Frame-like Lagrangians and presymplectic AKSZ-type sigma models

We study supergeometric structures underlying frame-like Lagrangians. We show that for the theory in n spacetime dimensions both the frame-like Lagrangian and its gauge symmetries are encoded in the target supermanifold equipped with the odd vector field, the closed 2-form of ghost degree n-1, and the scalar potential of ghost degree n. These structures satisfy a set of compatibility conditions ensuring the gauge invariance of the theory. The Lagrangian and the gauge symmetries have the same structures as those of AKSZ sigma model so that frame-like formulation can be seen as its presymplectic generalization. In contrast to the conventional AKSZ model the generalization allows to describe systems with local degrees of freedom in terms of finite-dimensional target space. We argue that the proposed frame-like approach is directly related de Donder-Weyl polymomentum Hamiltonian formalism. Along with the standard field-theoretical examples like Einstein-Yang-Mills theory we consider free higher spin fields, multi-frame gravity, and parameterized systems. In particular, we propose the frame-like action for free totally symmetric massless fields that involves all higher spin connections on an equal footing.Comment: 28 pages; v2: references added; v3: 34 pages, exposition improved, typos removed, comments and refs added, new section 3.6.3 added with an action for spin-s massless fields involving all HS connections on an equal footin

Uniformizing higher-spin equations

Vasiliev's higher-spin theories in various dimensions are uniformly represented as a simple system of equations. These equations and their gauge invariances are based on two superalgebras and have a transparent algebraic meaning. For a given higher-spin theory these algebras can be inferred from the vacuum higher-spin symmetries. The proposed system of equations admits a concise AKSZ formulation. We also discuss novel higher-spin systems including partially-massless and massive fields in AdS, as well as conformal and massless off-shell fields.Comment: 29 pages, references added, final versio

Electrostatic Point Charge Fitting as an Inverse Problem: Revealing the Underlying Ill-Conditioning

Atom-centered point charge model of the molecular electrostatics---a major workhorse of the atomistic biomolecular simulations---is usually parameterized by least-squares (LS) fitting of the point charge values to a reference electrostatic potential, a procedure that suffers from numerical instabilities due to the ill-conditioned nature of the LS problem. Here, to reveal the origins of this ill-conditioning, we start with a general treatment of the point charge fitting problem as an inverse problem, and construct an analytically soluble model with the point charges spherically arranged according to Lebedev quadrature naturally suited for the inverse electrostatic problem. This analytical model is contrasted to the atom-centered point-charge model that can be viewed as an irregular quadrature poorly suited for the problem. This analysis shows that the numerical problems of the point charge fitting are due to the decay of the curvatures corresponding to the eigenvectors of LS sum Hessian matrix. In part, this ill-conditioning is intrinsic to the problem and related to decreasing electrostatic contribution of the higher multipole moments, that are, in the case of Lebedev grid model, directly associated with the Hessian eigenvectors. For the atom-centered model, this association breaks down beyond the first few eigenvectors related to the high-curvature monopole and dipole terms; this leads to even wider spread-out of the Hessian curvature values. Using these insights, it is possible to alleviate the ill-conditioning of the LS point-charge fitting without introducing external restraints and/or constraints. Also, as the analytical Lebedev grid PC model proposed here can reproduce multipole moments up to a given rank, it may provide a promising alternative to including explicit multipole terms in a force field

Probing a Secluded U(1) at B-factories

A secluded U(1) gauge field, kinetically mixed with Standard Model hypercharge, provides a `portal' mediating interactions with a hidden sector at the renormalizable level, as recently exploited in the context of WIMP dark matter. The secluded U(1) symmetry-breaking scale may naturally be suppressed relative to the weak scale, and so this sector is efficiently probed by medium energy electron-positron colliders. We study the collider signatures of the minimal secluded U(1) model, focusing on the reach of B-factory experiments such as BaBar and BELLE. In particular, we show that Higgs-strahlung in the secluded sector can lead to multi-lepton signatures which probe the natural range for the kinetic mixing angle of 10^(-2)-10^(-3) over a large portion of the kinematically accessible parameter space.Comment: 14 pages, 3 figure

Genetic Algorithm Optimization of Point Charges in Force Field Development: Challenges and Insights

Evolutionary methods, such as genetic algorithms (GAs), provide powerful tools for optimization of the force field parameters, especially in the case of simultaneous fitting of the force field terms against extensive reference data. However, GA fitting of the nonbonded interaction parameters that includes point charges has not been explored in the literature, likely due to numerous difficulties with even a simpler problem of the least-squares fitting of the atomic point charges against a reference molecular electrostatic potential (MEP), which often demonstrates an unusually high variation of the fitted charges on buried atoms. Here, we examine the performance of the GA approach for the least-squares MEP point charge fitting, and show that the GA optimizations suffer from a magnified version of the classical buried atom effect, producing highly scattered yet correlated solutions. This effect can be understood in terms of the linearly independent, natural coordinates of the MEP fitting problem defined by the eigenvectors of the least-squares sum Hessian matrix, which are also equivalent to the eigenvectors of the covariance matrix evaluated for the scattered GA solutions. GAs quickly converge with respect to the high-curvature coordinates defined by the eigenvectors related to the leading terms of the multipole expansion, but have difficulty converging with respect to the low-curvature coordinates that mostly depend on the buried atom charges. The performance of the evolutionary techniques dramatically improves when the point charge optimization is performed using the Hessian or covariance matrix eigenvectors, an approach with a significant potential for the evolutionary optimization of the fixed-charge biomolecular force fields

On a Nonlocal Ostrovsky-Whitham Type Dynamical System, Its Riemann Type Inhomogeneous Regularizations and Their Integrability

Short-wave perturbations in a relaxing medium, governed by a special reduction of the Ostrovsky evolution equation, and later derived by Whitham, are studied using the gradient-holonomic integrability algorithm. The bi-Hamiltonicity and complete integrability of the corresponding dynamical system is stated and an infinite hierarchy of commuting to each other conservation laws of dispersive type are found. The well defined regularization of the model is constructed and its Lax type integrability is discussed. A generalized hydrodynamical Riemann type system is considered, infinite hierarchies of conservation laws, related compatible Poisson structures and a Lax type representation for the special case N=3 are constructed