[Paper Review] Superfield formulation of N=4 Super Yang-Mills theory in plane wave background

R.R. Metsaev|arXiv (Cornell University)|Jan 3, 2003

Black Holes and Theoretical Physics10 references3 citations

TL;DR

This paper develops a superfield formulation of N=4 Super Yang-Mills theory in a plane wave background using the light cone gauge, realizing superconformal symmetries through light cone superfields and providing an oscillator realization of these symmetries. The approach offers a covariant framework for studying the theory in curved spacetime with maximal supersymmetry.

ABSTRACT

The superfield light cone gauge formulation of N=4 SYM in plane wave background is developed. We find a realization of superconformal symmetries in terms of a light cone superfield. An oscillator realization of superconformal symmetries is also obtained.

Motivation & Objective

• To formulate N=4 Super Yang-Mills theory in a plane wave background using superfield techniques.
• To realize superconformal symmetries within the light cone gauge formalism.
• To construct an oscillator representation of the superconformal algebra in this background.
• To provide a manifestly supersymmetric and covariant framework for studying the theory in curved spacetime.

Proposed method

• Employing the light cone gauge to simplify the dynamics of N=4 SYM in a plane wave background.
• Introducing a light cone superfield that encodes all physical and auxiliary fields of the theory.
• Deriving the superconformal symmetry algebra in terms of the light cone superfield components.
• Constructing an oscillator realization of the superconformal generators using harmonic oscillators.
• Ensuring consistency of the superfield action with the equations of motion and gauge constraints.
• Demonstrating that the superconformal symmetry algebra closes on-shell in the light cone superfield formulation.

Experimental results

Research questions

• RQ1 How can N=4 SYM be consistently formulated in a plane wave background using superfield methods?
• RQ2 Can superconformal symmetries be realized explicitly in the light cone superfield formalism?
• RQ3 What is the oscillator representation of the superconformal generators in this background?
• RQ4 How does the light cone gauge simplify the structure of the superconformal algebra?
• RQ5 Is the superconformal algebra closed within the superfield formulation on-shell?

Key findings

• A consistent superfield formulation of N=4 SYM in a plane wave background is achieved using the light cone gauge.
• Superconformal symmetries are realized explicitly through the light cone superfield components.
• An oscillator realization of the superconformal generators is constructed, providing a Fock space representation.
• The superconformal algebra closes on-shell, confirming consistency of the formulation.
• The framework preserves manifest supersymmetry and provides a covariant description in curved spacetime.
• The construction offers a foundation for studying the AdS/CFT correspondence in non-trivial backgrounds.