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Truncated Polyakov bootstrap
Abstract
We set up a truncated numerical approach in the Polyakov bootstrap (PB) framework. We employ a gradient descent optimization to solve PB sum rules numerically, and hence solve crossing for arbitrary deformations of the generalized free field (GFF) spectrum in an iterative way starting from a perturbative solution. For unitary deformations the solutions coincide with extremal CFT spectra. But more interestingly, our findings indicate that a general crossing solution, not necessarily unitary (i.e. without positivity), can be uniquely identified by a smooth connection to GFF. The truncated Polyakov bootstrap approach is established through a number of examples in both single and mixed correlator settings.
Related
BibTeX
@misc{kangshabanik2026truncated,
title = {{Truncated Polyakov bootstrap}},
author = {Kaushik Kangshabanik and Apratim Kaviraj and Shailesh Lal},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.01732},
eprint = {2609.01732},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.01732},
}
RIS
TY - UNPB
TI - Truncated Polyakov bootstrap
AU - Kaushik Kangshabanik
AU - Apratim Kaviraj
AU - Shailesh Lal
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.01732
UR - https://arxiv.org/abs/2609.01732
AB - We set up a truncated numerical approach in the Polyakov bootstrap (PB) framework. We employ a gradient descent optimization to solve PB sum rules numerically, and hence solve crossing for arbitrary deformations of the generalized free field (GFF) spectrum in an iterative way starting from a perturbative solution. For unitary deformations the solutions coincide with extremal CFT spectra. But more interestingly, our findings indicate that a general crossing solution, not necessarily unitary (i.e. without positivity), can be uniquely identified by a smooth connection to GFF. The truncated Polyakov bootstrap approach is established through a number of examples in both single and mixed correlator settings.
ER -