[Paper Review] Massive Spin-2 Supermultiplets

Yu. M. Zinoviev|ArXiv.org|Jun 23, 2002

Black Holes and Theoretical Physics22 references16 citations

TL;DR

This paper presents a gauge-invariant Lagrangian formulation for massive spin-2 supermultiplets with $N = k$ supersymmetries ($k=1,2,3,4$), using a formulation of massive high-spin fields that maintains the correct physical degrees of freedom and a non-singular massless limit. The key result is that the massless limit of the $N=k$ supermultiplets can be uplifted to $N=2k$ local supersymmetry, revealing hidden extended supersymmetries and linking the models to five-dimensional extended supergravities.

ABSTRACT

In this paper we construct explicit Lagrangian formulation for the massive spin-2 supermultiplets with N = k supersymmetries k = 1,2,3,4. Such multiplets contain 2k particles with spin-3/2, so there must exist N = 2k local supersymmetries in the full nonlinear theories spontaneously broken so that only N = k global supersymmetries remain unbroken. In this paper we unhide these hidden supersymmetries by using gauge invariant formulation for massive high spin particles. Such formulation, operating with the right set of physical degrees of freedom from the very beginning and having non-singular massless limit, turns out to be very well suited for construction of massive supermultiplets from the well known massless ones. For all four cases considered we have managed to show that the massless limit of the supertransformations for N = k massive supermultiplet could be uplifted to N = 2k supersymmetry. This, in turn, allows one to investigate which extended supergravity models such massive multiplets could arise from. Our results show a clear connection of possible models with the five-dimensional extended supergravities.

Motivation & Objective

• To construct explicit Lagrangian formulations for massive spin-2 supermultiplets with $N = k$ supersymmetries for $k=1,2,3,4$.
• To reveal the hidden $N=2k$ local supersymmetries spontaneously broken in these massive theories.
• To establish a connection between the structure of these massive supermultiplets and five-dimensional extended supergravity models.
• To demonstrate that the massless limit of the supertransformations in $N=k$ massive supermultiplets can be uplifted to $N=2k$ supersymmetry.
• To show that the correct vector field mixing and scalar global symmetries in the models match those of dimensional reductions from 5D supergravities.

Proposed method

• Utilizes a gauge-invariant formulation for massive high-spin particles that starts with the correct number of physical degrees of freedom and ensures a non-singular massless limit.
• Starts from massless supermultiplets and adds low-derivative mass terms to the Lagrangian, along with corrections to fermionic supertransformation laws.
• Imposes invariance under supertransformations to fix unknown coefficients in the Lagrangian and transformation rules.
• Employs duality transformations to mix vector fields across supermultiplets, which is essential for constructing consistent massive models.
• Uses $SO(6) \approx SU(4)$ matrices and their algebraic identities to handle the $N=4$ case, including symmetric and antisymmetric tensor structures.
• Verifies that the resulting massive supermultiplets have supertransformations whose massless limit can be extended to $N=2k$ supersymmetry.

Experimental results

Research questions

• RQ1 How can a consistent Lagrangian formulation be constructed for massive spin-2 supermultiplets with $N=k$ supersymmetries for $k=1,2,3,4$?
• RQ2 What is the origin of the hidden $N=2k$ local supersymmetries in these massive theories, and how can they be revealed?
• RQ3 Can the massless limit of the supermultiplets with $N=k$ supersymmetry be uplifted to $N=2k$ supersymmetry?
• RQ4 Which extended supergravity models can give rise to these massive spin-2 supermultiplets?
• RQ5 Do these massive supermultiplets arise from dimensional reduction of five-dimensional supergravity theories?

Key findings

• The paper successfully constructs explicit Lagrangian formulations for massive spin-2 supermultiplets with $N=1,2,3,4$ supersymmetries using a gauge-invariant approach to massive high-spin fields.
• The massless limit of the supertransformations for $N=k$ massive supermultiplets can be uplifted to $N=2k$ local supersymmetry, revealing hidden extended supersymmetry.
• The models constructed are consistent with five-dimensional extended supergravity theories, as confirmed by matching vector field mixing and global symmetries.
• For all four cases, the correct number of physical degrees of freedom is maintained from the start, and the massless limit is non-singular.
• The use of duality transformations to mix vector fields across supermultiplets is essential for consistency and leads to models matching known 5D supergravity structures.
• The Dirac mass term for gravitini is the only viable option in these multiplets due to opposite axial charges, and it is consistently incorporated in the gauge-invariant formulation.