Graded Poisson-sigma models and dilaton-deformed 2D supergravity algebra

Abstract

Fermionic extensions of generic 2d gravity theories obtained from the graded Poisson-Sigma model (gPSM) approach show a large degree of ambiguity. In addition, obstructions may reduce the allowed range of fields as given by the bosonic theory, or even prohibit any extension in certain cases. In our present work we relate the finite W-algebras inherent in the gPSM algebra of constraints to algebras which can be interpreted as supergravities in the usual sense (Neuveu-Schwarz or Ramond algebras resp.), deformed by the presence of the dilaton field. With very straightforward and natural assumptions on them -like demanding rigid supersymmetry in a certain flat limit, or linking the anti-commutator of certain fermionic charges to the Hamiltonian constraint-in the "genuine" supergravity obtained in this way the ambiguities disappear, as well as the obstructions referred to above. Thus all especially interesting bosonic models (spherically reduced gravity, the Jackiw-Teitelboim model etc.) under these conditions possess a unique fermionic extension and are free from new singularities. The superspace supergravity model of Howe is found as a special case of this supergravity action. For this class of models the relation between bosonic potential and prepotential does not introduce obstructions as well.

Quantization of 2D dilaton supergravity with matter

“…Though the appearance of fermions in both, geometry and matter part, lead to some technical complications the final result is seen to retain the structure already found in the bosonic case [33,6,7,36]. For the purely geometrical part of the action the result of this analysis has been presented already in [24]. Nevertheless, a detailed formulation is given.…”

“…To this end the non-linear symmetry (2.3), which is closed on-shell only, is-in a first steprelated to the more convenient (off-shell closed) algebra of Hamiltonian constraints G I = ∂ 1 X I + P IJ (X)A 1J discussed in detail in Section 3. The Hamiltonian obtained from (2.1) is a linear combination of these constraints [33,6,24]:…”

“…In a second step a certain linear combination of the G I , suggested by the ADM parametrization [34,35,24], maps the G I algebra upon a deformed version of the superconformal algebra (deformed Neveu-Schwarz, resp. Ramond algebra).…”

Poisson-sigma model for 2D gravity with non-metricity

“…A novel feature is that (5) contains terms at most quadratic in X a , whereas in the traditional approach arbitrary coupling to X a X b η ab is allowed since η ab is introduced there as an external structure. This is interesting by itself because supergravity imposes a similar restriction to quadratic coupling [15], but we shall not pursue this issue any further here. As mentioned before the choice (7) was made for simplicity.…”

The tetralogy of Birkhoff theorems

“…The relation of the Birkhoff theorem to two-dimensional space-times is worked out in [67], [68], [69], [70], [71], [72], [73], [74], [75], [76], [77], [78], [79], [80], [81], [82], and [83]. For related work on black holes in Palatini gravity see e.g.…”