Relating Field Theories via Stochastic Quantization

TL;DR

This paper explores how various quantum field theories can be unified under stochastic quantization, revealing connections to string theory, topological models, and quantum crystals, and proposing new interpretations within these frameworks.

Contribution

It demonstrates that different models, including quantum crystals and topological theories, can be linked through stochastic quantization, offering new insights into their interrelations and interpretations.

Findings

Quantum field theories can be connected via stochastic quantization.

The quantum crystal model is a discrete analog of stochastic quantization.

Potential interpretations relate to string theory and topological M-theory.

Abstract

This note aims to subsume several apparently unrelated models under a common framework. Several examples of well-known quantum field theories are listed which are connected via stochastic quantization. We highlight the fact that the quantization method used to obtain the quantum crystal is a discrete analog of stochastic quantization. This model is of interest for string theory, since the (classical) melting crystal corner is related to the topological A-model. We outline several ideas for interpreting the quantum crystal on the string theory side of the correspondence, exploring interpretations in the Wheeler-De Witt framework and in terms of a non-Lorentz invariant limit of topological M-theory.