Phenomenological implications of $S$-duality symmetry
  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. 
Ashok Das and Jnanadeva Maharana
hep-ph hep-th