[Paper Review] Issues in (M)atrix Model Compactification

Michael R. Douglas, Hirosi Ooguri+1 more|arXiv (Cornell University)|Feb 27, 1997

Distributed and Parallel Computing Systems11 citations

TL;DR

This paper investigates (M)atrix model compactifications on curved manifolds, showing that excited string states fail to decouple in the D0-brane annulus amplitude due to the modified graviton propagator on curved space. This implies that finite-degree-of-freedom quantum mechanical systems cannot reproduce supergravity results in curved backgrounds, with implications for ALE spaces and potential higher-derivative corrections.

ABSTRACT

We discuss issues concerning (M)atrix model compactifications on curved spaces. We argue from the form of the graviton propagator on curved space that excited string states do not decouple from the annulus D0-brane $v^4$ amplitude, unlike the flat space case. This argument shows that a large class of quantum mechanical systems with a finite number of degrees of freedom cannot reproduce supergravity answers. We discuss the specific example of an ALE space and suggest sources of possible higher derivative terms that might help reproduce supergravity results.

Motivation & Objective

• To understand the limitations of (M)atrix models in reproducing supergravity on curved manifolds.
• To analyze the behavior of the graviton propagator in curved space and its impact on D0-brane amplitudes.
• To identify why finite quantum mechanical systems with a fixed number of degrees of freedom fail to reproduce supergravity results in curved compactifications.
• To explore potential higher-derivative terms that could resolve discrepancies in ALE space compactifications.

Proposed method

• Analyzing the form of the graviton propagator on curved manifolds to assess its effect on the D0-brane annulus amplitude.
• Comparing the behavior of the $v^4$ amplitude in curved versus flat space to detect non-decoupling of excited string states.
• Using the ALE space as a concrete example of a curved background to study quantum corrections and potential higher-derivative terms.
• Applying effective field theory reasoning to identify possible higher-derivative interactions that might restore supergravity consistency.

Experimental results

Research questions

• RQ1 Why do excited string states fail to decouple in the D0-brane annulus amplitude on curved manifolds, unlike in flat space?
• RQ2 To what extent can finite quantum mechanical systems with a fixed number of degrees of freedom reproduce supergravity results in curved compactifications?
• RQ3 What role does the modified graviton propagator on curved space play in the breakdown of decoupling for massive string states?
• RQ4 What higher-derivative terms might be necessary to restore consistency with supergravity in ALE space compactifications?
• RQ5 How does the structure of the graviton propagator differ in curved versus flat space, and what are its implications for (M)atrix model compactifications?

Key findings

• The graviton propagator on curved space leads to non-decoupling of excited string states in the D0-brane annulus amplitude, unlike in flat space.
• A large class of finite-degree-of-freedom quantum mechanical systems cannot reproduce supergravity results due to this non-decoupling.
• The failure of decoupling indicates a fundamental obstruction to recovering supergravity from (M)atrix models in curved compactifications.
• In the ALE space example, the non-decoupling suggests the need for additional higher-derivative terms in the effective action.
• The analysis implies that standard (M)atrix model constructions may require modification to be consistent with supergravity in curved backgrounds.