Aspects of univalence in holographic axion models

TL;DR

This paper investigates how univalence, a property of complex functions, can be used to derive bounds on physical quantities like diffusivity and sound speed in holographic axion models, enhancing understanding of transport phenomena.

Contribution

It applies univalence methods to concrete holographic models, providing new bounds and insights into transport properties and their relation to complex analysis constraints.

Findings

Univalence bounds are applicable to holographic axion models.

Bounds on diffusivity and sound speed are consistent with exact values.

Conditions for conformal bounds and their violations are identified.

Abstract

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