[Paper Review] From Wrapped Supermembrane to M(atrix) Theory From Wrapped Supermembrane to M(atrix) Theory

Tamiaki Yoneya|ArXiv.org|Oct 25, 2002

Quantum-Dot Cellular Automata4 citations

TL;DR

This paper presents a direct derivation of Matrix-string theory from an eleven-dimensional supermembrane wrapped on a circle, without relying on string dualities. It shows that two distinct boosts—of an unwrapped membrane and a wrapped membrane in orthogonal directions—yield the same Matrix theory in the 11D limit (R→∞, N→∞), unifying two perspectives on M(atrix) theory and suggesting a deeper connection between membrane dynamics and matrix models.

ABSTRACT

The issue of justifying the matrix-theory proposal is revisited. We first discuss how the matrix-string theory is derived directly starting from the eleven dimensional supermembrane wrapped around a circle of radius $R=g_s\ell_s$, without invoking any stringy assumptions, such as S- and T-dualities. This derivation provides us a basis for studying both string ($R o 0)$- and M ($R o \infty$)-theory limits of quantum membrane theory in a single unified framework. In particular, we show that two different boosts of supermembrane, namely one of unwrapped membrane along the M-theory circle and the other of membrane wrapped about a transervse direction which is orthogonal to the M-theory circle, give the same matrix theory in the 11 dimensional limit, $R o \infty$ (with $N o \infty$). We also discuss briefly the nature of possible covariantized matrix (string) theories.

Motivation & Objective

• To provide a unified framework for deriving Matrix theory from supermembrane dynamics without invoking S- or T-duality.
• To clarify the relationship between the infinite momentum frame (IMF) and wrapped membrane approaches to M(atrix) theory.
• To demonstrate that two different membrane boosts lead to the same Matrix theory in the 11D decompactification limit.
• To explore the feasibility of covariantized matrix (string) theories based on membrane regularization.
• To lay a foundation for constructing a manifestly Lorentz-covariant formulation of M(atrix) theory.

Proposed method

• Derives Matrix-string theory directly from a supermembrane compactified on a circle of radius R = g_s ℓ_s, using a regularization scheme based on matrix degrees of freedom.
• Applies a light-cone gauge quantization to the wrapped supermembrane, avoiding reliance on string duality or perturbative string theory.
• Performs two distinct boosts: one along the M-theory circle (unwrapped membrane) and one along a transverse direction (wrapped membrane).
• Shows that both boost procedures yield the same Matrix theory action in the 11D limit (R→∞, N→∞), confirming consistency between the two approaches.
• Analyzes the role of supersymmetry breaking in the presence of D-particles and anti-D-particles, particularly in the context of nonlinear realizations.
• Considers the possibility of covariant matrix models via two paths: direct covariantization (pIMF) and membrane-based covariantization (pWM), favoring the latter for conceptual consistency.

Experimental results

Research questions

• RQ1 Can Matrix-string theory be derived directly from a wrapped supermembrane without invoking string dualities?
• RQ2 Do two different boosts of the supermembrane—along the M-theory circle and along a transverse direction—yield the same Matrix theory in the 11D limit?
• RQ3 What is the role of supersymmetry breaking in the construction of covariantized matrix models?
• RQ4 How can a manifestly Lorentz-covariant formulation of M(atrix) theory be achieved?
• RQ5 Is the 11D limit of the proposed matrix-string theory equivalent to 11D supergravity?

Key findings

• The derivation of Matrix-string theory from a wrapped supermembrane is achieved without assuming any string duality, providing a new, direct regularization of membrane dynamics.
• Two distinct boosts of the supermembrane—one of an unwrapped membrane and one of a wrapped membrane in a transverse direction—yield identical Matrix theory actions in the 11D decompactification limit (R→∞, N→∞).
• The equivalence of the two boost procedures confirms the consistency of the IMF and wrapped membrane pictures within a single unified framework.
• The membrane-based approach (pWM) avoids the conceptual difficulties of the direct covariantization (pIMF), particularly regarding spontaneous supersymmetry breaking and changing gauge groups under Lorentz boosts.
• The results suggest that the 11D limit of the proposed matrix-string theory is consistent with 11D supergravity, assuming the 10D limit correctly describes IIA string theory.
• The framework supports the possibility of constructing a covariantized matrix (string) theory using the pure-spinor formalism, with potential for further development.