Dual gravity with $R$ flux from graded Poisson algebra

Abstract

We suggest a new action for a "dual" gravity in a stringy R, Q flux background. The construction is based on degree-2 graded symplectic geometry with a homological vector field. The structure we consider is non-canonical and features a curvature-free connection. It is known that the data of Poisson structures of degree 2 with a Hamiltonian correspond to a Courant algebroid on T M ⊕ T * M, the bundle of generalized geometry. With the bracket for the Courant algebroid and a further bracket which resembles the Lie bracket of vector fields, we get a connection with nonzero curvature for the bundle of generalized geometry. The action is the (almost) Hilbert-Einstein action for that connection.

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

“…In this way, and by the chosen particular deformation with a 2-form B and a bivector Π, dependent on B, we could interpret the stringy 3-form H and the connection coefficients Q and R (where the first has 1 contravariant and 2 covariant indices, and the latter is a trivector) as formal "field strengths" of B and Π. In our companion work [30] we considered a deformation based only the open string quantities G −1 and Π, and obtained the same action functional. Usually in dg-symplectic geometry the stringy fluxes appear in the Hamiltonian, and are responsible for a twisting of the Dorfman bracket of the associated CA.…”

“…In this context we do not need a deeper understanding of closed and open string theory but the relation between the quadruplet of tensors (g, B, G, Π) stated by (2.24). In our related work [30] we analyzed a similar generalized vielbein, with the upper right block put to zero. The vielbein used here returns a class of block diagonal metrics, i.e.…”

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

“…In the connections, we could interpret the stringy 3-form H and the connection coefficients Q and R (where the first has 1 contravariant and 2 covariant indices, and the latter is a trivector) as formal "field strengths" of B and Π. In our companion work [37] we considered a deformation based only on the open string quantities G −1 and Π, and obtained the same connection for the 1-forms. Hence our approach via deformation yields global objects (connections, actions) and brings up the non-geometric fluxes while retaining the NS-NS sector of Supergravity.…”

“…In this context we do not need a deeper understanding of closed and open string theory but the relation between the quadruplet of tensors (g, B, G, Π) stated by (2.24). In our related work [37] we analyzed a similar generalized vielbein, with the upper right block put to zero. The vielbein used here returns a class of block diagonal metrics, i.e.…”