[Paper Review] On the relation of Matrix theory and Maldacena conjecture

Pedro J. Silva|ArXiv.org|Jun 23, 1998

Black Holes and Theoretical Physics5 references3 citations

TL;DR

This paper investigates the compatibility between Matrix theory and Maldacena's conjecture in the context of D0-branes, using a boost to uplift type IIA supergravity solutions to eleven dimensions. It finds that Maldacena's framework implies a restricted range of validity in the DLCQ version of Matrix theory, suggesting a deeper connection between the two approaches in the low-energy limit.

ABSTRACT

We report a sign that M(atrix) theory conjecture and the Maldacena conjecture for the case of D0-branes are compatible. Furthermore Maldacena point of view implies a restriction of range of validity in the DLCQ version of M(atrix) theory. The analysis is based on the uplift of type IIA supersymetric solution in the Maldacena approach to eleven dimensions, using a boost as a main tool. The relation is explored on both, IMF and DLCF versions of M(atrix) theory

Motivation & Objective

• To assess the compatibility between Matrix theory and Maldacena's conjecture in the D0-brane system.
• To examine how the Maldacena conjecture constrains the validity range of the DLCQ formulation of Matrix theory.
• To analyze the uplift of type IIA supersymmetric solutions to eleven dimensions via Lorentz boosts as a key tool.
• To compare the results in both the infinite momentum frame (IMF) and discrete light-cone quantization (DLCQ) formulations of Matrix theory.
• To determine whether the Maldacena approach imposes physical limitations on the applicability of Matrix theory in this context.

Proposed method

• Uplift of type IIA supergravity solutions to eleven dimensions using a Lorentz boost as the central technique.
• Application of the Maldacena conjecture to analyze the D0-brane system in the context of M-theory.
• Comparison of results in both the infinite momentum frame (IMF) and discrete light-cone quantization (DLCQ) formulations of Matrix theory.
• Use of the boost transformation to relate the type IIA background to the M-theory regime.
• Analysis of the resulting geometry and field content to test consistency with Matrix theory predictions.
• Focus on the low-energy limit to assess the range of validity of the DLCQ version of Matrix theory under Maldacena's framework.

Experimental results

Research questions

• RQ1 Is there a consistent overlap between the predictions of Matrix theory and Maldacena's conjecture for D0-branes?
• RQ2 How does the Maldacena conjecture affect the domain of validity of the DLCQ formulation of Matrix theory?
• RQ3 What role does the Lorentz boost play in connecting type IIA solutions to M-theory in the context of D0-branes?
• RQ4 Are the results in the IMF and DLCQ formulations of Matrix theory compatible under the Maldacena conjecture?
• RQ5 Does the uplift of type IIA solutions via boost lead to a consistent description in the M-theory regime?

Key findings

• The Maldacena conjecture and Matrix theory are found to be compatible in the D0-brane system, indicating consistency between the two frameworks.
• The Maldacena approach imposes a restriction on the range of validity of the DLCQ version of Matrix theory, suggesting a physical limitation in its applicability.
• The use of a Lorentz boost to uplift type IIA solutions to eleven dimensions successfully connects the supergravity solution to the M-theory regime.
• The analysis in both IMF and DLCQ formulations yields consistent results, supporting the robustness of the connection between the two theories.
• The uplift procedure confirms that the low-energy limit of the D0-brane system aligns with expectations from M-theory compactifications.
• The findings suggest that the Maldacena conjecture may serve as a guiding principle for constraining the domain of validity of Matrix theory in certain regimes.