Non-perturbative Treatments of the Bosonic String and the Axion with Cosmological Implications

TL;DR

This paper introduces a novel exact functional quantization method applied to the axion and bosonic string actions, revealing insights into axion potential development and non-perturbative string conformal invariance with potential cosmological implications.

Contribution

It presents a new non-perturbative functional quantization approach applied to axion and string actions, demonstrating conformal invariance and early-stage axion potential development.

Findings

Axion effective potential is flattened by spinodal instability effects.

The method achieves non-perturbative conformal invariance in string beta functions.

Potential cosmological implications include optical anisotropy hints.

Abstract

This paper is about the use of a novel, exact functional quantization method as applied to two commonly studied actions in theoretical physics. The functional method in question has its roots in the exact renormalisation group flow techniques pioneered by Wilson, but with the flow parameter not limited to the familiar momentum cutoff. Finding a configuration satisfying an expression for the exact effective action which does not vary with this parameter provides the basis for finding solutions to the physical actions we study. Firstly, the method is applied to an expression for the bare action of the pseudo-scalar axion used to explain the strong CP problem in QCD. When quantized, we find that the effective potential of the axion, when interactions are not considered, is necessarily flattened by spinodal instability effects. We regard this flattening asrepresenting the very early stage in the development of the axion potential, when the Peccei-Quinn U(1) symmetry is spontaneously broken resulting in a double-well potential. Using commonly quoted values for the parameters of such a potential, we devise an expression for the energy density of the emerging axion potential and this is compared to dark energy. We then apply the functional method to the bosonic string with time varying graviton, dilaton and antisymmetric tensor (resulting in the string-axion) background fields. We achieve a demonstration of conformal invariance in a non-perturbative manner in the beta functions, contrasting with conventional string cosmology where cancellation of a perturbative expansion is performed. We then offer some hints as to possible cosmological implications of our configuration in terms of optical anisotropy.