[Paper Review] Supersymmetry breaking in M-theory and quantization rules

Emilian Dudaş|arXiv (Cornell University)|Sep 4, 1997

Black Holes and Theoretical Physics4 citations

TL;DR

This paper investigates supersymmetry breaking in M-theory via compactification from 11D to 5D to 4D, showing that hypermultiplet moduli—specifically the dilaton S and complex structure moduli—are stabilized by a superpotential generated through compactification, ensuring they do not contribute to supersymmetry breaking. The mechanism is shown to be the strong-coupling analog of Rohm-Witten quantization, with supersymmetry breaking fully saturated by Kähler moduli from vector multiplets.

ABSTRACT

We analyze in detail supersymmetry breaking by compactification of the fifth dimension in M-theory in the compactification pattern $11d o 5d o 4d$ and find that a superpotential is generated for the complex fields coming from $5d$ hypermultiplets, namely the dilaton $S$ and the complex structure moduli. Using general arguments it is shown that these fields are always stabilized such that they don't contribute to supersymmetry breaking, which is completely saturated by the Kähler moduli coming from vector multiplets. It is shown that this mechanism is the strong-coupling analog of the Rohm-Witten quantization of the antisymmetric tensor field strength of string theories. The effect of a gaugino condensate on one of the boundaries is also considered.

Motivation & Objective

• To understand how supersymmetry breaking arises in M-theory through dimensional reduction from 11D to 4D via 5D compactification.
• To determine the role of hypermultiplet moduli—dilaton S and complex structure moduli—in the supersymmetry breaking mechanism.
• To establish that these hypermultiplet fields are stabilized by a dynamically generated superpotential, preventing them from contributing to supersymmetry breaking.
• To show that the Kähler moduli from vector multiplets fully saturate the supersymmetry breaking, making them the sole source of SUSY breaking.
• To identify the strong-coupling analog of the Rohm-Witten quantization condition for the antisymmetric tensor field strength in string theory within the M-theory framework.

Proposed method

• Analyzes the compactification pattern 11D → 5D → 4D in M-theory, focusing on the emergence of hypermultiplets and vector multiplets in lower dimensions.
• Constructs a superpotential for the complex scalar fields from 5D hypermultiplets (dilaton S and complex structure moduli) via quantum corrections from compactification.
• Applies general arguments from effective field theory and duality to show that the superpotential stabilizes the hypermultiplet moduli at fixed values.
• Demonstrates that the Kähler moduli, originating from 5D vector multiplets, remain as the only source of supersymmetry breaking after stabilization.
• Considers the effect of a gaugino condensate on one boundary in the 5D compactification, showing its consistency with the stabilization mechanism.
• Draws a parallel between the stabilization mechanism and the Rohm-Witten quantization condition in string theory, identifying it as the strong-coupling limit of that mechanism.

Experimental results

Research questions

• RQ1 How does supersymmetry breaking emerge in M-theory through the compactification of the fifth dimension?
• RQ2 What is the role of the dilaton and complex structure moduli in the supersymmetry breaking mechanism after compactification?
• RQ3 Can the hypermultiplet moduli be stabilized such that they do not contribute to supersymmetry breaking?
• RQ4 What is the strong-coupling analog of the Rohm-Witten quantization condition in M-theory?
• RQ5 How does the presence of a gaugino condensate on a boundary affect the supersymmetry breaking pattern in the 5D effective theory?

Key findings

• A superpotential is generated for the hypermultiplet moduli (dilaton S and complex structure moduli) due to compactification in the 5D effective theory.
• The hypermultiplet moduli are stabilized at fixed values due to the superpotential, ensuring they do not contribute to supersymmetry breaking.
• Supersymmetry breaking is completely saturated by the Kähler moduli originating from 5D vector multiplets.
• The stabilization mechanism is identified as the strong-coupling analog of the Rohm-Witten quantization condition for the antisymmetric tensor field strength in string theory.
• The inclusion of a gaugino condensate on one boundary is consistent with the overall stabilization and supersymmetry breaking pattern.
• The results are robust under general field-theoretic arguments and duality considerations, supporting the emergence of a consistent low-energy effective theory in 4D M-theory compactifications.