Trace anomaly induced effective action and 2d black holes for dilaton coupled supersymmetric theories

TL;DR

This paper constructs the effective action for 2D dilatonic supergravity with matter, analyzes quantum effects like Hawking radiation, and explores back-reaction on black hole solutions, providing insights into supersymmetric quantum gravity models.

Contribution

It introduces the supersymmetric effective action for 2D dilatonic supergravity with matter, including quantum corrections and back-reaction analysis on black holes.

Findings

Hawking radiation is zero in the supersymmetric CGHS model.

One-loop and large-N effective actions are explicitly calculated.

Back-reaction effects of quantum matter on black hole solutions are estimated.

Abstract

The action for 2d dilatonic supergravity with dilaton coupled matter and dilaton multiplets is constructed. Trace anomaly and anomaly induced effective action (in components as well as in supersymmetric form) for matter supermultiplet on bosonic background are found. The one-loop effective action and large-$N$ effective action for quantum dilatonic supergravity are also calculated. Using induced effective action one can estimate the back-reaction of dilaton coupled matter to the classical black hole solutions of dilatonic supergravity. That is done on the example of supersymmetric CGHS model with dilaton coupled quantum matter where Hawking radiation which turns out to be zero is calculated. Similar 2d analysis maybe used to study spherically symmetric collapse for other models of 4d supergravity.