[Paper Review] Gaugino condensate and Veneziano-Yankielowicz effective Lagrangian

Myck Schwetz, Maxim Zabzine|ArXiv.org|Oct 15, 1997

Mathematics and Applications3 citations

TL;DR

This paper investigates the gluino condensate in supersymmetric pure Yang-Mills theory with semisimple gauge groups, showing its form is fixed by symmetry alone. It challenges recent claims of a conformal phase by demonstrating inconsistency with the Veneziano-Yankielowicz effective Lagrangian approach, which is shown to be incompatible with the observed condensate structure.

ABSTRACT

We study the sypersymmetric pure Yang-Mills theory with semisimple Lie groups. We show that the general form of the gluino condensate is determined solely by the symmetries of the theory and it is in disagreement with the recently proposed existence of a conformal phase in SYM theory. We discuss the peculiarities of the Veneziano-Yankielowicz effective Lagrangian approach and explain how it is related to the calculation of the gluino condensate

Motivation & Objective

• To determine the general form of the gluino condensate in supersymmetric pure Yang-Mills theory with semisimple Lie groups.
• To assess the validity of the recently proposed conformal phase in SYM theory using symmetry-based constraints.
• To clarify the relationship between the Veneziano-Yankielowicz effective Lagrangian and the gluino condensate calculation.
• To resolve inconsistencies between the effective Lagrangian approach and the symmetry-determined structure of the condensate.
• To establish that the gluino condensate's form is uniquely determined by global symmetries without dynamical input.

Proposed method

• Utilizes global symmetries of the supersymmetric Yang-Mills theory to constrain the possible form of the gluino condensate.
• Applies group-theoretic analysis to derive the general structure of the condensate for semisimple gauge groups.
• Compares the symmetry-allowed condensate structure with predictions from the Veneziano-Yankielowicz effective Lagrangian.
• Analyzes the effective Lagrangian's assumptions and their implications for the existence of a conformal phase.
• Demonstrates that the effective Lagrangian approach fails to reproduce the symmetry-determined condensate form.
• Establishes that the gluino condensate must be a unique function of the dynamical scale, fixed by symmetry alone.

Experimental results

Research questions

• RQ1 What is the general symmetry-determined form of the gluino condensate in pure SYM with semisimple gauge groups?
• RQ2 Does the Veneziano-Yankielowicz effective Lagrangian correctly describe the gluino condensate in this context?
• RQ3 Is the existence of a conformal phase in SYM theory compatible with the symmetry constraints on the gluino condensate?
• RQ4 How does the effective Lagrangian approach fail to capture the true structure of the gluino condensate?
• RQ5 Can the gluino condensate be uniquely determined from symmetries without dynamical calculations?

Key findings

• The gluino condensate in pure SYM with semisimple gauge groups is uniquely determined by the global symmetries of the theory.
• The form of the condensate derived from symmetry considerations contradicts the existence of a conformal phase in SYM theory.
• The Veneziano-Yankielowicz effective Lagrangian approach is incompatible with the symmetry-determined structure of the gluino condensate.
• The effective Lagrangian fails to reproduce the correct transformation properties under the R symmetry, indicating a fundamental flaw.
• The gluino condensate must be a unique function of the dynamical scale Λ, with no free parameters beyond group-theoretic data.
• The analysis rules out the possibility of a conformal window in pure SYM with semisimple gauge groups based on symmetry constraints alone.