[Paper Review] Deconstructing Supergravity, I: Massive Supermultiplets

Nicholas A. Ondo, Andrew J. Tolley|arXiv (Cornell University)|Dec 27, 2016

Black Holes and Theoretical Physics43 references3 citations

TL;DR

This paper proposes a supersymmetric deconstruction procedure to derive massive supermultiplets in 4D from 5D supergravity, showing that a 1-site deconstruction yields the N=1 Zinoviev theory as the linearized supersymmetric extension of massive gravity. The method preserves half of the original 5D supersymmetry and successfully reproduces the 4D supersymmetry algebra and Stueckelberg symmetry from the 5D parent theory.

ABSTRACT

Given the success of the deconstruction program in obtaining ghost-free massive gravity from 5-D Einstein gravity, we propose a modification of the deconstruction procedure that incorporates supersymmetry at the linear level. We discuss the relevant limits of a conjectured interacting theory of a massive spin 2 supermultiplet, and determine the linear theory to be the N=1 Zinoviev theory, a supersymmetric extension of Fierz-Pauli theory. We develop a family of 1-site deconstruction procedures for fermionic fields (yielding Dirac and Majorana mass terms). The deconstruction procedure appropriate for giving fermions a Dirac mass is found to preserve half of the supersymmetry of the 5-D theory. We explicitly check this by deconstructing 5-D N=2 super-Maxwell theory down to 4-D N=1 super-Proca theory, and deconstructing linear 5-D N=2 supergravity down to 4-D N=1 Zinoviev theory, and derive the full 4-D supersymmetry algebras and Stueckelberg symmetries from the 5-D superalgebras and gauge symmetries, respectively. We conjecture that this procedure should admit a generalization to fully non-linear theories.

Motivation & Objective

• To extend the deconstruction program to include supersymmetry at the linear level in massive gravity theories.
• To determine the linear theory resulting from a conjectured interacting massive spin-2 supermultiplet in 5D.
• To develop a 1-site deconstruction framework for fermionic fields that generates Dirac and Majorana mass terms.
• To verify that the deconstruction procedure preserves half of the original 5D supersymmetry in the 4D effective theory.
• To derive the full 4D supersymmetry algebra and Stueckelberg symmetry from the 5D superalgebra and gauge symmetries.

Proposed method

• Adapts the deconstruction program to incorporate supersymmetry by constructing a 1-site lattice model for fermions with Dirac and Majorana mass terms.
• Identifies the linearized effective theory as the N=1 Zinoviev theory, a supersymmetric extension of the Fierz-Pauli theory for massive spin-2 particles.
• Uses dimensional reduction and Kaluza-Klein mode decomposition to relate 5D N=2 super-Maxwell and supergravity to 4D N=1 super-Proca and Zinoviev theories.
• Analyzes the preserved supersymmetry by comparing the 4D supercharges to those in the 5D parent theory.
• Derives the 4D supersymmetry algebra and Stueckelberg symmetry algebra from the 5D superalgebra and gauge symmetry structure.
• Demonstrates consistency by explicitly constructing the 4D algebra and symmetry structures from the 5D counterparts in two concrete examples.

Experimental results

Research questions

• RQ1 What is the linear effective theory obtained from deconstructing a conjectured interacting massive spin-2 supermultiplet in 5D?
• RQ2 How much supersymmetry is preserved in the 4D deconstructed theory when fermions acquire Dirac masses?
• RQ3 Can the 4D N=1 Zinoviev theory be derived as the low-energy limit of 5D N=2 supergravity via deconstruction?
• RQ4 How are the 4D supersymmetry charges and Stueckelberg symmetries reconstructed from the 5D superalgebra and gauge symmetries?
• RQ5 Does the deconstruction procedure admit a generalization to fully non-linear supersymmetric massive gravity theories?

Key findings

• The linearized effective theory resulting from the deconstruction is identified as the N=1 Zinoviev theory, a supersymmetric extension of the Fierz-Pauli theory for massive spin-2 particles.
• The 1-site deconstruction procedure that gives fermions Dirac masses preserves exactly half of the original 5D supersymmetry.
• The full 4D N=1 supersymmetry algebra is successfully reconstructed from the 5D N=2 superalgebra via the deconstruction procedure.
• The 4D Stueckelberg symmetry algebra is derived from the 5D gauge symmetry structure, confirming the consistency of the massive vector multiplet realization.
• Explicit deconstruction of 5D N=2 super-Maxwell theory yields 4D N=1 super-Proca theory, and deconstruction of 5D N=2 supergravity yields 4D N=1 Zinoviev theory.
• The results support the conjecture that the deconstruction procedure can be generalized to fully non-linear supersymmetric massive gravity theories.