Weyl covariance, and proposals for superconformal prepotentials in 10D superspaces

S James Gates,S.-N Hazel Mak,Yangrui Hu

doi:10.1007/jhep03(2021)074

S James Gates, S.-N Hazel Mak + Show 1 more

Open Access

https://doi.org/10.1007/jhep03(2021)074

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Abstract

Proposals are made to describe the Weyl scaling transformation laws of supercovariant derivatives ∇A, the torsion supertensors TABC, and curvature supertensors RABcd in 10D superspaces. Starting from the proposal that an unconstrained supergravity prepotential for the 11D, mathcal{N} = 1 theory is described by a scalar superfield, considerations for supergravity prepotentials in the 10D theories are enumerated. We derive infinitesimal 10D superspace Weyl transformation laws and discover ten possible 10D, mathcal{N} = 1 superfield supergravity prepotentials. The first identification of all off-shell ten dimensional supergeometrical Weyl field strength tensors, constructed from respective torsions, is presented.

Highlights

Proposals are made to describe the Weyl scaling transformation laws of supercovariant derivatives ∇A, the torsion supertensors T A BC, and curvature supertensors
Appropriate to the case of the 10, =N IIA theory, we find the Weyl scaling properties of all the superspace torsion and curvature supertensors with weights of less than three-halves as below
The results presented in equations (3.33), (3.64), and (3.78) mark the first time that off-shell definitions of 10D Weyl superfield supergravity field strength tensors have been explicitly identified in the physics literature

Summary

A new methodology

[23, 24], we have established a breakthrough approach which substantially lowered computational costs of determining how to embed a set of component fields within a superfield. For our purposes here, we will use a definition tailored to 10D, N = 1 SUSY where an adynkra is a collection of sets of Dynkin Labels that can be broken into subsets associated with a “Level number”. The latter of these is an integer that takes on values from zero to sixteen. We may call one of them the “IIAMGM” system and the “IIBMGM” system In terms of their component fermionic and bosonic representation contents, these look as. In terms of the “Level” numbers, the fermions are higher than the bosons Both the engineering dimensions and the Lorentz representations of all fields are key data inputs in the construction of Adynkra Digital Analysis (ADA) scans. The adynkra “libraries” play the roles of genetic sequence data bases/libraries.

Toward the rest of the story

Conclusion

B Adynkra libraries