The monodromic axion-photon coupling
Prateek Agrawal, Arthur Platschorre
Abstract
A bstract We consider the general form of the axion coupling to photons in the axion-Maxwell theory. On general grounds this coupling takes the form of a monodromic function of the axion, which we call g ( a ), multiplying the Chern-Pontryagin density $$ F\overset{\sim }{F} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>F</mml:mi> <mml:mover> <mml:mi>F</mml:mi> <mml:mo>~</mml:mo> </mml:mover> </mml:math> of the photon. We show that the non-linearity of g ( a ) is a spurion for the shift symmetry of the axion. In this context, when g ( a ) ≠ ℤ a , the linearized coupling of the axion g ′( a ) is not quantized and there is a correlated mass term for the axion. Singularities in g ( a ) due to the fast rearrangement of degrees of freedom are shown to have corresponding cusps and singularities in the axion potential. We derive the general form of g ( a ) for the QCD axion, axions with perturbatively broken shift symmetries and axions descending from extra dimensions. In all cases, we show that there is a uniform general form of the monodromic function g ( a ) and it is connected to the axion potential.