Quantization of 2D dilaton supergravity with matter

TL;DR

This paper develops a background-independent quantization approach for 2D dilaton supergravity with matter, revealing the structure of quantum correlators, virtual black holes, and S-matrix invariance.

Contribution

It extends the exact quantization method from bosonic to supersymmetric 2D dilaton gravity with matter, analyzing constraints, correlators, and quantum effects.

Findings

Nonlocal correlators respect quantum triviality

Virtual black holes influence the S-matrix

One-loop corrections are addressed with proper measure

Abstract

General N=(1,1) dilaton supergravity in two dimensions allows a background independent exact quantization of the geometric part, if these theories are formulated as specific graded Poisson-sigma models. The strategy developed for the bosonic case can be carried over, although considerable computational complications arise when the Hamiltonian constraints are evaluated in the presence of matter. Nevertheless, the constraint structure is the same as in the bosonic theory. In the matterless case gauge independent nonlocal correlators are calculated non-perturbatively. They respect local quantum triviality and allow a topological interpretation. In the presence of matter the ensuing nonlocal effective theory is expanded in matter loops. The lowest order tree vertices are derived and discussed, entailing the phenomenon of virtual black holes which essentially determine the corresponding S-matrix. Not all vertices are conformally invariant, but the S-matrix is invariant, as expected. Finally, the proper measure for the 1-loop corrections is addressed. It is argued how to exploit the results from fixed background quantization for our purposes.