[Paper Review] Duality Symmetry and Soldering in Different Dimensions

Rudra Banerjee, C. Wotzasek|ArXiv.org|Oct 7, 1997

Mechanical and Optical Resonators1 references3 citations

TL;DR

This paper develops a systematic method to construct duality-symmetric actions in various dimensions—quantum mechanics, 2D scalar field theory, and 4D Maxwell theory—using dual formulations. By 'soldering' these dual actions, a master action emerges that exhibits enhanced duality symmetry, and the concept of 'swapping duality' is introduced to explore deeper symmetry structures, with implications for gravity coupling and generalization to arbitrary dimensions.

ABSTRACT

We develop a systematic method of obtaining duality symmetric actions in different dimensions. This technique is applied for the quantum mechanical harmonic oscillator, the scalar field theory in two dimensions and the Maxwell theory in four dimensions. In all cases there are two such distinct actions. Furthermore, by soldering these distinct actions in any dimension a master action is obtained which is duality invariant under a much bigger set of symmetries than is usually envisaged. The concept of swapping duality is introduced and its implications are discussed. The effects of coupling to gravity are also elaborated. Finally, the extension of the analysis for arbitrary dimensions is indicated.

Motivation & Objective

• To develop a general method for constructing duality-symmetric actions in different spacetime dimensions.
• To unify dual formulations of physical theories into a single master action via soldering.
• To introduce and analyze the concept of 'swapping duality' as a new symmetry structure.
• To examine the effects of coupling duality-symmetric theories to gravity.
• To extend the formalism to arbitrary dimensions.

Proposed method

• Construct two distinct duality-symmetric actions for each system (e.g., harmonic oscillator, scalar field, Maxwell theory) in their respective dimensions.
• Apply a soldering procedure to merge the dual actions into a single master action invariant under a larger duality group.
• Utilize a generalized action principle that treats dual fields on equal footing, preserving duality symmetry.
• Introduce the notion of 'swapping duality' as a transformation that exchanges dual field configurations.
• Analyze the symmetry structure of the master action and identify its enhanced duality invariance.
• Extend the formalism to arbitrary dimensions by generalizing the soldering and duality conditions.

Experimental results

Research questions

• RQ1 How can duality-symmetric actions be systematically constructed in different dimensions?
• RQ2 What is the role of the soldering procedure in unifying dual field theories into a single invariant action?
• RQ3 How does the concept of 'swapping duality' extend the known duality symmetries in field theories?
• RQ4 What are the implications of coupling duality-symmetric actions to gravity?
• RQ5 Can the soldering and duality framework be generalized to arbitrary spacetime dimensions?

Key findings

• For each system—harmonic oscillator, 2D scalar field, and 4D Maxwell theory—two distinct duality-symmetric actions are derived, reflecting dual descriptions.
• The soldering of these dual actions results in a master action that is invariant under a significantly larger duality symmetry group than the individual dual actions.
• The introduction of 'swapping duality' reveals a new symmetry structure that exchanges dual field configurations, enriching the duality framework.
• Coupling to gravity preserves the duality structure, suggesting compatibility with general relativistic backgrounds.
• The formalism is extended to arbitrary dimensions, indicating broad applicability beyond specific cases.