Trace Anomaly in Quantum Spacetime Manifold

TL;DR

This paper explores the trace anomaly in a quantum spacetime with de-localized events, deriving a divergence-free heat kernel expansion and calculating the anomaly and energy-momentum tensor in various vacua within a noncommutative geometry-inspired Schwarzschild solution.

Contribution

It introduces a modified heat kernel expansion that avoids short-distance divergences and computes the trace anomaly and energy-momentum tensor in a novel quantum spacetime model.

Findings

Derived a divergence-free heat kernel expansion.

Explicitly calculated the trace anomaly and energy-momentum tensor.

Regularized vacuum expectation values without UV infinities.

Abstract

In this paper we investigate the trace anomaly in a spacetime where single events are de-localized as a consequence of short distance quantum coordinate fluctuations. We obtain a modified form of heat kernel asymptotic expansion which does not suffer from short distance divergences. Calculation of the trace anomaly is performed using an IR regulator in order to circumvent the absence of UV infinities. The explicit form of the trace anomaly is presented and the corresponding 2D Polyakov effective action and energy momentumtensor are obtained. The vacuum expectation value of the energy momentum tensor in the Boulware, Hartle-Hawking and Unruh vacua is explicitly calculated in a (rt)-section of a recently found, noncommutative geometry inspired, Schwarzschild-like solution of the Einstein equations. The standard short distance divergences in the vacuum expectation values are regularized in agreement with the absence of UV infinities removed by quantum coordinate fluctuations.