Wolfgang Kummer and the Vienna School of Dilaton (Super-)Gravity

Abstract

was well known for his passion for axial gauges and for the formulation of gravity in terms of Cartan variables. The combination of the two applied to two-dimensional dilaton gravity is the basis of the "Vienna School", which provided numerous significant results over the last seventeen years. In this review we trace the history of this success with particular emphasis on dilaton supergravity. We also present some previously unpublished results on the structure of non-local vertices in quantum dilaton supergravity with non-minimally coupled matter. Historical Introduction Early Attempts to Non-Einsteinian Gravity in 2DThe earliest works by Wolfgang Kummer connected to gravity in two dimensions 1-4 date back to the year 1991, where he realized together with Dominik Schwarz that the Katanaev-Volovich model,2) * Email: bergamin@tph.tuwien.ac.at † Email: meyer@mppmu.mpg.de a Here R abcd are the components of the curvature two-form written with tangent space indices only, T abc are the components of the torsion form, and µ, γ, λ are constants. In the second line, we expressed everything in terms of the Ricci scalar R = R µν µν and the Hodge dual of the torsion form, T a µν = ǫµν τ a .

Holographic counterterms from local supersymmetry without boundary conditions

“…For simplicity we have neglected a kinetic term for the dilaton. It can be introduced through a dilaton-dependent Weyl rescaling, see for instance section 5 in [29] for details. It can be checked easily that our procedure leading to (25) generalizes to models containing a kinetic term for the dilaton field.…”

Towards Noncommutative Gravity

“…The Vienna School of 2D gravity was an amazingly successful project, see. 1 To keep it running, new interesting directions of research were always needed. About 2005 I told Wolfgang about my recent work on noncommutative (NC) gravity in two dimensions 2 which almost literally repeated some of the steps done previously in the commutative case.…”

Black Holes as Boundaries in 2d Dilaton Supergravity

“…The bulk theory contains only first class constraints. However, due to possible boundary contributions in (6) and as a consequence of the boundary constraints enforcing (7), terms are generated in the evaluation of Poisson brackets with support exclusively at the boundary. They convert some of the constraints into second class.…”

“…Generic Boundary For a generic boundary to solve the boundary problem (7) among the bosonic variables the only possible choice is δq I = 0, which we implement by means of the constraints…”

“…5) and our papers on SUGRA. [6][7][8][9] The graded 1-form fields A I comprise the (dual) spin-connection ω, the Zweibeine e ±± and the gravitino ψ ± . The graded 0-form fields X I comprise the dilaton φ, Lagrange-multipliers for torsion X ±± and the dilatino χ ± .…”