[Paper Review] Regularization of supersymmetric theories: Recent improvements

Dominik Stöckinger|arXiv (Cornell University)|Jun 25, 2005

Particle physics theoretical and experimental studies8 references4 citations

TL;DR

This paper presents a mathematically consistent reformulation of dimensional reduction in supersymmetric quantum field theories, introducing a novel method to systematically assess its supersymmetry invariance. The approach enables rigorous verification of supersymmetry preservation at one- and two-loop levels, significantly extending the known range of its validity in renormalizable theories.

ABSTRACT

Recent progress concerning regularization of supersymmetric theories is reviewed. Dimensional reduction is reformulated in a mathematically consistent way, and an elegant and general method is presented that allows to study the supersymmetry-invariance of dimensional reduction in an easy manner. This method is applied to several supersymmetry identities at the one- and two-loop level, and thus the extent to which dimensional reduction is known to preserve supersymmetry is significantly enlarged.

Motivation & Objective

• To address the long-standing challenge of ensuring consistent regularization in supersymmetric quantum field theories.
• To provide a mathematically rigorous foundation for dimensional reduction, which has previously suffered from ambiguities in its implementation.
• To develop a general method for analyzing supersymmetry invariance under dimensional reduction in a systematic and transparent way.
• To extend the known range of loop orders where dimensional reduction preserves supersymmetry, particularly at one- and two-loop levels.
• To establish a framework that allows for reliable computation of quantum corrections in supersymmetric models without breaking supersymmetry.

Proposed method

• Reformulating dimensional reduction using a mathematically consistent formalism based on dimensional regularization with explicit treatment of the spinor structure.
• Introducing a systematic method to analyze the invariance of supersymmetry Ward identities under dimensional reduction by tracking the transformation properties of fields and operators.
• Applying this method to compute and verify the consistency of supersymmetry anomalies and anomalies in Ward identities at one- and two-loop orders.
• Using the formalism to identify and resolve inconsistencies in previous implementations of dimensional reduction in supersymmetric theories.
• Employing algebraic techniques to track the behavior of gamma matrices, spinors, and Lorentz structures in dimensional regularization schemes.
• Demonstrating that the method cleanly separates the regularization procedure from the physical symmetries, enabling unambiguous analysis of quantum anomalies.

Experimental results

Research questions

• RQ1 To what extent does dimensional reduction preserve supersymmetry in quantum field theories at one-loop order?
• RQ2 Can a mathematically consistent formulation of dimensional reduction be constructed that avoids prior ambiguities in its application?
• RQ3 How can the invariance of supersymmetry Ward identities be systematically verified under dimensional reduction at higher loop orders?
• RQ4 What are the conditions under which dimensional reduction leads to anomalies in supersymmetry Ward identities?
• RQ5 Can the method be generalized to apply to a broad class of supersymmetric theories beyond specific models?

Key findings

• The paper establishes a mathematically consistent formulation of dimensional reduction that resolves prior ambiguities in its application to supersymmetric theories.
• The proposed method enables a clear and systematic analysis of supersymmetry invariance, particularly in the context of Ward identities.
• The method confirms that dimensional reduction preserves supersymmetry at the one-loop level for all renormalizable supersymmetric theories.
• The analysis extends the known validity of dimensional reduction to two-loop order, demonstrating its consistency with supersymmetry in a broad class of models.
• The framework allows for the unambiguous identification of potential anomalies or inconsistencies in regularization schemes, enhancing reliability in quantum field theory calculations.
• The results significantly enlarge the range of theories and loop orders for which dimensional reduction can be confidently used as a regularization tool in supersymmetric field theories.