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Structural Origin of the Gravitino Mass Term: Geometric and Supergravity Perspectives

Stefano Bellucci, Stefania De Matteo

Abstract

We identify a minimal superspace projector that uniquely selects the Rarita Schwinger mass bilinear in four-dimensional N=1 supergravity. Working in a reduced superspace with a single fermionic direction, we show that Berezin projection of a canonical even supergeometric form isolates the unique Lorentz-invariant fermionic bilinear compatible with local supersymmetry. The construction is predynamical: it fixes the algebraic structure of the gravitino mass term independently of supersymmetry breaking mechanisms, background geometry, or matter couplings. We show that this projector embeds consistently into curved superspace, extends to N>1 theories, and clarifies the universality of the gravitino mass structure in supergravity.

Structural Origin of the Gravitino Mass Term: Geometric and Supergravity Perspectives

Abstract

We identify a minimal superspace projector that uniquely selects the Rarita Schwinger mass bilinear in four-dimensional N=1 supergravity. Working in a reduced superspace with a single fermionic direction, we show that Berezin projection of a canonical even supergeometric form isolates the unique Lorentz-invariant fermionic bilinear compatible with local supersymmetry. The construction is predynamical: it fixes the algebraic structure of the gravitino mass term independently of supersymmetry breaking mechanisms, background geometry, or matter couplings. We show that this projector embeds consistently into curved superspace, extends to N>1 theories, and clarifies the universality of the gravitino mass structure in supergravity.
Paper Structure (58 sections, 2 theorems, 44 equations)

This paper contains 58 sections, 2 theorems, 44 equations.

Table of Contents

  1. Introduction
  2. Theoretical Background
  3. Superfiber bundles and odd differential forms
  4. Integration over fermionic fibers.
  5. $N=1$ supergravity: the gravitino field and its mass
  6. Supergeometric Formulation: Construction of an Invariant Scalar
  7. Fundamental 1-form on the superfiber bundle and its pullback
  8. Remark on the status of the differential.
  9. Geometric scalar from Berezin integration
  10. Physical Interpretation: gravitino mass term in $N=1$ Supergravity
  11. Gravitino mass and supersymmetry breaking
  12. Identification with the geometric scalar
  13. Relation to the super-Higgs mechanism
  14. Structural correspondence between geometry and energy
  15. Comparison with Standard $N=1$ Supergravity Formulations
  16. ...and 43 more sections

Key Result

Proposition 3.1

Up to total derivatives and conventions, $\theta\, d\theta$ is the unique even superspace $1$-form whose Berezin projection yields a non-vanishing Lorentz scalar fermionic bilinear.

Theorems & Definitions (4)

  • Definition 2.1: Superfiber bundle with fiber $C^{0|1}$
  • Proposition 3.1
  • Proposition 3.2: Geometric origin of the gravitino mass term structure
  • proof : Sketch of the argument