Constraint Analysis of Two-Dimensional Quadratic Gravity from BF Theory

TL;DR

This paper analyzes the constraint structure of two-dimensional quadratic gravity formulated as a BF theory using Hamiltonian methods, and compares it with generalized dilaton gravity results.

Contribution

It provides a detailed Hamiltonian constraint analysis of 2D quadratic gravity as a BF theory and applies the Batalin-Fradkin-Vilkovisky formalism to derive the transition amplitude.

Findings

Constraint structure elucidated for 2D quadratic BF gravity

Transition amplitude obtained via Batalin-Fradkin-Vilkovisky formalism

Comparison made with generalized dilaton gravity results

Abstract

Quadratic gravity in two dimensions can be formulated as a Background Field (BF) theory plus an interaction term which is polynomial in both, the gauge and Background fields. This formulation is similar to the one given by Freidel and Starodubtsev to obtain MacDowell-Mansouri gravity in four dimensions. In this article we use the Dirac's Hamiltonian formalism to analyze the constraint structure of the two-dimensional Polynomial BF action. After we obtain the constraints of the theory, we proceed with the Batalin-Fradkin-Vilkovisky procedure to obtain the transition amplitude. We also compare our results with the ones obtained from generalized dilaton gravity.