Trace Anomaly in Geometric Discretization

TL;DR

This paper introduces a simple geometric discretization of 2D scalar field theory that reproduces the trace anomaly and offers a new interpretation involving electric-magnetic duality in resistor networks.

Contribution

It presents the first geometric-discretized analogue of 2D scalar field theory that captures the trace anomaly and links it to duality transformations in resistor networks.

Findings

Discretized model qualitatively reproduces the trace anomaly.

Provides a duality-based interpretation of the anomaly.

Connects scalar field theory with resistor network dualities.

Abstract

I develop the simplest geometric-discretized analogue of two dimensional scalar field theory, which qualitatively reproduces the trace anomaly of the continuous theory. The discrete analogue provides an interpretation of the trace anomaly in terms of a non-trivial transformation of electric-magnetic duality-invariant modes of resistor networks that accommodate both electric and magnetic charge currents.