This file was generated on 2026-03-20 by Yann Proto


A GENERAL INFORMATION

1. Title of the dataset: 
Extended KMV algebras of rational BPS strings

2. Brief description of the research project and its aims:
This dataset accompanies the paper "Rational points in the 6d supergravity landscape and simple current extensions". It contains data for five multivariable Jacobi forms, expressed as expansions in Kac–Moody–Virasoro (KMV) characters. These KMV expansions uniquely determine the elliptic genus of the hyperplane string superconformal field theory at five rational points in its moduli space.

3. Author Information
	A. Investigator Contact Information
		Name: Yann Proto
		Institution: Bethe Center for Theoretical Physics, University of Bonn
		Address: Wegelerstraße 10, 53115 Bonn, Germany
		Email: yproto@uni-bonn.de

	B. Project Supervisor (Principal Investigator) Contact Information
		Name: Guglielmo Lockhart
		Institution: Bethe Center for Theoretical Physics, University of Bonn
		Address: Wegelerstraße 10, 53115 Bonn, Germany
		Email: glockhar@uni-bonn.de

	C. In case of questions related to this dataset, please contact:
		Name: Yann Proto
		Institution: Bethe Center for Theoretical Physics, University of Bonn
		Address: Wegelerstraße 10, 53115 Bonn, Germany
		Email: yproto@uni-bonn.de

4. Date of data collection: 2026-02-03

5. Information about funding sources that supported the collection of the data: 
ERC project "Extended degrees of freedom in QFT: EXTENDED" (grant agreement No. 101078365)



B DATA & FILE OVERVIEW

There are five files, each containing a KMV expansion. They are uniquely identified by the spacetime gauge group G.
- KMV multiplicities for the model with G = E_6, written in terms of e_6 and Potts characters: Ee6.sage
- KMV multiplicities for the model with G = A_7, written in terms of a_7 and Ising characters: Ea7.sage
- KMV multiplicities for the model with G = A_5 x D_4, written in terms of a_5 + d_4 and Ising characters: Ea5d4.sage
- KMV multiplicities for the model with G = A_3 x A_3 x E_7, written in terms of a_3 + a_3 + a_3 and tricritical Ising characters: Ea3a3e7.sage
- KMV multiplicities for the model with G = A_3 x A_11, written in terms of a_3 + a_11 and tricritical Potts characters: Ea3a11.sage



C SHARING/ACCESS INFORMATION

1. Licenses/restrictions placed on the data: CC BY 4.0

2. Links to publications that cite or use the data:
Guglielmo Lockhart, Yann Proto, "Rational points in the 6d supergravity landscape and simple current extensions" (2026)
https://doi.org/10.48550/arXiv.2603.17713 


D METHODOLOGICAL INFORMATION

1. Description of methods used for manipulation of data:
The data were generated using the open-source mathematics software system SageMath.
Each file contains a single list, named after the file itself (e.g. Ee6.sage contains the list Ee6), which we generically denote by E.
Each entry E[i], for i=0,1,...,len(E), is associated to a non-trivial monomial in the elliptic genus expansion. For a given E[i]:
- E[i][0] is an integer: it corresponds to the multiplicity of the monomial;
- E[i][1] is a dominant weight of the corresponding Lie group, labeled by its Dynkin labels;
- E[i][2] is a pair of integers: the Kac labels determining the irreducible representation of the unitary Virasoro minimal model.

3. Instrument- and/or software-specific information needed to interpret the data:
The files in this dataset can be analyzed using the free open-source mathematics software system SageMath (version 10.8).
Altenatively, they can be easily opened and processed by replacing their ".sage" extension by ".txt".