Intrinsic Moment of Inertia of Membranes as bounds for the mass gap of Yang-Mills Theories

TL;DR

This paper establishes a condition based on membrane inertia that guarantees a discrete spectrum and provides bounds for the mass gap in Yang-Mills theories, especially analyzing the physically relevant case D=3.

Contribution

It introduces a novel criterion involving membrane moment of inertia to determine spectrum discreteness and bounds the mass gap in Yang-Mills theories in various dimensions.

Findings

Derived a precise condition on potentials for spectrum discreteness.

Provided bounds for the mass gap in D+1 Yang-Mills theories.

Identified classes of potentials with classical instabilities but discrete quantum spectra.

Abstract

We obtain the precise condition on the potentials of Yang-Mills theories in 0+1 dimensions and D0 brane quantum mechanics ensuring the discretness of the spectrum. It is given in terms of a moment of inertia of the membrane. From it we obtain a bound for the mass gap of any D+1 Yang-Mills theory in the slow-mode regime. In particular we analyze the physical case D=3. The quantum mechanical behavior of the theories, concerning its spectrum, is determined by harmonic oscillators with frequencies given by the inertial tensor of the membrane. We find a class of quantum mechanic potential polynomials of any degree, with classical instabilities that at quantum level have purely discrete spectrum.