Constraint Analysis and Quantization of Anomalous 2-D Thomas-Whitehead Gravity
Abstract
The two-dimensional effective Polyakov action is often realized as the anomalous contributions of string theories and fermions coupled to gravity in two-dimensions. However, as a result of the reparameterization invariance, one finds that the effective action produces vanishing Hamiltonians as constraints even in disparate gauges such as the dynamical light-cone and the ADM formalism of the metric. On the other hand, two-dimensional gravitational theories naturally arise as geometric actions on the coadjoint orbits of the Virasoro algebra. The Thomas-Whitehead gravity formalism extends the effective Polyakov action in such a way that the defining coadjoint element for the orbit becomes a dynamical field, viz the diffeomorphism field. In this work, we examine the constraint analysis and quantization of the Hamiltonian in the context of Thomas-Whitehead gravity using both the dynamical light-cone and the ADM formalisms of the metric. Constraint analysis is then repeated in a Minkowski background and with a dynamical action for the diffeomorphisms field arising from the Thomas-Whitehead action. Adding dynamics to the diffeomorphism field subsequently removes the vanishing Hamiltonians.
Cite
@article{arxiv.2603.06995,
title = {Constraint Analysis and Quantization of Anomalous 2-D Thomas-Whitehead Gravity},
author = {Eric Biedke and Salvatore Quaid and Vincent Rodgers},
journal= {arXiv preprint arXiv:2603.06995},
year = {2026}
}