PT-symmetric interpretation of double-scaling

TL;DR

This paper demonstrates that replacing the traditional quartic quantum field theory with its PT-symmetric analog resolves issues with negative critical coupling and unbounded potentials, enabling a consistent double-scaling limit.

Contribution

It introduces a PT-symmetric approach to the double-scaling limit in O(N)-symmetric quartic models, providing explicit calculations in a zero-dimensional case.

Findings

The PT-symmetric analog yields a well-defined partition function.

The approach avoids the negative coupling and unbounded potential problems.

Explicit double-scaling limit calculation for the PT-symmetric model.

Abstract

The conventional double-scaling limit of an O(N)-symmetric quartic quantum field theory is inconsistent because the critical coupling constant is negative. Thus, at the critical coupling the Lagrangian defines a quantum theory with an upside-down potential whose energy appears to be unbounded below. Worse yet, the integral representation of the partition function of the theory does not exist. It is shown that one can avoid these difficulties if one replaces the original theory by its PT-symmetric analog. For a zero-dimensional O(N)-symmetric quartic vector model the partition function of the PT-symmetric analog is calculated explicitly in the double-scaling limit.