Aspects of univalence in holographic axion models

Baggioli, MatteoShanghai Jiao Tong Univ, Wilczek Quantum Ctr, Sch Phys & Astron, Shanghai 200240, Peoples R China.;Shanghai Res Ctr Quantum Sci, Shanghai 201315, Peoples R China. (författare)

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 characterising 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.

Grieninger, SebastianCSIC, Inst Fis Teor UAM, Calle Nicolas Cabrera 13-15, Madrid 28049, Spain.;Univ Autonoma Madrid, Dept Fis Teor, Campus Cantoblanco, Madrid 28049, Spain. (författare)
Grozdanov, SasoUniv Edinburgh, Higgs Ctr Theoret Phys, Edinburgh EH8 9YL, Midlothian, Scotland.;Univ Ljubljana, Fac Math & Phys, Jadranska Ulica 19, SI-1000 Ljubljana, Slovenia. (författare)
Luo, ZhengkangUppsala universitet,Institutionen för fysik och astronomi(Swepub:uu)luozh160 (författare)
Shanghai Jiao Tong Univ, Wilczek Quantum Ctr, Sch Phys & Astron, Shanghai 200240, Peoples R China.;Shanghai Res Ctr Quantum Sci, Shanghai 201315, Peoples R China.CSIC, Inst Fis Teor UAM, Calle Nicolas Cabrera 13-15, Madrid 28049, Spain.;Univ Autonoma Madrid, Dept Fis Teor, Campus Cantoblanco, Madrid 28049, Spain. (creator_code:org_t)

Av författaren/redakt...: Baggioli, Matteo; Grieninger, Seba ...; Grozdanov, Saso; Luo, Zhengkang

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