Phenomenological implications of $S$-duality symmetry

TL;DR

This paper explores the hypothesis that $S$-duality is a fundamental, spontaneously broken symmetry of nature, with implications for axion, dilaton, and fermion interactions, and discusses its phenomenological consequences.

Contribution

It introduces a model where $S$-duality symmetry is spontaneously broken at a high scale, affecting fermion interactions and providing a new perspective on axion and dilaton roles.

Findings

$S$-duality is proposed as a fundamental symmetry of nature.

The symmetry breaking scale is linked to the axion decay constant.

The model predicts negligible corrections to fermion masses in QCD.

Abstract

It is proposed that $S$-duality is a fundamental symmetry of nature which is spontaneously broken. Axion and dilaton are identified with the doublet of the $S$-duality symmetry group $SL(2,\mathbbm{R})$. The symmetry is broken at a high scale corresponding to the experimentally estimated axion decay constant $f_{\chi}$. The symmetry breaking mechanism is discussed in analogy with PCAC in pion physics. $S$-duality invariant interactions of fermions with axion and dilaton doublet are introduced. The symmetry breaking mechanism contributes negligibly small corrections to fermion masses in the QCD sector. Inspired by universality in string theory, the $S$-duality invariant interaction of the axion-dilaton doublet to QCD fermions is proposed to generalize to all fermions. Phenomenological consequences of this broken symmetry are explored.