Aleph_null Hypergravity in Three-Dimensions

TL;DR

This paper develops a three-dimensional hypergravity theory featuring an infinite extension of local hypersymmetries, incorporating gravitinos with arbitrary half-integer spins and real gauge group representations.

Contribution

It constructs a novel three-dimensional hypergravity model with infinitely many extended hypersymmetries and arbitrary half-integer spins, expanding the scope of supergravity theories.

Findings

Introduces -hypergravity with infinite hypersymmetries.

Allows arbitrary large real gauge group representations.

Defines conditions for antisymmetric generator matrices.

Abstract

We construct hypergravity theory in three-dimensions with the gravitino \psi_{\mu m_1... m_n}{}^A with an arbitrary half-integral spin n+3/2, carrying also the index A for certain real representations of any gauge group G. The possible real representations are restricted by the condition that the matrix representation of all the generators are antisymmetric: (T^I)^{A B} = - (T^I)^{B A}. Since such a real representation can be arbitrarily large, this implies \aleph_0-hypergravity with infinitely many (\aleph_0) extended local hypersymmetries.