S-matrices in the holomorphic modular bootstrap approach
Suresh Govindarajan, Aditya Jain, Akhila Sadanandan, Abhiram Kidambi
TL;DR
This paper develops a method to numerically and exactly determine S-matrices within the holomorphic modular bootstrap framework using MLDEs and cyclotomic fields, illustrated through examples.
Contribution
It introduces an intrinsic MLDE-based approach to compute S-matrices, leveraging connection formulae and cyclotomic extensions for exact results.
Findings
Numerical determination of S-matrices using connection formulae.
Exact formulae for S-matrices via cyclotomic field entries.
Method applicable within the MLDE framework without external inputs.
Abstract
We numerically determine the S-matrix by using connection formulae in the modular linear differential equation (MLDE) approach to the holomorphic modular bootstrap. We then determine exact formulae using the fact that entries in the -matrix are integer entries in a cyclotomic extension of the field of rational numbers. This provides a method that is intrinsic to the MLDE setup and does not require inputs outside this framework. The method is illustrated with a selection of examples.
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Taxonomy
TopicsPolynomial and algebraic computation · Nonlinear Waves and Solitons · Advanced Differential Equations and Dynamical Systems