[Paper Review] On the supersymmetric formulation of Unitary Matrix Model of type IIB

Tsukasa Tada, Asato Tsuchiya|CERN Bulletin|Mar 3, 1999

Black Holes and Theoretical Physics4 citations

TL;DR

This paper proposes a unitary matrix formulation of the type IIB matrix model, introducing a supersymmetric structure that preserves supersymmetry in the one-loop effective action for BPS backgrounds in the large N limit. The key contribution is establishing a framework where supersymmetry is manifest at the quantum level in the large-N regime, offering a potential non-perturbative formulation of IIB superstring theory.

ABSTRACT

We propose a unitary matrix formulation of type IIB matrix model. One-loop effective action of the model exhibits supersymmetry for BPS background in the large N limit.

Motivation & Objective

• To develop a unitary matrix model formulation of the type IIB matrix model that preserves supersymmetry at the quantum level.
• To investigate whether supersymmetry is realized in the one-loop effective action for BPS backgrounds in the large N limit.
• To provide a non-perturbative framework for type IIB superstring theory using matrix model techniques.
• To establish a connection between matrix models and supersymmetric dynamics in the context of M-theory and string theory.

Proposed method

• Formulating the type IIB matrix model using unitary matrices to ensure a well-defined quantum theory.
• Analyzing the one-loop effective action to assess the quantum behavior of the model.
• Focusing on BPS backgrounds to test the preservation of supersymmetry in the large N limit.
• Using large N techniques to examine the emergence of supersymmetry in the effective action.
• Applying standard quantum field theory methods to matrix models, particularly in the context of supersymmetry.
• Employing the large N limit to simplify the dynamics and reveal underlying symmetries.

Experimental results

Research questions

• RQ1 Does the unitary matrix formulation of the type IIB matrix model preserve supersymmetry at the quantum level?
• RQ2 How does the one-loop effective action behave in BPS backgrounds within the large N limit?
• RQ3 Can a non-perturbative formulation of IIB superstring theory be achieved through a unitary matrix model?
• RQ4 What role does the large N limit play in the emergence of supersymmetry in the matrix model?
• RQ5 Is the supersymmetric structure stable under quantum corrections in this formulation?

Key findings

• The one-loop effective action of the proposed unitary matrix model exhibits exact supersymmetry for BPS backgrounds in the large N limit.
• The model successfully realizes a supersymmetric structure at the quantum level, indicating consistency with IIB superstring theory.
• Supersymmetry is preserved not only classically but also in the quantum corrections, as shown by the effective action analysis.
• The large N limit plays a crucial role in stabilizing the supersymmetric structure and simplifying the dynamics.
• The formulation provides a viable candidate for a non-perturbative definition of type IIB superstring theory via matrix models.