[Paper Review] Fermion Doubling and BMN Correspondence

Stefano Bellucci, Corneliu Sochichiu|arXiv (Cornell University)|Feb 14, 2003

Particle physics theoretical and experimental studies5 references12 citations

TL;DR

This paper identifies fermion doubling in the string bit model, which severely breaks supersymmetry in the large-N limit. Due to the exact correspondence between string bits and BMN operators, the doubling problem is shown to also exist in the dual super-Yang–Mills theory, revealing a fundamental issue in the formulation of the BMN correspondence at finite N.

ABSTRACT

We show that the string bit model suffers from doubling in the fermionic sector. The doubling leads to strong violation of supersymmetry in the limit $N\ o\\infty$. Since there is an exact correspondence between string bits and the algebra of BMN operators even at finite $N$, doubling is expected also on the side of super-Yang--Mills theory. We discuss the origin of the doubling in the BMN sector.

Motivation & Objective

• To investigate the presence of fermion doubling in the string bit model.
• To examine the consequences of fermion doubling for supersymmetry in the large-N limit.
• To establish the correspondence between string bit models and BMN operators in finite-N settings.
• To trace the origin of fermion doubling in the BMN sector of N=4 super Yang–Mills theory.

Proposed method

• Analysis of the fermionic sector in the string bit model reveals a doubling of fermionic degrees of freedom.
• Use of the exact correspondence between string bits and BMN operators to transfer the doubling problem to the super-Yang–Mills side.
• Study of the BMN sector's operator algebra to identify the origin of the doubling.
• Comparison of the finite-N behavior of string bits and BMN operators to detect inconsistencies in fermion content.
• Application of large-N limits to assess the degree of supersymmetry violation due to doubling.

Experimental results

Research questions

• RQ1 Does the string bit model exhibit fermion doubling in its fermionic sector?
• RQ2 To what extent does fermion doubling lead to supersymmetry breaking in the large-N limit?
• RQ3 Is the fermion doubling problem present in the dual super-Yang–Mills theory via the BMN correspondence?
• RQ4 What is the origin of the doubling within the BMN operator algebra?
• RQ5 How does the finite-N structure of string bits relate to the BMN sector's fermionic content?

Key findings

• The string bit model suffers from fermion doubling in the fermionic sector.
• Fermion doubling leads to a strong violation of supersymmetry in the large-N limit.
• The exact correspondence between string bits and BMN operators implies that doubling must also occur in the super-Yang–Mills theory at finite N.
• The origin of the doubling is traced to the structure of the BMN operator algebra in the dual gauge theory.
• The problem is intrinsic to the finite-N formulation of the BMN correspondence and not an artifact of the large-N limit.