Pre‐NQ Manifolds and Correspondence Spaces: the Nilmanifold Example

Deser, Andreas

doi:10.1002/prop.201910006

Cited by 2 publications

(2 citation statements)

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“…When a nilpotent differential operator is also part of the geometrical data, there are immediate applications in the context of BRST and BV-BFV quantization of theories, whose action is degenerate because of the gauge redundancies, and in the context of AKSZ sigma models. There has also been a recent proposal for a formulation of T-duality in this framework, see [26]. This section aims at presenting the canonical Poisson structure of a specific graded manifold, together with a naturally associated differential operator.…”

Section: Graded Poisson Structurementioning

confidence: 99%

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

Boffo,

Schupp

2021

Preprint

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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 Π, 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 [1], 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 E ∼ = T M ⊕ 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.deformation 6 2.3 Gauge symmetries 9 2.4 Deformation and open-closed string relation 10 3 Courant algebroids and graded Poisson structures 11 3.1 Correspondence between 2-graded QP-manifolds and exact Courant algebroids 12 3.2 Courant algebroid for a non-canonical QP-manifold 13 4 Differential geometry of T M ⊕ T * M 14 4.1 Generalized Lie bracket, connection and torsion tensor 14 4.2 Connections on tangent space and on cotangent space for the given deformation 17 4.3 Curvature tensor 19 5 Gravitational actions with fluxes 20 5.1 Invariance under gauge symmetries of Π 22

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Section: Graded Poisson Structurementioning

confidence: 99%

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

Boffo,

Schupp

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…whose action is degenerate because of the gauge redundancies, and in the context of AKSZ sigma models. There has also been a recent proposal for a formulation of T-duality in this framework, see [33]. This section aims at presenting the canonical Poisson structure of a specific graded manifold, together with a naturally associated differential operator.…”

Section: Jhep12(2021)143mentioning

confidence: 99%