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Supersymmetry reduction of N-extended supergravities in four dimensions

Laura Andrianopoli, Riccardo D'Auria, Sergio Ferrara

TL;DR

This work demonstrates that consistent truncations of N-extended supergravities to lower N' are nontrivial in four dimensions and are governed by precise geometric and group-theoretical constraints. It develops a unified framework linking gravitino truncations to submanifolds of the original scalar cosets, requiring reductions of Special-Kähler and quaternionic geometries to yield Kahler–Hodge manifolds and compatible holonomy. The core result is a detailed N=2→N=1 reduction in the presence of gauging, deriving the induced D-terms, superpotential, and the reduced scalar potential, with explicit mappings of vector and hypermultiplet sectors and consistency checks via supersymmetry Ward identities. The paper also extends the analysis to D=3,5,6 and provides concrete construction templates (e.g., Z_2 orbifolds, c-map cousins) to realize N=1 gauged supergravity theories from higher-N parents, illuminating connections to string/M-theory compactifications and brane dynamics.

Abstract

We consider the possible consistent truncation of N-extended supergravities to lower N' theories. The truncation, unlike the case of N-extended rigid theories, is non trivial and only in some cases it is sufficient just to delete the extra N-N' gravitino multiplets. We explore different cases (starting with N=8 down to N'\geq 2) where the reduction implies restrictions on the matter sector. We perform a detailed analysis of the interesting case N=2 \to N=1. This analysis finds applications in different contexts of superstring and M-theory dynamics.

Supersymmetry reduction of N-extended supergravities in four dimensions

TL;DR

This work demonstrates that consistent truncations of N-extended supergravities to lower N' are nontrivial in four dimensions and are governed by precise geometric and group-theoretical constraints. It develops a unified framework linking gravitino truncations to submanifolds of the original scalar cosets, requiring reductions of Special-Kähler and quaternionic geometries to yield Kahler–Hodge manifolds and compatible holonomy. The core result is a detailed N=2→N=1 reduction in the presence of gauging, deriving the induced D-terms, superpotential, and the reduced scalar potential, with explicit mappings of vector and hypermultiplet sectors and consistency checks via supersymmetry Ward identities. The paper also extends the analysis to D=3,5,6 and provides concrete construction templates (e.g., Z_2 orbifolds, c-map cousins) to realize N=1 gauged supergravity theories from higher-N parents, illuminating connections to string/M-theory compactifications and brane dynamics.

Abstract

We consider the possible consistent truncation of N-extended supergravities to lower N' theories. The truncation, unlike the case of N-extended rigid theories, is non trivial and only in some cases it is sufficient just to delete the extra N-N' gravitino multiplets. We explore different cases (starting with N=8 down to N'\geq 2) where the reduction implies restrictions on the matter sector. We perform a detailed analysis of the interesting case N=2 \to N=1. This analysis finds applications in different contexts of superstring and M-theory dynamics.

Paper Structure

This paper contains 12 sections, 313 equations, 5 tables.

Table of Contents

  1. Introduction
  2. $N=8\longrightarrow N'$ reduction without gauging
  3. $D=3$, $D=5$ and $D=6$ reduction of maximal supergravity to theories with eight supercharges.
  4. Geometrical interpretation
  5. Consistency constraints from supersymmetry
  6. $N=2\longrightarrow N=1$ reduction
  7. Reduction of the $N=2$ vector multiplet sector
  8. $N=2$ vector multiplets $\longrightarrow N=1$ matter multiplets
  9. Reduction of the hypermultiplet sector
  10. Further consequences of the gauging
  11. $N=2 \rightarrow N=1$ scalar potential
  12. Examples of truncation to $N=1$ gauged supergravity