Construction Of Lagrangian Research Articles

Minisuperspace description for inhomogeneous cosmological models and the role of the Lie symmetries

We explore the application of Lie symmetries to simplify the gravitational field equations of inhomogeneous cosmology. By employing these symmetries, we demonstrate the construction of a point-like Lagrangian and establish the existence of a minisuperspace description. Finally we show how the Lie symmetries can be applied to construct new solutions for the Wheeler-DeWitt equation.

Complete tree-level dictionary between simplified BSM models and SMEFT d≤7 operators

Finding all possible UV resonances of effective operators is an important task in the bottom-up approach of effective field theory. We present all the tree-level UV resonances for the dimension-5, -6, and -7 operators in the Standard Model effective field theory (SMEFT) and then obtain the correspondence between the UV resonances and the effective operators from the relations among their Wilson coefficients, through the functional matching and operator reduction procedure. This provides a cross-dimension UV/IR dictionary for the SMEFT at tree level, and the methods used here, especially the on shell construction of general UV Lagrangian and the systematic reduction of operators, are extendable for UV resonances of d≥8 operators in SMEFT and other effective field theories. Published by the American Physical Society 2024

Flavour constraints on light spin-1 bosons within a chiral Lagrangian approach

We discuss the construction of the chiral Lagrangian for a light spin-1 boson, here denoted as X, featuring both vector and axial-vector couplings to light u, d, s quarks. Focusing on ∆S = 1 transitions, we show that there are model-independent tree-level contributions to K±→ π±X, sourced by Standard Model charged currents, which receive an mK2/mX2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {m}_K^2/{m}_X^2 $$\\end{document} enhancement from the emission of a longitudinally polarized X. This flavour observable sets the strongest to date model-independent bound on the diagonal axial-vector couplings of X to u, d, s quarks for mX< mK– mπ, superseding the bounds arising from beam-dump and collider searches.

A Lagrangian construction of rotating star models

ABSTRACTWe present a new formulation for numerically obtaining axisymmetric equilibrium structures of rotating stars in two spatial dimensions. With a view to apply it to the secular evolution of rotating stars, we base it on the Lagrangian description, i.e. we solve the force-balance equations to find the spatial positions of fluid elements endowed individually with a mass, specific entropy and angular momentum. The system of non-linear equations obtained by finite-differencing the basic equations is solved with the W4 method, which is a new multidimensional root-finding scheme of our own devising. We augment it with a remapping scheme to avoid distortions of the Lagrangian coordinates. In this first one of a series of papers, we will give a detailed description of these methods initially. We then present the results of some test calculations, which include the construction of both rapidly rotating barotropic and baroclinic equilibrium states. We gauge their accuracies quantitatively with some diagnostic quantities as well as via comparisons with the counterparts obtained with an Eulerian code. For a demonstrative purpose, we apply the code to a toy-model cooling calculation of a rotating white dwarf.

A → πππ decay at next-to-leading order in chiral perturbation theory

We discuss the construction of the two-flavour axion-pion effective Lagrangian at the next-to-leading order (NLO) in chiral perturbation theory and present, as a phenomenological application, the calculation of the decay rate of a GeV-scale axion-like particle via the channel a → πππ. Through the NLO calculation, we assess the range of validity of the effective field theory and show that the chiral expansion breaks down just above the kinematic threshold. Alternative non-perturbative approaches are called for in order to extend the chiral description of axion-pion interactions.

Higher derivative scalar tensor theory in unitary gauge

Ostrogradsky instability generally appears in nondegenerate higher-order derivative theories and this issue can be resolved by removing any existing degeneracy present in such theories. We consider an action involving terms that are at most quadratic in second derivatives of the scalar field and non-minimally coupled with the curvature tensors. We perform a 3+1 decomposition of the Lagrangian to separate second-order time derivative terms from rest. This decomposition is useful for checking the degeneracy hidden in the Lagrangian and helps us find conditions under which Ostrogradsky instability does not appear. We show that our construction of Lagrangian resembles that of a GR-like theory for a particular case in the unitary gauge. As an example, we calculate the equation of motion for the flat FRW. We also write the action for open and closed cases, free from higher derivatives for a particular choice derived from imposing degeneracy conditions.

Quasi-split symmetric pairs of 𝑈(𝔰𝔩_{𝔫}) and Steinberg varieties of classical type

We provide a Lagrangian construction for the fixed-point subalgebra, together with its idempotent form, in a quasi-split symmetric pair of type A n − 1 A_{n-1} . This is obtained inside the limit of a projective system of Borel-Moore homologies of the Steinberg varieties of n n -step isotropic flag varieties. Arising from the construction are a basis of homological origin for the idempotent form and a geometric realization of rational modules.

Weyl group action on weight zero Mirković-Vilonen basis and equivariant multiplicities

We state a conjecture about the Weyl group action coming from Geometric Satake on zero-weight spaces in terms of equivariant multiplicities of Mirković-Vilonen cycles. We prove it for small coweights in type A. In this case, using work of Braverman, Gaitsgory and Vybornov, we show that the Mirković-Vilonen basis agrees with the Springer basis. We rephrase this in terms of equivariant multiplicities using work of Joseph and Hotta. We also have analogous results for Ginzburg's Lagrangian construction of sln representations.

Towards Lagrangian construction for infinite half-integer spin field

We formulate the conditions for the generalized fields in the space with additional commuting Weyl spinor coordinates which define the infinite half-integer spin representation of the four-dimensional Poincaré group. Using this formulation we develop the BRST approach and derive the Lagrangian for the half-integer infinite spin fields.

On-shell gauge invariant three-point fermion and boson amplitudes

A polynomial basis for parity-even three-point amplitudes of higher-spin massless fermions and bosons are derived in four-dimensional space–time from first principles. This basis can be used to construct three-point amplitudes of polarizations of any rank. The results are presented using polarization tensors and tensor-spinors, which is convenient when they are applied to Lagrangian construction.

On a global Lagrangian construction for ordinary variational equations on 2-manifolds

Locally variational systems of differential equations on smooth manifolds, having certain de Rham cohomology group trivial, automatically possess a global Lagrangian. This important result due to Takens is, how-ever, of sheaf-theoretic nature. A new constructive method of finding a global Lagrangian for second-order ODEs on 2-manifolds is described on the basis of solvability of exactness equation for Lepage 2-forms, and the top-cohomology theorems. Examples from geometry and mechanics are discussed.

Lagrangian description of the partially massless higher spin N = 1 supermultiplets in AdS4 space

In the recent paper [1] the classification of non-unitary representations of the three dimensional superconformal group has been constructed. From AdS/CFT they must correspond to N = 1 supermultiplets containing partially massless fields in AdS4. Moreover, the simplest example of such supermultiplets which contains a partially massless spin-2 was explicitly constructed. In this paper we extend this result and develop explicit Lagrangian construction of general N = 1 supermultiplets containing partially massless fields with arbitrary superspin. We use the frame-like gauge invariant description of partially massless higher spin bosonic and fermionic fields. For the two types of the supermultiplets (with integer and half-integer superspins) each one containing two partially massless bosonic and two partially massless fermionic fields we derive the supertransformations leaving the sum of their free Lagrangians invariant such that the AdS4 superalgebra is closed on-shell.

Lagrangian formulation for the infinite spin N = 1 supermultiplets in d = 4

We provide an explicit Lagrangian construction for the massless infinite spin N=1 supermultiplet in four dimensional Minkowski space. Such a supermultiplet contains a pair of massless bosonic and a pair of massless fermionic infinite spin fields with properly adjusted dimensionful parameters. We begin with the gauge invariant Lagrangians for such massless infinite spin bosonic and fermionic fields and derive the supertransformations which leave the sum of their Lagrangians invariant. It is shown that the algebra of these supertransformations is closed on-shell.

Lagrangian formulation of the massive higher spin N = 1 supermultiplets in AdS4 space

We give an explicit component Lagrangian construction of massive higher spin on-shell N=1 supermultiplets in four-dimensional Anti-de Sitter space AdS4. We use a frame-like gauge invariant description of massive higher spin bosonic and fermionic fields. For the two types of the supermultiplets (with integer and half-integer superspins) each one containing two massive bosonic and two massive fermionic fields we derive the supertransformations leaving the sum of four their free Lagrangians invariant such that the algebra of these supertransformations is closed on-shell.

Generalized AdS-Lorentz deformed supergravity on a manifold with boundary

The purpose of this paper is to explore the supersymmetry invariance of a particular supergravity theory, which we refer to as D = 4 generalized AdS-Lorentz deformed supergravity, in the presence of a non-trivial boundary. In particular, we show that the so-called generalized minimal AdS-Lorentz superalgebra can be interpreted as a peculiar torsion deformation of $\mathfrak{osp} (4 \vert 1)$ , and we present the construction of a bulk Lagrangian based on the aforementioned generalized AdS-Lorentz superalgebra. In the presence of a non-trivial boundary of space-time, that is when the boundary is not thought of as set at infinity, the fields do not asymptotically vanish, and this has some consequences on the invariances of the theory, in particular on supersymmetry invariance. In this work, we adopt the so-called rheonomic (geometric) approach in superspace and show that a supersymmetric extension of a Gauss-Bonnet-like term is required in order to restore the supersymmetry invariance of the theory. The action we end up with can be recast as a MacDowell-Mansouri-type action, namely as a sum of quadratic terms in the generalized AdS-Lorentz covariant super field-strengths.

On Lagrangian Construction of Massive Higher Spins Supermultiplets in 3D AdS

We give the component Lagrangian construction of the on-shell $$\mathcal{N} = 1$$ massive higher spin supermultiplets in three dimensional (3D) anti de Sitter ( $$AdS$$ ) space. The approach is based on the frame-like gauge invariant formulation, where massive higher spin fields are realized through a system of massless ones. We construct massive supermultiplets using a formulation of the massive fields in terms of the set of gauge invariant objects (curvatures) in the process of their consistent supersymmetric deformation.

BRST approach to Lagrangian construction for bosonic continuous spin field

We formulate the conditions defining the irreducible continuous spin representation of the four-dimensional Poincaré group based on spin-tensor fields with dotted and undotted indices. Such a formulation simplifies analysis of the Bargmann–Wigner equations and reduces the number of equations from four to three. Using this formulation we develop the BRST approach and derive the covariant Lagrangian for the continuous spin fields.

Higher derivative theories for interacting massless gravitons in Minkowski spacetime

We study a novel class of higher derivative theories for interacting massless gravitons in Minkowski spacetime. These theories were first discussed by Wald decades ago, and are characterized by scattering amplitudes essentially different from general relativity and many of its modifications. We discuss various aspects of these higher derivative theories, including the Lagrangian construction, violation of asymptotic causality, scattering amplitudes, non-renormalization, and possible implications in emergent gravitons from condensed matter systems.

A dual approach to solving a multi-objective assignment problem

Two approximation algorithms applied for solving the multi-objective assignment problem (MOAP) are proposed. The reduction to the single-objective problem is realized and dual Uzawa method is applied. The differences between algorithms are the Lagrangian construction technics, the application technics of Hungarian method or independent column minimization in each iteration. The results of the comparative computational experiment are presented.

Supersymmetric Higher Spin Models in Three Dimensional Spaces

We review the component Lagrangian construction of the supersymmetric higher spin models in three-dimensional (3D) Minkowski and anti de Sitter ( A d S ) spaces. The approach is based on the frame-like gauge-invariant formulation, where massive higher spin fields are realized through a system of massless ones. We develop a supersymmetric generalization of this formulation to the Lagrangian construction of the on-shell N = 1 , 3D higher spin supermultiplets. In 3D Minkowski space, we show that the massive supermultiplets can be constructed from one extended massless supermultiplet by adding the mass terms to the Lagrangian and the corresponding corrections to the supertransformations of the fermionic fields. In 3D A d S space, we construct massive supermultiplets using a formulation of the massive fields in terms of the set of gauge-invariant objects (curvatures) in the process of their consistent supersymmetric deformation.