Interpolation Parameter and Expansion for the Three Dimensional Non-Trivial Scalar Infrared Fixed Point

We compute the non--trivial infrared $\phi^4_3$--fixed point by means of an interpolation expansion in fixed dimension. The expansion is formulated for an infinitesimal momentum space renormalization group. We choose a coordinate representation for the fixed point interaction in derivative expansion, and compute its coordinates to high orders by means of computer algebra. We compute the series for the critical exponent $\nu$ up to order twenty five of interpolation expansion in this representation, and evaluate it using \pade, Borel--\pade, Borel--conformal--\pade, and Dlog--\pade resummation. The resummation returns $0.6262(13)$ as the value of $\nu$.Comment: 29 pages, Latex2e, 2 Postscript figure

Chiral Modulations in Curved Space I: Formalism

The goal of this paper is to present a formalism that allows to handle four-fermion effective theories at finite temperature and density in curved space. The formalism is based on the use of the effective action and zeta function regularization, supports the inclusion of inhomogeneous and anisotropic phases. One of the key points of the method is the use of a non-perturbative ansatz for the heat-kernel that returns the effective action in partially resummed form, providing a way to go beyond the approximations based on the Ginzburg-Landau expansion for the partition function. The effective action for the case of ultra-static Riemannian spacetimes with compact spatial section is discussed in general and a series representation, valid when the chemical potential satisfies a certain constraint, is derived. To see the formalism at work, we consider the case of static Einstein spaces at zero chemical potential. Although in this case we expect inhomogeneous phases to occur only as meta-stable states, the problem is complex enough and allows to illustrate how to implement numerical studies of inhomogeneous phases in curved space. Finally, we extend the formalism to include arbitrary chemical potentials and obtain the analytical continuation of the effective action in curved space.Comment: 22 pages, 3 figures; version to appear in JHE

Limited transfer and retention of locomotor adaptations from virtual reality obstacle avoidance to the physical world.

Locomotor training based in virtual reality (VR) is promising for motor skill learning, with transfer of VR skills in turn required to benefit daily life locomotion. This study aimed to assess whether VR-adapted obstacle avoidance can be transferred to a physical obstacle and whether such transfer is retained after 1 week. Thirty-two young adults were randomly divided between two groups. A control group (CG) merely walked on a treadmill and an intervention group (IG) trained crossing 50 suddenly-appearing virtual obstacles. Both groups crossed three physical obstacles (transfer task) immediately after training (T1) and 1 week later (T2, transfer retention). Repeated practice in VR led to a decrease in toe clearance along with greater ankle plantarflexion and knee extension. IG participants crossed physical obstacles with a lower toe clearance compared to CG but revealed significantly higher values compared to the VR condition. VR adaptation was fully retained over 1 week. For physical obstacle avoidance there were differences between toe clearance of the third obstacle at T1 and the first obstacle at T2, indicating only partial transfer retention. We suggest that perception-action coupling, and thus sensorimotor coordination, may differ between VR and the physical world, potentially limiting retained transfer between conditions. [Abstract copyright: © 2022. The Author(s).

New bounds on trilinear R-parity violation from lepton flavor violating observables

Many extensions of the leptonic sector of the Minimal Supersymmetric Standard Model (MSSM) are known, most of them leading to observable flavor violating effects. It has been recently shown that the 1-loop contributions to lepton flavor violating three-body decays $l_i \to 3 l_j$ involving the $Z^0$ boson may be dominant, that is, much more important than the usual photonic penguins. Other processes like $\mu$-$e$ conversion in nuclei and flavor violating $\tau$ decays into mesons are also enhanced by the same effect. This is for instance also the case in the MSSM with trilinear R-parity violation. The aim of this work is to derive new bounds on the relevant combinations of R-parity violating couplings and to compare them with previous results in the literature. For heavy supersymmetric spectra the limits are improved by several orders of magnitude. For completeness, also constraints coming from flavor violating $Z^0$-decays and tree-level decay channels $l \to l_i l_j l_k$ are presented for a set of benchmark points.Comment: 21 pages; 5 figures; v2: corrected bug, conclusion unchange

Critical behavior of two-dimensional cubic and MN models in the five-loop renormalization-group approximation

The critical thermodynamics of the two-dimensional N-vector cubic and MN models is studied within the field-theoretical renormalization-group (RG) approach. The beta functions and critical exponents are calculated in the five-loop approximation and the RG series obtained are resummed using the Borel-Leroy transformation combined with the generalized Pad\'e approximant and conformal mapping techniques. For the cubic model, the RG flows for various N are investigated. For N=2 it is found that the continuous line of fixed points running from the XY fixed point to the Ising one is well reproduced by the resummed RG series and an account for the five-loop terms makes the lines of zeros of both beta functions closer to each another. For the cubic model with N\geq 3, the five-loop contributions are shown to shift the cubic fixed point, given by the four-loop approximation, towards the Ising fixed point. This confirms the idea that the existence of the cubic fixed point in two dimensions under N>2 is an artifact of the perturbative analysis. For the quenched dilute O(M) models ($MN$ models with N=0) the results are compatible with a stable pure fixed point for M\geq1. For the MN model with M,N\geq2 all the non-perturbative results are reproduced. In addition a new stable fixed point is found for moderate values of M and N.Comment: 26 pages, 3 figure

Theory of combined exciton-cyclotron resonance in a two-dimensional electron gas: The strong magnetic field regime

I develop a theory of combined exciton-cyclotron resonance (ExCR) in a low-density two-dimensional electron gas in high magnetic fields. In the presence of excess electrons an incident photon creates an exciton and simultaneously excites one electron to higher-lying Landau levels. I derive exact ExCR selection rules that follow from the existing dynamical symmetries, magnetic translations and rotations about the magnetic field axis. The nature of the final states in the ExCR is elucidated. The relation between ExCR and shake-up processes is discussed. The double-peak ExCR structure for transitions to the first electron Landau level is predicted.Comment: 5 pages, 3 figures, replaced with the published versio

New extended high temperature series for the N-vector spin models on three-dimensional bipartite lattices

High temperature expansions for the susceptibility and the second correlation moment of the classical N-vector model (O(N) symmetric Heisenberg model) on the sc and the bcc lattices are extended to order $\beta^{19}$ for arbitrary N. For N= 2,3,4.. we present revised estimates of the critical parameters from the newly computed coefficients.Comment: 11 pages, latex, no figures, to appear in Phys. Rev.

Obstacle avoidance training in virtual environments leads to limb-specific locomotor adaptations but not to interlimb transfer in healthy young adults.

Obstacle avoidance is one of the skills required in coping with challenging situations encountered during walking. This study examined adaptation in gait stability and its interlimb transfer in a virtual obstacle avoidance task. Twelve young adults walked on a treadmill while wearing a virtual reality headset with their body state represented in the virtual environment. At random times, but always at foot touchdown, 50 virtual obstacles of constant size appeared 0.8 m in front of the participant requiring a step over with the right leg. Early, mid and late adaptation phases were investigated by pooling data from trials 1-3, 24-26 and 48-50. One left-leg obstacle appearing after 50 right-leg trials was used to investigate interlimb transfer. Toe clearance and the anteroposterior margin of stability (MoS) at foot touchdown were calculated for the stepping leg. Toe clearance decreased over repeated practice between early and late phases from 0.13 ± 0.05 m to 0.09 ± 0.04 m (mean ± SD, p < 0.05). MoS increased from 0.05 ± 0.02 m to 0.08 ± 0.02 m (p < 0.05) between early and late phases, with no significant differences between mid and late phases. No differences were found in toe clearance and MoS between the practiced right leg for early phase and the single trial of the left leg. Obstacle avoidance during walking in a virtual environment stimulated adaptive gait improvements that were related in a nonlinear manner to practice dose, though such gait adaptations seemed to be limited in their transferability between limbs. [Abstract copyright: Copyright © 2021 Elsevier Ltd. All rights reserved.