular we addressed possible alterations in cardiovascular autonomic control, as can be assessed by spectral analysis of R-R interval and systolic arterial pressure variability. With this approach, in subjects complaining of unexplained fatigue, we obtained data suggesting a condition of prevailing sympathetic modulation of the sino-atrial node at rest, and reduced responsiveness to excitatory stimuli. Far from considering the issue resolved, we propose that in the context of the multiple physiological and psychological interactions involved in the perception and self-reporting of symptoms, attendant changes in physiological equivalents might furnish a convenient assessment independent from subjective components. Indices of sympathetic modulation could, accordingly, provide quantifiable signs of the interaction between subject's efforts and environmental demands, independently of self descriptions, which could provide convenient measurable outcomes, both for diagnosis and treatment titration in chronic fatigue syndrome

SO(2N) and SU(N) gauge theories in 2+1 dimensions

We perform an exploratory investigation of how rapidly the physics of SO(2N) gauge theories approaches its N=oo limit. This question has recently become topical because SO(2N) gauge theories are orbifold equivalent to SU(N) gauge theories, but do not have a finite chemical potential sign problem. We consider only the pure gauge theory and, because of the inconvenient location of the lattice strong-to-weak coupling 'bulk' transition in 3+1 dimensions, we largely confine our numerical calculations to 2+1 dimensions. We discuss analytic expectations in both D=2+1 and D=3+1, show that the SO(6) and SU(4) spectra do indeed appear to be the same, and show that a number of mass ratios do indeed appear to agree in the large-N limit. In particular SO(6) and SU(3) gauge theories are quite similar except for the values of the string tension and coupling, both of which differences can be readily understood.Comment: 27 pages, 9 figure

QCD strings and the thermodynamics of the metastable phase of QCD at large NcN_c

The thermodyanmics of a metastable hadronic phase of QCD at large $N_C$ are related to properties of an effective QCD string. In particular, it is shown that in the large $N_c$ limit and near the maximum hadronic temperature, $T_H$, the energy density and pressure of the metastable phase scale as ${\cal E} \sim (T_H-T)^{-(D_\perp-6)/2}$ (for $D_\perp <6$) and $P \sim (T_H-T)^{-(D_\perp-4)/2}$ (for $D_\perp <4$) where $D_\perp$ is the effective number of transverse dimensions of the string theory. It is shown, however, that for the thermodynamic quantities of interest the limits $T \to T_H$ and $N_c \to \infty$ do not commute. The prospect of extracting $D_\perp$ via lattice simulations of the metastable hadronic phase at moderately large $N_c$ is discussed.Comment: After this paper was published, the author became aware of an important early paper by Charles Thorn on the subject of the QCD phase transition at large N_c and its relation to the Hagedorn spectrum. Given the pioneering nature of Thorn's paper, and the fact that it is not as widely known as it should be, it is important to cite it in the present work. This updated version cites Thorn's wor

Inverse Renormalization Group in Quantum Field Theory

We propose inverse renormalization group transformations within the context of quantum field theory that produce the appropriate critical fixed point structure, give rise to inverse flows in parameter space, and evade the critical slowing down effect in calculations pertinent to criticality. Given configurations of the two-dimensional φ4 scalar field theory on sizes as small as V=82, we apply the inverse transformations to produce rescaled systems of size up to V′=5122 which we utilize to extract two critical exponents. We conclude by discussing how the approach is generally applicable to any method that successfully produces configurations from a statistical ensemble and how it can give novel insights into the structure of the renormalization group

Ergodic sampling of the topological charge using the density of states

In lattice calculations, the approach to the continuum limit is hindered by the severe freezing of the topological charge, which prevents ergodic sampling in configuration space. In order to significantly reduce the autocorrelation time of the topological charge, we develop a density of states approach with a smooth constraint and use it to study SU(3) pure Yang Mills gauge theory near the continuum limit. Our algorithm relies on simulated tempering across a range of couplings, which guarantees the decorrelation of the topological charge and ergodic sampling of topological sectors. Particular emphasis is placed on testing the accuracy, efficiency and scaling properties of the method. In their most conservative interpretation, our results provide firm evidence of a sizeable reduction of the exponent z related to the growth of the autocorrelation time as a function of the inverse lattice spacing