Aspects of univalence in holographic axion models

A bstract Univalent functions are complex, analytic (holomorphic) and injective that have been widely discussed in complex analysis. It was recently proposed the stringent constraints univalence imposes on growth of combined with sufficient analyticity conditions could be used to derive rigorous lower upper bounds hydrodynamic dispersion relation, i.e., all terms appearing their convergent series representations. The results exact physical quantities such as diffusivity speed sound. purpose this paper is further explore these ideas, investigate them concrete holographic examples, work towards a better intuitive understanding role physics. More concretely, we study diffusive sound modes family axion models offer set observations, arguments tests support applicability methods for bounding observables described effective field theories. Our provides insight into expected ‘typical’ regions univalence, comparisons between tightness corresponding values certain characterising transport, relations diffusion involve chaotic pole-skipping, well condition implies conformal bound complementary its violation.