A toy model for background independent string field theory

Grigoriev, Maxim; Meyer, Adiel; Sachs, Ivo

doi:10.1007/jhep05(2022)020

Cited by 4 publications

(1 citation statement)

References 40 publications

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“…The above BFV-BRST interpretation of the off-shell Segal system was proposed in [47] (see also [71,131]). It is a useful starting point to construct the respective parent reformulation [47], from which the parent Segal system is obtained by gauge-fixing the gauge fields associated to Weyl transformations.…”

Section: Data Availability Statementmentioning

confidence: 95%

Covariant action for conformal higher spin gravity

Basile,

Grigoriev,

Skvortsov

2023

J. Phys. A: Math. Theor.

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Conformal Higher Spin Gravity is a higher spin extension of Weyl gravity and is a family of local higher spin theories, which was put forward by Segal and Tseytlin. We propose a manifestly covariant and coordinate-independent action for these theories. The result is based on an interplay between higher spin symmetries and deformation quantization: a locally equivalent but manifestly background-independent reformulation, known as the parent system, of the off-shell multiplet of conformal higher spin fields (Fradkin--Tseytlin fields) can be interpreted in terms of Fedosov deformation quantization of the underlying cotangent bundle. This brings into the game the invariant quantum trace, induced by the Feigin--Felder--Shoikhet cocycle of Weyl algebra, which extends Segal's action into a gauge invariant and globally well-defined action functional on the space of configurations of the parent system. The same action can be understood within the worldline approach as a correlation function in the topological quantum mechanics on the circle.

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Section: Data Availability Statementmentioning

confidence: 95%

Covariant action for conformal higher spin gravity

Basile,

Grigoriev,

Skvortsov

2023

J. Phys. A: Math. Theor.

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Manifestly covariant worldline actions from coadjoint orbits. Part I. Generalities and vectorial descriptions

Basile,

Joung,

2024

J. High Energ. Phys.

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We derive manifestly covariant actions of spinning particles starting from coadjoint orbits of isometry groups, by using Hamiltonian reductions. We show that the defining conditions of a classical Lie group can be treated as Hamiltonian constraints which generate the coadjoint orbits of another, dual, Lie group. In case of (inhomogeneous) orthogonal groups, the dual groups are (centrally-extended inhomogeneous) symplectic groups. This defines a symplectic dual pair correspondence between the coadjoint orbits of the isometry group and those of the dual Lie group, whose quantum version is the reductive dual pair correspondence à la Howe. We show explicitly how various particle species arise from the classification of coadjoint orbits of Poincaré and (A)dS symmetry. In the Poincaré case, we recover the data of the Wigner classification, which includes continuous spin particles, (spinning) tachyons and null particles with vanishing momenta, besides the usual massive and massless spinning particles. In (A)dS case, our classification results are not only consistent with the pattern of the corresponding unitary irreducible representations observed in the literature, but also contain novel information. In dS, we find the presence of partially massless spinning particles, but continuous spin particles, spinning tachyons and null particles are absent. The AdS case shows the largest diversity of particle species. It has all particles species of Poincaré symmetry except for the null particle, but allows in addition various exotic entities such as one parameter extension of continuous particles and conformal particles living on the boundary of AdS. Notably, we also find a large class of particles living in “bitemporal” AdS space, including ones where mass and spin play an interchanged role. We also discuss the relative inclusion structure of the corresponding orbits.

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Yang-Mills theory from the worldline

Bonezzi

2024

Phys. Rev. D

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We construct off-shell vertex operators for the bosonic spinning particle. Using the language of homotopy algebras, we show that the full nonlinear structure of Yang-Mills theory, including its gauge transformations, is encoded in the commutator algebra of the worldline vertex operators. To do so, we deform the worldline Becchi-Rouet-Stora-Tyutin (BRST) operator by coupling it to a background gauge field and show that the coupling is consistent on a suitable truncation of the Hilbert space. On this subspace, the square of the BRST operator is proportional to the Yang-Mills field equations, which we interpret as an operator Maurer-Cartan equation for the background. This allows us to define further vertex operators in different ghost numbers, which correspond to the entire L∞ algebra of Yang-Mills theory. Besides providing a precise map of a fully nonlinear field theory into a worldline model, we expect these results will be valuable to investigate the kinematic algebra of Yang-Mills theory, which is central to the double copy program. Published by the American Physical Society 2024

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A toy model for background independent string field theory

Cited by 4 publications

References 40 publications

Covariant action for conformal higher spin gravity

Covariant action for conformal higher spin gravity

Manifestly covariant worldline actions from coadjoint orbits. Part I. Generalities and vectorial descriptions

Yang-Mills theory from the worldline

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