What does this research mean for the field?

Incorporating exact S-matrix computations into the holomorphic modular bootstrap yields admissible and tenable solutions for Modular Linear Differential Equations with up to six characters, enabling their classification into specific Conformal Field Theories and Modular Tensor Categories. Novelty: ClaimNovelty.INCREMENTAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

To update the holomorphic modular bootstrap framework by integrating exact S-matrix solutions and systematically classifying admissible solutions to modular linear differential equations.

August 28, 2026Journal of High Energy PhysicsOpen Access

Updating the holomorphic modular bootstrap

View Full Paper

Ask AI

Bookmark

To update the holomorphic modular bootstrap framework by integrating exact S-matrix solutions and systematically classifying admissible solutions to modular linear differential equations.
Incorporated exact S-matrix calculations within the Modular Linear Differential Equation (MLDE) framework.
Evaluated allowed exponents modulo one for MLDEs having up to six characters, Wronskian index < 6, one accessory parameter, and effective central charge c_eff ≤ 24.
Filtered admissible solutions to identify tenable candidates with valid fusion rules and mapped them to conformal field theory (CFT) and modular tensor category (MTC) classes.
Obtained all admissible solutions to the specified family of MLDEs within the bounds of six characters and Wronskian index < 6.
Identified which admissible solutions possess consistent fusion rules, defining them as tenable solutions.
Successfully mapped tenable solutions to their corresponding CFT models and unitary MTC classifications.

Implication

Theoretical analysis uncovers tenable modular linear differential equation solutions, highlighting exact classifications for conformal field theories.

Abstract

A bstract We update the holomorphic modular bootstrap incorporating a recent result that computes the exact S -matrix within the Modular Linear Differential Equation (MLDE) setting. Further, using knowledge of the allowed exponents modulo one, we obtain admissible solutions to all MLDE’s with up to six characters and Wronskian index < 6 and one accessory parameter with c eff ≤ 24. We then identify which of the admissible solutions have good fusion rules — we call such solutions tenable . When possible, we identify the CFT and in the unitary cases the MTC class they belong to.

Discussion

No takes yet. Share an insight, caveat, or question.

Cite This Study

Govindarajan et al. (2026) studied this question.

synapsesocial.com/papers/6a914599d15324a1df3a8eab https://doi.org/10.1007/jhep08(2026)216

View Full Paper

Ask AI

Bookmark

Implication

Theoretical analysis uncovers tenable modular linear differential equation solutions, highlighting exact classifications for conformal field theories.

Updating the holomorphic modular bootstrap

Key Points

Implication

Abstract

Discussion

Cite This Study

Updating the holomorphic modular bootstrap

Key Points

Implication

Abstract

Discussion

Cite This Study

Keep reading

Keep reading