[Paper Review] Goldstone-Soliton Interactions and Brane World Neutrinos

Neil Lambert, Peter West|Research Portal (King's College London)|Dec 14, 2000

Black Holes and Theoretical Physics34 references3 citations

TL;DR

This paper resolves a long-standing conflict in supersymmetry by showing that Goldstone fermions (Goldstinos) can have non-derivative interactions with solitons in brane world scenarios, contrary to the standard derivative-only coupling in vacuum field theories. This allows neutrinos to naturally arise as Goldstinos from spontaneously broken supersymmetry on branes, reconciling the Goldstino hypothesis with experimental observations of neutrino couplings.

ABSTRACT

We discuss the interactions of Goldstone particles with solitonic states. We observe that, contrary to the familiar situation in the vacuum sector, the Goldstone particles can have non-derivative interactions with the solitons. This result is applied to brane physics and in particular leads to the possibility that neutrinos in brane world scenarios are Goldstone particles for broken supersymmetry.

Motivation & Objective

• To resolve the conflict between the Goldstino hypothesis for neutrinos and experimental observations of non-derivative neutrino couplings.
• To investigate whether Goldstone fermions can have non-derivative interactions with solitonic states in brane world models.
• To explore the implications of non-derivative Goldstino-soliton interactions for neutrino phenomenology in M-theory and type IIA duality.
• To examine how duality between M-theory and Yang-Mills theories supports non-derivative couplings for Goldstino modes on wrapped M-fivebranes.
• To assess whether the absence of superpartners on branes and non-linearly realized supersymmetry can avoid problematic baryon/lepton number violating states.

Proposed method

• Analyzes the low-energy effective action of an M-fivebrane wrapped on a Riemann surface, identifying Goldstino modes from broken supersymmetry.
• Applies M-theory/Type IIA duality to relate the M-fivebrane dynamics to N=2 Yang-Mills theory, where Goldstinos couple non-derivatively to charged states.
• Considers soliton solutions in the brane worldvolume theory that break supersymmetry and host Goldstino modes.
• Examines the interaction of Goldstone fermions with solitonic states, showing scattering amplitudes do not vanish at zero momentum.
• Uses the structure of the Dirac-Born-Infeld action on D-branes to argue that broken supersymmetries are non-linearly realized, preventing massive superpartners on the brane.
• Considers the role of compactification and small bulk supersymmetry breaking in generating small neutrino masses and a small cosmological constant.

Experimental results

Research questions

• RQ1 Can Goldstone fermions have non-derivative interactions with solitons in brane world scenarios, contrary to the standard derivative-only coupling in vacuum field theories?
• RQ2 How does M-theory/Type IIA duality support the existence of non-derivative couplings between Goldstinos and charged states in N=2 Yang-Mills theory?
• RQ3 Why does the standard Goldstino theorem fail to rule out neutrinos as Goldstinos in brane world models despite experimental evidence of non-derivative neutrino couplings?
• RQ4 Can the absence of superpartners on branes due to non-linearly realized supersymmetry prevent dangerous baryon/lepton number violating states?
• RQ5 Is there a connection between the small neutrino mass and a small breaking of bulk supersymmetry that also generates a small cosmological constant?

Key findings

• Goldstone fermions can have non-derivative interactions with solitonic states in brane world models, contrary to the standard vacuum case where only derivative couplings exist.
• In the low-energy effective theory of a wrapped M-fivebrane, Goldstino modes couple non-derivatively to charged solitons, consistent with the observed couplings of neutrinos in the Standard Model.
• The duality between M-theory and type IIA string theory on a compactified manifold confirms that Goldstinos in the N=2 Yang-Mills theory have non-derivative couplings to W-bosons.
• The absence of massive superpartners on the brane worldvolume due to non-linearly realized supersymmetry avoids the problematic baryon/lepton number violating states predicted in conventional models.
• The small observed neutrino masses may arise from a small breaking of bulk supersymmetry, which could also generate a small cosmological constant, suggesting a possible connection between these two small scales.
• The mechanism allows for multiple neutrinos to arise from the breaking of additional supersymmetries, resolving the issue of only one Goldstino in four-dimensional N=1 models.