Abstract Loewner driving functions encode simple curves in 2D simply connected domains by real-valued functions. We prove that the Loewner driving function of a $C^{1,\beta }$ curve (differentiable parametrization with $\beta$-Hölder continuous derivative) is in the class $C^{1,\beta -1/2}$ if $1/2<\beta \leq 1$, and in the class $C^{0,\beta + 1/2}$ if $0 \leq \beta \leq 1/2$. This is the converse of a result of Carto Wong [26] and is optimal. We also introduce the Loewner energy of a rooted planar loop and use our regularity result to show the independence of this energy from the basepoint.
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This content will become publicly available on July 1, 2025
Physical Running of Couplings in Quadratic Gravity
We argue that the well-known beta functions of quadratic gravity do not correspond to the physical dependence of scattering amplitudes on external momenta, and derive the correct physical beta functions. Asymptotic freedom turns out to be compatible with the absence of tachyons.
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- Award ID(s):
- 2112800
- PAR ID:
- 10525775
- Publisher / Repository:
- American Physical Society
- Date Published:
- Journal Name:
- Physical Review Letters
- Volume:
- 133
- Issue:
- 2
- ISSN:
- 0031-9007
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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