Abstract
Any local gauge theory can be represented as an AKSZ sigma model (upon parameterization if necessary). However, for non-topological models in dimension higher than 1 the target space is necessarily infinite-dimensional. The interesting alternative known for some time is to allow for degenerate presymplectic structure in the target space. This leads to a very concise AKSZ-like representation for frame-like Lagrangians of gauge systems. In this work we concentrate on Einstein gravity and show that not only the Lagrangian but also the full-scale Batalin-Vilkovisky (BV) formulation is naturally encoded in the presymplectic AKSZ formulation, giving an elegant supergeometrical construction of BV for Cartan-Weyl action. The same applies to the main structures of the respective Hamiltonian BFV formulation.
Highlights
This approach known as the Lagrangian parent formulation has certain remarkable features
In this work we concentrate on Einstein gravity and show that the Lagrangian and the full-scale Batalin-Vilkovisky (BV) formulation is naturally encoded in the presymplectic AKSZ formulation, giving an elegant supergeometrical construction of BV for Cartan-Weyl action
These have the form of finite-dimensional AKSZ sigma models whose target space presymplectic structure is allowed to be degenerate
Summary
Let (V, η) be a Minkowski space V of n-dimensions. In the basis ea the metric coefficients are ηab = η(ea, eb). It is useful to identify translations with V itself and Lorentz subalgebra as V ∧ V This gives a natural basis Ta = ea, Lbc = eb ∧ ec in the Poincare algebra. Functions eaμ(x), ωμab(x) can be taken as coordinates on the space of maps and are naturally identified with the components of the frame field and Lorentz connection. In view of this identification it is natural to restrict to maps such that eaμ(x) is invertible. Where fields ea, ωab parameterize σ according to (2.7) and the wedge product of space-time differential forms is assumed
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
