Accurate bootstrap bounds from optimal interpolation
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866916048083615744 |
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| author | Chang, Cyuan-Han Dommes, Vasiliy Kravchuk, Petr Poland, David Simmons-Duffin, David |
| author_facet | Chang, Cyuan-Han Dommes, Vasiliy Kravchuk, Petr Poland, David Simmons-Duffin, David |
| contents | We develop new methods for approximating conformal blocks as positive functions times polynomials, with applications to the numerical bootstrap. We argue that to obtain accurate bootstrap bounds, conformal block approximations should minimize a certain error norm related to the asymptotics of dispersive functionals. This error norm can be made small using interpolation nodes with an appropriate optimal density. The optimal density turns out to satisfy a kind of force-balance equation for charges in one dimension, which can be solved using standard techniques from large-N matrix models. We also describe how to use optimal density interpolation nodes to improve condition numbers inside the semidefinite program solver SDPB. Altogether, our new approximation scheme and improvements to condition numbers lead to more accurate bootstrap bounds with fewer computational resources. They were crucial in the recent bootstrap study of stress tensors in the 3d Ising CFT. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_14307 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Accurate bootstrap bounds from optimal interpolation Chang, Cyuan-Han Dommes, Vasiliy Kravchuk, Petr Poland, David Simmons-Duffin, David High Energy Physics - Theory Statistical Mechanics Strongly Correlated Electrons High Energy Physics - Lattice We develop new methods for approximating conformal blocks as positive functions times polynomials, with applications to the numerical bootstrap. We argue that to obtain accurate bootstrap bounds, conformal block approximations should minimize a certain error norm related to the asymptotics of dispersive functionals. This error norm can be made small using interpolation nodes with an appropriate optimal density. The optimal density turns out to satisfy a kind of force-balance equation for charges in one dimension, which can be solved using standard techniques from large-N matrix models. We also describe how to use optimal density interpolation nodes to improve condition numbers inside the semidefinite program solver SDPB. Altogether, our new approximation scheme and improvements to condition numbers lead to more accurate bootstrap bounds with fewer computational resources. They were crucial in the recent bootstrap study of stress tensors in the 3d Ising CFT. |
| title | Accurate bootstrap bounds from optimal interpolation |
| topic | High Energy Physics - Theory Statistical Mechanics Strongly Correlated Electrons High Energy Physics - Lattice |
| url | https://arxiv.org/abs/2509.14307 |