A gravitational action with stringy $Q$ and $R$ fluxes via deformed differential graded Poisson algebras

DOI10.1007/JHEP12(2021)143arXiv2106.09601MaRDI QIDQ6370568

Peter Schupp, Eugenia Boffo

Publication date: 17 June 2021

Abstract: We study a deformation of a $2$-graded Poisson algebra where the functions of the phase space variables are complemented by linear functions of parity odd velocities. The deformation is carried by a $2$-form $B$-field and a bivector $Pi$, that we consider as gauge fields of the geometric and non-geometric fluxes $H$, $f$, $Q$ and $R$ arising in the context of string theory compactification. The technique used to deform the Poisson brackets is widely known for the point particle interacting with a $U(1)$ gauge field, but not in the case of non-abelian or higher spin fields. The construction is closely related to Generalized Geometry: With an element of the algebra that squares to zero, the graded symplectic picture is equivalent to an exact Courant algebroid over the generalized tangent bundle $EcongTMoplus{T}^{*}M$, and to its higher gauge theory. A particular idempotent graded canonical transformation is equivalent to the generalized metric. Focusing on the generalized differential geometry side we construct an action functional with the Ricci tensor of a connection on covectors, encoding the dynamics of a gravitational theory for a contravariant metric tensor and $Q$ and $R$ fluxes. We also extract a connection on vector fields and determine a non-symmetric metric gravity theory involving a metric and $H$-flux.

Mathematics Subject Classification ID

String and superstring theories in gravitational theory (83E30) Supergravity (83E50) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) String and superstring theories; other extended objects (e.g., branes) in quantum field theory (81T30) Finite-dimensional groups and algebras motivated by physics and their representations (81R05) Poisson manifolds; Poisson groupoids and algebroids (53D17) Graded Lie (super)algebras (17B70) Relativistic gravitational theories other than Einstein's, including asymmetric field theories (83D05) Poisson algebras (17B63)

This page was built for publication: A gravitational action with stringy $Q$ and $R$ fluxes via deformed differential graded Poisson algebras

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6370568)