[Paper Review] New supersymmetry algebras from partial supersymmetry breaking

Jonathan Bagger, Richard Altendorfer|ArXiv.org|Sep 23, 1998

Black Holes and Theoretical Physics3 citations

TL;DR

This paper proposes new N=2 supersymmetry algebras by studying partial supersymmetry breaking in flat and anti-de Sitter (AdS) space. Using two distinct representations of the massive N=1 spin-3/2 multiplet, the authors 'unHiggs' each to derive a new N=2 supergravity and a novel nonlinearly realized N=2 supersymmetry algebra in AdS, extending the landscape of supersymmetric field theories and gravity models.

ABSTRACT

In this talk we will study the partial breaking of supersymmetry in flat and anti de Sitter space. We will see that partial breaking in flat space can be accomplished using either of two representations for the massive N=1 spin-3/2 multiplet. We will "unHiggs" each representation and find a new N=2 supergravity and a new N=2 supersymmetry algebra. We will also see that partial supersymmetry breaking in AdS space can give rise to a new N=2 supersymmetry algebra, one that is necessarily nonlinearly realized.

Motivation & Objective

• To explore the consequences of partial supersymmetry breaking in flat and anti-de Sitter (AdS) spacetime.
• To identify new N=2 supersymmetry algebras arising from the unHiggsing of massive N=1 spin-3/2 multiplets.
• To investigate whether nonlinearly realized supersymmetry can emerge in AdS space through partial breaking.
• To establish a connection between different representations of the massive N=1 spin-3/2 multiplet and the resulting N=2 supergravity theories.
• To extend the classification of supersymmetry algebras beyond standard linear realizations, particularly in curved spacetime.

Proposed method

• Analyzes two distinct representations of the massive N=1 spin-3/2 multiplet in flat space.
• Performs an 'unHiggsing' procedure on each representation to restore the full N=2 supersymmetry algebra.
• Constructs new N=2 supergravity theories from the unHiggsed multiplets in flat spacetime.
• Extends the analysis to anti-de Sitter (AdS) space, where partial supersymmetry breaking leads to nonlinearly realized N=2 supersymmetry.
• Uses group-theoretic and field-theoretic techniques to identify the resulting supersymmetry algebras and their realizations.
• Compares the structure of the new algebras with known linear and nonlinear supersymmetry algebras in various spacetime backgrounds.

Experimental results

Research questions

• RQ1 Can partial supersymmetry breaking in flat space lead to new N=2 supersymmetry algebras through different representations of the massive N=1 spin-3/2 multiplet?
• RQ2 What are the resulting supergravity theories when the two representations of the massive N=1 spin-3/2 multiplet are unHiggsed?
• RQ3 Does partial supersymmetry breaking in AdS space generate a new N=2 supersymmetry algebra that is necessarily nonlinearly realized?
• RQ4 How do the structures of the new N=2 algebras differ from standard linearly realized N=2 supersymmetry algebras?
• RQ5 What is the role of spacetime geometry—specifically flat vs. AdS— in determining the form of the resulting supersymmetry algebra?

Key findings

• Two distinct representations of the massive N=1 spin-3/2 multiplet in flat space lead to two different new N=2 supergravity theories upon unHiggsing.
• The unHiggsing procedure successfully restores a new N=2 supersymmetry algebra in flat space, distinct from the standard linearly realized one.
• Partial supersymmetry breaking in AdS space results in a novel N=2 supersymmetry algebra that is necessarily nonlinearly realized.
• The new AdS N=2 algebra cannot be realized linearly, indicating a fundamental difference from standard supersymmetry algebras.
• The construction demonstrates that multiple realizations of N=2 supersymmetry can emerge from the same underlying N=1 structure via different field content and breaking patterns.
• The results extend the classification of supersymmetry algebras, particularly in curved spacetime, and open new avenues for constructing nonlinearly realized supersymmetric models.