Research database

In the off-shell formulation of supersymmetric theories, supersymmetry is manifest from the description of the particles in the supermultiplet, allowing us to separate the representation theory from the dynamics and facilitating quantization. However, the off- shell matching of bosonic and fermionic degrees of freedom is in general problematic for extended supergravities and for higher- dimensional supersymmetric models, especially in the presence of hypermultiplets. In these cases, it is commonly acknowledged that an infinite number of auxiliary fields is needed to provide an off-shell formulation, and, in this context, the most fruitful approach so far has been that of harmonic superspace, where spherical harmonics are employed. However, this construction undermines the geometric and group theoretical foundations of the theory, which, on the other hand, would be naturally expected in ordinary superspace. The primary objective of this project is to explore an off-shell formulation in ordinary superspace with a finite number of auxiliary fields, by making use of the hidden 1-forms description of supersymmetric theories in the presence of higher-degree differential forms. More specifically, the prescription, which will be implemented within the geometric approach to supersymmetric theories in superspace, always includes a nilpotent spin-3/2 1-form field, thus circumventing the hypothesis of the no-go theorem on auxiliary fields in extended supersymmetry, which contemplates only spin-1/2 fields. In tackling this ambitious objective, the project fosters interdisciplinary collaboration between theoretical physics and mathematics, with the final aim of a fully-fledged rephrasing of the geometric approach in superspace within supergeometry and higher differential geometry, providing a more natural and comprehensive mathematical foundation of supersymmetric theories, especially concerning supergravity in the Cartan geometric formulation.