One-loop beta-function for an infinite-parameter family of gauge theories

We continue to study an infinite-parametric family of gauge theories with an arbitrary function of the self-dual part of the field strength as the Lagrangian. The arising one-loop divergences are computed using the background field method. We show that they can all be absorbed by a local redefinition of the gauge field, as well as multiplicative renormalisations of the couplings. Thus, this family of theories is one-loop renormalisable. The infinite set of beta-functions for the couplings is compactly stored in a renormalisation group flow for a single function of the curvature. The flow is obtained explicitly.Comment: 17 pages, no figure

Extracting excited states from lattice QCD: the Roper resonance

We present a new method for extracting excited states from a single two-point correlation function calculated on the lattice. Our method simply combines the correlation function evaluated at different time slices so as to ``subtract'' the leading exponential decay (ground state) and to give access to the first excited state. The method is applied to a quenched lattice study (volume = 24^3 x 64, beta = 6.2, 1/a = 2.55 GeV) of the first excited state of the nucleon using the local interpolating operator O = [uT C gamma5 d] u. The results are consistent with the identification of our extracted excited state with the Roper resonance N'(1440). The switching of the level ordering with respect to the negative-parity partner of the nucleon, N*(1535), is not seen at the simulated quark masses and, basing on crude extrapolations, is tentatively expected to occur close to the physical point.Comment: version to apper in Phys. Lett. B; additions in the presentation of the method; 3 references added; no change in the results and in the figure

Virasoro conformal blocks in closed form

Virasoro conformal blocks are fixed in principle by symmetry, but a closed-form expression is unknown in the general case. In this work, we provide three closed-form expansions for the four-point Virasoro blocks on the sphere, for arbitrary operator dimensions and central charge $c$. We do so by solving known recursion relations. One representation is a sum over hypergeometric global blocks, whose coefficients we provide at arbitrary level. Another is a sum over semiclassical Virasoro blocks obtained in the limit in which two external operator dimensions scale linearly with large $c$. In both cases, the $1/c$ expansion of the Virasoro blocks is easily extracted. We discuss applications of these expansions to entanglement and thermality in conformal field theories and particle scattering in three-dimensional quantum gravity.Comment: 24 pages + appendices. v2: added refs, minor corrections, improved discussion of Sec.

Integrability in the mesoscopic dynamics

The Mesoscopic Mechanics (MeM), which has been introduced in a previous paper, is relevant to the electron gas confined to two spatial dimensions. It predicts a special way of collective response of correlated electrons to the external magnetic field. The dynamic variable of this theory is a finite-dimensional operator, which is required to satisfy the mesoscopic Schr\"{o}dinger equation (cf. text). In this article, we describe general solutions of the mesoscopic Schr\"{o}dinger equation. Our approach is specific to the problem at hand. It relies on the unique structure of the equation and makes no reference to any other techniques, with the exception of the geometry of unitary groups. In conclusion, a surprising fact comes to light. Namely, the mesoscopic dynamics "filters" through the (microscopic) Schr\"odinger dynamics as the latter turns out to be a clearly separable part, in fact an autonomous factor, of the evolution. This is a desirable result also from the physical standpoint

Partial order and a T0T_0-topology in a set of finite quantum systems

A `whole-part' theory is developed for a set of finite quantum systems $\Sigma (n)$ with variables in ${\mathbb Z}(n)$. The partial order `subsystem' is defined, by embedding various attributes of the system $\Sigma (m)$ (quantum states, density matrices, etc) into their counterparts in the supersystem $\Sigma (n)$ (for $m|n$). The compatibility of these embeddings is studied. The concept of ubiquity is introduced for quantities which fit with this structure. It is shown that various entropic quantities are ubiquitous. The sets of various quantities become $T_0$-topological spaces with the divisor topology, which encapsulates fundamental physical properties. These sets can be converted into directed-complete partial orders (dcpo), by adding `top elements'. The continuity of various maps among these sets is studied