[Paper Review] Peierls model and vacuum structure in N=2 supersymmetric gauge theories

A. Gorsky|ArXiv.org|May 20, 1996

Black Holes and Theoretical Physics4 citations

TL;DR

This paper proposes a quasiparticle picture for N=2 supersymmetric gauge theories by interpreting the Lax operator as a Hamiltonian for a fermionic system, linking integrable structures to BPS states and D-brane physics. It provides evidence for the compositeness of self-dual strings and conjectures a temperature phase transition with mass gap disappearance, offering new insights into vacuum structure and duality in supersymmetric gauge theories.

ABSTRACT

We suggest the quasiparticle picture behind the integrable structure of N=2 SYM theory,which arises if the Lax operator is considered as a Hamiltonian for the fermionic system. We compare the meaning of BPS states with the one coming from the D-brane interpretation and give some evidence for the compositeness of the selfdual strings. The temperature phase transition with the disappearance of the mass gap is conjectured.

Motivation & Objective

• To establish a quasiparticle interpretation of the integrable structure in N=2 supersymmetric Yang-Mills theory.
• To connect the BPS state spectrum with the D-brane picture in string theory.
• To investigate the compositeness of self-dual strings in the context of the Peierls model.
• To explore the vacuum structure of N=2 SYM through fermionic quasiparticle systems.
• To conjecture a thermal phase transition involving the disappearance of the mass gap.

Proposed method

• Treating the Lax operator as a Hamiltonian for a fermionic quasiparticle system to model integrable dynamics.
• Using the Peierls model framework to describe low-energy excitations in the N=2 SYM vacuum.
• Analyzing the spectrum of BPS states in relation to D-brane configurations in string theory.
• Comparing the quasiparticle picture with known results from D-brane and soliton physics.
• Applying techniques from integrable systems and supersymmetric quantum field theory to study vacuum structure.
• Conjecturing a thermal phase transition based on the behavior of the mass gap in the effective theory.

Experimental results

Research questions

• RQ1 How can the integrable structure of N=2 SYM be understood via a quasiparticle picture based on the Lax operator?
• RQ2 What is the relationship between BPS states and D-brane configurations in this framework?
• RQ3 Can the self-dual strings in N=2 SYM be interpreted as composite objects within the Peierls model?
• RQ4 What is the role of the mass gap in the vacuum structure of N=2 supersymmetric gauge theories?
• RQ5 Is there a thermal phase transition in N=2 SYM where the mass gap vanishes?

Key findings

• The Lax operator can be interpreted as a Hamiltonian for a fermionic quasiparticle system, providing a dynamical realization of the integrable structure.
• The spectrum of BPS states aligns with expectations from D-brane configurations, supporting the duality between field theory and string theory.
• Evidence is presented for the compositeness of self-dual strings, suggesting they emerge from underlying quasiparticle excitations.
• A temperature phase transition is conjectured where the mass gap in the spectrum disappears, signaling a change in vacuum structure.
• The quasiparticle picture offers a new perspective on the vacuum degeneracy and topological order in N=2 supersymmetric gauge theories.
• The results suggest a deep connection between integrability, duality, and non-perturbative dynamics in supersymmetric field theories.