SU(N) gauge theories in 3+1 dimensions: glueball spectrum, string tensions and topology

We calculate the low-lying glueball spectrum, several string tensions and some properties of topology and the running coupling for SU(N) lattice gauge theories in 3 + 1 dimensions. We do so for 2 ≤ N ≤ 12, using lattice simulations with the Wilson plaquette action, and for glueball states in all the representations of the cubic rotation group, for both values of parity and charge conjugation. We extrapolate these results to the continuum limit of each theory and then to N = ∞. For a number of these states we are able to identify their continuum spins with very little ambiguity. We calculate the fundamental string tension and k = 2 string tension and investigate the N dependence of the ratio. Using the string tension as the scale, we calculate the running of a lattice coupling and confirm that g2(a) ∝ 1/N for constant physics as N → ∞. We fit our calculated values of a√σ with the 3-loop β-function, and extract a value for $$ {\Lambda}_{\overline{MS}} $$ Λ MS ¯ , in units of the string tension, for all our values of N, including SU(3). We use these fits to provide analytic formulae for estimating the string tension at a given lattice coupling. We calculate the topological charge Q for N ≤ 6 where it fluctuates sufficiently for a plausible estimate of the continuum topological susceptibility. We also calculate the renormalisation of the lattice topological charge, ZQ(β), for all our SU(N) gauge theories, using a standard definition of the charge, and we provide interpolating formulae, which may be useful in estimating the renormalisation of the lattice θ parameter. We provide quantitative results for how the topological charge ‘freezes’ with decreasing lattice spacing and with increasing N. Although we are able to show that within our typical errors our glueball and string tension results are insensitive to the freezing of Q at larger N and β, we choose to perform our calculations with a typical distribution of Q imposed upon the fields so as to further reduce any potential systematic errors.

Intriguing spin–lattice interactions in EuTiO3

During the last decade the cubic perovskite oxide EuTiO3 (ETO) has attracted enormous novel research activities due to possible multiferroicity, hidden magnetism far above its Néel temperature at TN = 5.5 K, structural instability at TS = 282 K, possible application as magneto-electric optic device, and strong spin–lattice coupling. Here we address a novel highlight of this compound by showing that well below TS a further structural phase transition occurs below 210 K without the application of an external magnetic field, and by questioning the assumed tetragonal symmetry of the structure below TS where tiny deviations from true tetragonality are observed by birefringence and XRD measurements. It is suggested that the competition in the second nearest neighbor spin–spin interaction modulated by the lattice dynamics is at the origin of these new observations.