Frame-like Lagrangians and presymplectic AKSZ-type sigma models

Abstract

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.

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 footing

References in corpus (7)

• Interacting Spin-2 Fields
• Frame-like Actions for Massless Mixed-Symmetry Fields in Minkowski space
• Toward frame-like gauge invariant formulation for massive mixed symmetry bosonic fields
• First Order Formalism for Mixed Symmetry Tensor Fields
• First order parent formulation for generic gauge field theories
• Parent formulations, frame-like Lagrangians, and generalized auxiliary fields
• Parent formulation at the Lagrangian level

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• Presymplectic BV-AKSZ formulation of Conformal Gravity
• Minimal models of field theories: SDYM and SDGR
• General Relativity and the AKSZ construction
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• Chiral approach to partially-massless fields
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• Massless chiral fields in six dimensions
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• Gravity from AKSZ-Manin theories in two, three, and four dimensions
• On presymplectic structures for massless higher-spin fields
• Consistent deformations in the presymplectic BV-AKSZ approach
• Homotopy Manin Theories: Generalising Third-Way, Yang-Mills and Integrable Sigma Models
• Generalized sigma model with dynamical antisymplectic potential and non-Abelian de Rham's differential