Aspects of univalence in holographic axion models

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.

v2: minor revision, matching the published version

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• Kasner interiors from analytic hairy black holes
• On pole-skipping with gauge-invariant variables in holographic axion theories
• Deep learning-based holography for T-linear resistivity
• The Algebraic Structure Underlying Pole-Skipping Points
• Phase transitions in a holographic superfluid model with non-linear terms beyond the probe limit
• Bulk Spacetime Encoding via Boundary Ambiguities
• Hydrodynamic modes in holographic multiple-axion model