[Paper Review] Supersymmetric Gauge Theories

David S. Berman, Eliezer Rabinovici|arXiv (Cornell University)|Oct 4, 2002

Black Holes and Theoretical Physics4 citations

TL;DR

This paper provides a comprehensive overview of supersymmetric gauge theories, introducing foundational concepts in supersymmetric quantum mechanics and field theory, and exploring advanced topics such as phase structure, superconformal invariance, and infrared duality in both field and string theories. It establishes a connection between conformal symmetry and vanishing vacuum energy, offering insights into the cosmological constant problem.

ABSTRACT

We introduce simple and more advanced concepts that have played a key role in the development of supersymmetric systems. This is done by first describing various supersymmetric quantum mechanics models. Topics covered include the basic construction of supersymmetric field theories, the phase structure of supersymmetric systems with and without gauge particles, superconformal theories and infrared duality in both field theory and string theory. A discussion of the relation of conformal symmetry to a vanishing vacuum energy (cosmological constant) is included.

Motivation & Objective

• To introduce fundamental concepts in supersymmetric quantum mechanics as a foundation for understanding more complex systems.
• To analyze the phase structure of supersymmetric systems, both with and without gauge particles, to clarify stability and dynamics.
• To investigate superconformal theories and their role in infrared duality, linking field theory and string theory.
• To examine the relationship between conformal symmetry and the vanishing of the cosmological constant, addressing a key issue in theoretical physics.

Proposed method

• Constructing supersymmetric quantum mechanics models using supercharges and Hamiltonians to illustrate basic supersymmetry algebra.
• Formulating supersymmetric field theories via Lagrangians with chiral and vector multiplets, ensuring invariance under supersymmetry transformations.
• Analyzing the phase structure of supersymmetric systems through effective potential methods and vacuum degeneracy.
• Applying the concept of superconformal invariance to classify fixed points in the renormalization group flow.
• Using dualities—such as Seiberg duality in 4D and AdS/CFT in string theory—to explore infrared equivalence between different gauge theories.
• Relating vanishing vacuum energy to conformal symmetry by examining the trace anomaly and the role of the dilaton in the effective action.

Experimental results

Research questions

• RQ1 How do supersymmetric quantum mechanics models illustrate the algebraic structure of supersymmetry and its implications for energy spectra?
• RQ2 What determines the phase structure of supersymmetric gauge theories, especially in the presence or absence of gauge bosons?
• RQ3 In what ways do superconformal theories exhibit infrared duality, and how do these dualities manifest in both field and string theories?
• RQ4 How is conformal symmetry connected to the vanishing of the cosmological constant, and what are the implications for vacuum stability?

Key findings

• Supersymmetric quantum mechanics models exhibit degenerate energy spectra between bosonic and fermionic states, confirming the algebraic consistency of supersymmetry.
• The phase structure of supersymmetric systems is determined by the interplay between mass terms, gauge dynamics, and the existence of non-trivial vacua.
• Superconformal theories emerge at fixed points of the renormalization group flow, exhibiting enhanced symmetry and enabling duality relations.
• Infrared duality in 4D supersymmetric gauge theories, such as Seiberg duality, demonstrates equivalence between distinct gauge groups with different matter content.
• Conformal symmetry is linked to a vanishing cosmological constant through the trace anomaly and the emergence of the dilaton as a Nambu-Goldstone mode of spontaneously broken scale invariance.