10D Supergravity Numerical Data Sets for L & R Matrices

TL;DR

This work provides, for the first time, a complete on-shell data foundation for ten-dimensional $\mathcal{N}=1$ supergravity by deriving the supercurrent and performing a thorough closure analysis of the linearized theory. Through a 0-brane reduction, the authors construct and present the left and right adjacency matrices $L_I$ and $R_I$ (16 matrices at sizes $82\times176$ and $176\times82$, respectively) that realize the Garden algebra in 1D. These matrices, together with the associated non-closure tensors, form a publicly accessible data library intended to seed future off-shell constructions and prepotential searches via adinkra/superspace methods. The paper additionally outlines concrete pathways to integrate the on-shell data with superspace proposals and adinkra-based off-shell programs, aiming to advance toward a full off-shell description of 10D supergravity. The availability of the data at a public repository enables researchers to perform systematic off-shell explorations and cross-validate with 10D superspace and prepotential frameworks, with potential implications for string-theory effective actions and higher-dimensional SUSY structures.

Abstract

After reviewing the development of 10D, superspace theories, and their relations to superstring and heterotic string theories, explicit calculations are undertaken in the on-shell $\cal N$ = 1 linearized supergravity, the associated super-current is derived, and non-closure terms are explicitly given. The $L_{\rm I}$ and $R_{\rm I}$ adjacency matrices are then computed in complete numerical form as data sets. This is the preliminary step required to perform a scan to embed the on-shell matrices into off-shell ones.

Figures (1)

• Figure 1: Off-shell and on-shell Adinkras for the 4D, $\mathcal{N}=1$ chiral supermultiplet.