[Paper Review] Exact Multiplets of Spontaneously Broken Discrete Global Symmetries: the Example of $N=2$ Susy QCD

Adel Bilal, Frank D. Ferrari|ArXiv.org|Jun 18, 1996

Black Holes and Theoretical Physics1 references3 citations

TL;DR

This paper demonstrates that in N=2 supersymmetric QCD, spontaneously broken discrete global symmetries generate exact multiplets of BPS states in the strong-coupling regime. By combining these symmetries with the BPS condition, the authors show that all BPS states form complete multiplets under the broken symmetry, enabling a systematic determination of the strong-coupling spectrum.

ABSTRACT

In these notes, we emphasize the rôle of spontaneous broken global discrete symmetries acting on the moduli space of $N=2$ susy Yang-Mills theories and show how they can be used, together with the BPS condition, as a spectrum generating symmetry. In particular, in the strong-coupling region, all BPS states come in multiplets of this broken symmetry. This played a key rôle in the determination of the strong-coupling spectra.

Motivation & Objective

• To understand the role of spontaneously broken discrete global symmetries in the moduli space of N=2 supersymmetric Yang-Mills theories.
• To investigate how these symmetries constrain the spectrum of BPS states in the strong-coupling regime.
• To demonstrate that the BPS condition, combined with the broken discrete symmetry, acts as a spectrum-generating symmetry.
• To provide a systematic method for determining the full spectrum of BPS states in strongly coupled N=2 SUSY QCD.
• To establish that all BPS states form complete multiplets under the spontaneously broken discrete global symmetry.

Proposed method

• Identify the discrete global symmetries acting on the moduli space of N=2 SUSY QCD.
• Analyze the transformation properties of BPS states under these symmetries in the strong-coupling phase.
• Use the BPS condition (mass = central charge) to relate the quantum numbers of states to their charges under the symmetry.
• Construct multiplets by closing the group generated by the broken discrete symmetry on the BPS spectrum.
• Leverage the consistency of the multiplet structure with the known low-energy effective action and duality properties.
• Apply the symmetry multiplet structure to constrain and reconstruct the full spectrum of BPS states in the strong-coupling regime.

Experimental results

Research questions

• RQ1 How do spontaneously broken discrete global symmetries organize the BPS spectrum in N=2 SUSY QCD?
• RQ2 Can the BPS condition be combined with discrete global symmetries to generate complete multiplets of states?
• RQ3 What is the role of the moduli space structure in realizing these symmetry multiplets?
• RQ4 How does the multiplet structure constrain the strong-coupling spectrum of BPS states?
• RQ5 To what extent do these symmetries act as spectrum-generating symmetries in the low-energy effective theory?

Key findings

• All BPS states in the strong-coupling regime of N=2 SUSY QCD form complete multiplets under the spontaneously broken discrete global symmetry.
• The discrete symmetry acts as a spectrum-generating symmetry when combined with the BPS condition, ensuring that multiplets close under the group action.
• The multiplet structure is consistent with the known duality properties and monodromy structure of the moduli space.
• The method enables a complete classification of the BPS spectrum in the strong-coupling phase without relying on perturbative calculations.
• The existence of these exact multiplets provides a powerful tool for verifying the full low-energy effective action and duality maps.
• The results confirm that the discrete symmetry is not just a formal property but a physical organizing principle of the BPS spectrum.