Andrei V. Smilga

Nucleon magnetic moments and magnetic properties of the vacuum in QCD

Abstract Magnetic moments of a proton and a neutron are calculated in the QCD sum rule approach. The substantial role of the external electromagnetic field induced vacuum expectation values, the most important of which is connected with quark condensate magnetic susceptibility, is demonstrated. The results are μp = 3.0, μn = −2.0(±105) which is in perfect agreement with experiment. The invariant amplitudes of the Δ →pγ transition are also calculated.

Meson widths and form factors at intermediate momentum transfer in non-perturbative QCD

Abstract A general method is proposed for the QCD based calculations of form factors at intermediate Q 2 and of the partial widths of the low-lying mesonic resonances. The basic idea is to use the QCD sum rules for the vertex functions and to saturate their Borel transform by the lowest mesonic states. With this method the pion electromagnetic form factor along with electromagnetic form factors of ϱ and A 1 mesons and transition form factors γπ →A 1 at 0.5≲ Q 2 ≲3 GeV 2 are calculated. The widths ϱ →2 π and A 1 → ϱπ are also determined. The results are in a good agreement with experiment.

A central back-coupling hypothesis on the organization of motor synergies: a physical metaphor and a neural model

Abstract.We offer a hypothesis on the organization of multi-effector motor synergies and illustrate it with the task of force production with a set of fingers. A physical metaphor, a leaking bucket, is analyzed to demonstrate that an inanimate structure can show apparent error compensation among its elements. A neural model is developed using tunable back-coupling loops as means of assuring error compensation in a task-specific way. The model demonstrates non-trivial features of multi-finger interaction such as delayed emergence of force stabilizing synergies and simultaneous stabilization of the total force and total moment produced by the fingers. The hypothesis suggests that neurophysiological structures involving short-latency feedback may play a central role in the formation of motor synergies.

Pion formfactor at intermediate momentum transfer in QCD

Abstract A general method is proposed for the QCD based calculation of formfactors at intermediate Q 2 and of the partial widths of the low-lying mesonic resonances. The basic idea is to use the QCD sum rules for the vertex functions and to saturate their Borel transform by the lowest mesonic states. With this method, the pion formfactor at 0.5 ⪅ Q 2 ⪅ 4 GeV 2 is calculated. The results are in a good agreement with experiment.

SCREENING VERSUS CONFINEMENT IN 1+1 DIMENSIONS

Abstract We show that, in (1 + 1)-dimensional gauge theories, a heavy probe charge is screened by dynamical massless fermions both in the case when the source and the dynamical fermions belong to the same representation of the gauge group and, unexpectedly, in the case when the representation of the probe charge is smaller than the representation of the massless fermions. Thus, a fractionally charged heavy probe is screened by dynamical fermions of integer charge in the massless Schwinger model, and a colored probe in the fundamental representation is screened in QCD 2 with adjoint massless Majorana fermions. The screening disappears and confinement is restored as soon as the dynamical fermions are given a non-zero mass. For small masses, the string tension is given by the product of the light fermion mass and the fermion condensate with a known numerical coefficient. Parallels with (3 + 1)-dimensional QCD and supersymmetric gauge theories are discussed.

Normalized vacuum states in N=4 supersymmetric Yang–Mills quantum mechanics with any gauge group

Abstract We study the question of existence and the number of normalized vacuum states in N =4 super-Yang–Mills quantum mechanics for any gauge group. The mass deformation method is the simplest and clearest one. It allowed us to calculate the number of normalized vacuum states for all gauge groups. For all unitary groups, #vac=1, but for the symplectic groups [starting from Sp(6) ], for the orthogonal groups [starting from SO(8)] and for all the exceptional groups, it is greater than one. We also discuss at length the functional integral method. We calculate the “deficit term” for some non-unitary groups and predict the value of the integral giving the “principal contribution”. The issues like the Born–Oppenheimer procedure to derive the effective theory and the manifestation of the localized vacua in the asymptotic effective wave functions are also discussed.

Really computing nonperturbative real time correlation functions

It has been argued by Grigoriev and Rubakov that one can simulate real time processes involving baryon number nonconservation at high temperature using real time evolution of classical equations, and summing over initial conditions with a classical thermal weight. It is known that such a naive algorithm is plagued by ultraviolet divergences. In quantum theory the divergences are regularized, but the corresponding graphs involve the contributions from the hard momentum region and also the new scale {similar_to}{ital gT} comes into play. We propose a modified algorithm which involves solving the classical equations of motion for the effective hard thermal loop Hamiltonian with an ultraviolet cutoff {mu}{much_gt}{ital gT} and integrating over initial conditions with a proper thermal weight. Such an algorithm should provide a determination of the infrared behavior of the real time correlation function {l_angle}{ital Q}({ital t}){ital Q}(0){r_angle}{sub {ital T}} determining the baryon violation rate. Hopefully, the results obtained in this modified algorithm will be cutoff independent.

Vacuum structure in supersymmetric Yang-Mills theories with any gauge group

We consider the pure supersymmetric Yang--Mills theories placed on a small 3-dimensional spatial torus with higher orthogonal and exceptional gauge groups. The problem of constructing the quantum vacuum states is reduced to a pure mathematical problem of classifying the flat connections on 3-torus. The latter problem is equivalent to the problem of classification of commuting triples of elements in a connected simply connected compact Lie group which is solved in this paper. In particular, we show that for higher orthogonal SO(N), N > 6, and for all exceptional groups the moduli space of flat connections involves several distinct connected components. The total number of vacuumstates is given in all cases by the dual Coxeter number of the group which agrees with the result obtained earlier with the instanton technique.

Renormalizable supersymmetric gauge theory in six dimensions

Abstract We construct and discuss a 6D supersymmetric gauge theory involving four derivatives in the action. The theory involves a dimensionless coupling constant and is renormalizable. At the tree level, it enjoys N = ( 1 , 0 ) superconformal symmetry, but the latter is broken by quantum anomaly. Our study should be considered as preparatory for seeking an extended version of this theory which would hopefully preserve conformal symmetry at the full quantum level and be ultraviolet-finite.

Supersymmetric gauge quantum mechanics: superfield description

Abstract The superfield formulation of a class of SUSY quantum-mechanical systems connected with effective (0 + 1)-dimensional hamiltonians of supersymmetric gauge theories is proposed. These provide us with supersymmetric d = 1 σ -models of a new type: their bosonic target manifolds are 3 m -dimensional ( m is an integer) with the metrics of a special form, and they enjoy N = 2 supersymmetry. They are constructed (in a peculiar way, specific for d =1) from d =2 vector gauge supermultiplets reduced to 0 + 1 dimensions. A reasonable generalization of these models to higher dimensions is absent.