Worldline Path Integrals for the Graviton and 1-Loop Divergences in Quantum Gravity

In this talk, I will discuss perturbative quantum gravity at the 1-loop level by reviewing and systematizing old results on UV divergences and presenting new findings along with new methods for their calculation. The traditional approach to this problem employs the Schwinger-DeWitt heat kernel method. We extend this approach by incorporating worldline path integrals to compute the perturbative expansion at small proper time. In addition, we explore a more principled approach that utilizes the BRST path integral quantization of the N=4 spinning particle, which describes the graviton in first quantization. Using these methods, we calculate the one-loop divergences in quantum gravity with a cosmological constant in arbitrary dimensions. When evaluated on-shell, these calculations yield a set of gauge-invariant coefficients that characterize pure quantum gravity with a cosmological constant. These coefficients may serve as benchmarks for comparing various approaches to quantum gravity.