As on arXiv
Abstract
After an introductory chapter on the quantum supersymmetric string, in which particular attention will be devoted to the techniques via which phenomenologically viable models can be obtained from the ultraviolet microscopic degrees of freedom, and a brief review of the swampland program, the technical tools required to deal with geometric flows will be outlined. The evolution of a broad family of scalar and metric bubble solutions under Perelman's combined flow will be then discussed, together with their asymptotic behaviour. Thereafter, the geometric flow equations associated to a generalised version of Perelman's entropy function will be derived and employed in defining the action-induced flow associated to a given theory for a scalar field and a dynamical metric. The problem of preserving Einstein field equations along the corresponding moduli space trajectories will be cured by allowing a supplementary energy-momentum tensor term to appear along the flow. In a particular example, such contribution will be shown to precisely reproduce the infinite tower of states with exponentially dropping masses postulated by the distance conjecture.
Comments: 175 pages
Its neighbourhood
Connected papers
The 8 papers on this site closest to this one, judged by the topics they share, the words and phrases in their titles and abstracts, and their authors. They are not its citations, but a map of the work around it. Papers here go back to 2021, plus the canon.
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On-Shell Flow
Topics Physics · Same author Davide De Biasio · Shared terms “geometric flows”, “Swampland”, “action induced”
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Topics Perelman entropy, Physics · Shared terms “Swampland”, “geometric flows”, “scalar field”
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Monotonicity of RG flow in emergent dual holography of worldsheet nonlinear model
Topics Perelman entropy, Physics · Shared terms “microscopic”
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Topics Perelman entropy, Physics · Shared terms “field equations”, “Einstein”
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Nonassicative cosmological solitonic R-flux deformations in gauge gravity and G. Perelman geometric flow thermodynamics
Topics Perelman entropy, Physics · Shared terms “geometric flows”
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Topics Perelman entropy · Shared terms “dynamical”
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Topics Perelman entropy, Physics · Shared terms “geometric flows”, “defining”
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Stochastic Thermodynamics on Time-Evolving Curved Spaces
Topics Perelman entropy · Shared terms “contribution”
Read around it
Background reading
The guides for the topics of this paper: what each idea is, why it matters, and the papers to read first.
In the guidebook
- 6A.12Entropy, Information and Diffusion
Entropy along the heat flow, the log-Sobolev inequality and Li–Yau: the ancestors of Perelman’s entropy.
- 6A.13Self-Similar Variables and Monotonicity
Changing variables so that self-similar solutions stand still: convergence to the Gaussian, Giga–Kohn blow-up, Gaussian-weighted monotonicity formulas, frequency functions, and the blow-up logic of Huisken, Struwe and Perelman.
- 6B.16Eigenvalue Problems and Perelman’s λ
Rayleigh quotients and min–max, Faber–Krahn and Cheeger’s inequality, ground states of Schrödinger operators, spectral clustering, and the first eigenvalue of −4Δ + R that begins Perelman’s first preprint.