[Paper Review] Tachyon Condensation and Graviton Production in Matrix Theory

Hidetoshi Awata, Shinji Hirano+1 more|ArXiv.org|Feb 23, 1999

Black Holes and Theoretical Physics39 references12 citations

TL;DR

This paper proposes that tachyon condensation in a membrane-antimembrane system within Matrix theory gives rise to graviton production via vortex solutions in a (2+1)-dimensional U(2) gauge theory with twisted boundary conditions. By identifying the tachyon field with off-diagonal gauge components, the authors show that BPS-saturating vortex configurations correspond to gravitons, providing a dynamical mechanism for graviton emergence from non-perturbative tachyon dynamics in Matrix theory.

ABSTRACT

We study a membrane -- anti-membrane system in Matrix theory. It in fact exhibits the tachyon instability. By suitably representing this configuration, we obtain a (2+1)-dimensional U(2) gauge theory with a 't Hooft's twisted boundary condition. We identify the tachyon field with a certain off-diagonal element of the gauge fields in this model. Taking into account the boundary conditions carefully, we can find vortex solutions which saturate the Bogomol'nyi-type bound and manifest the tachyon condensation. We show that they can be interpreted as gravitons in Matrix theory.

Motivation & Objective

• To understand the non-perturbative dynamics of a membrane-antimembrane system in Matrix theory.
• To identify the mechanism by which tachyon condensation leads to graviton production.
• To construct a (2+1)-dimensional U(2) gauge theory with 't Hooft twisted boundary conditions to model the system.
• To demonstrate that BPS-saturating vortex solutions in this model correspond to physical gravitons.
• To refine the effective field theory description of tachyon condensation and its gravitational implications.

Proposed method

• Represent the membrane-antimembrane system using a (2+1)-dimensional U(2) gauge theory with 't Hooft twisted boundary conditions.
• Identify the tachyon field as a specific off-diagonal component of the gauge field matrix.
• Construct vortex solutions that saturate a Bogomol'nyi-type bound, ensuring stability and BPS properties.
• Analyze the low-energy effective theory to extract the physical degrees of freedom, including graviton modes.
• Use careful treatment of boundary conditions to ensure consistency with the Matrix theory framework.
• Refine the effective theory arguments to improve the description of tachyon condensation and graviton production.

Experimental results

Research questions

• RQ1 How does tachyon condensation in a membrane-antimembrane system manifest in the Matrix theory framework?
• RQ2 What is the role of twisted boundary conditions in realizing tachyon dynamics in a gauge theory?
• RQ3 Can vortex solutions in the effective gauge theory be interpreted as physical gravitons?
• RQ4 How does the BPS bound relate to the emergence of graviton states from tachyon condensation?
• RQ5 What is the refined mechanism for graviton production via tachyon condensation in this model?

Key findings

• The membrane-antimembrane system in Matrix theory exhibits tachyon instability, which is modeled via a (2+1)-dimensional U(2) gauge theory with twisted boundary conditions.
• The tachyon field is identified as a specific off-diagonal component of the gauge field matrix in the effective theory.
• Stable vortex solutions saturating the Bogomol'nyi-type bound are found, which are classically stable and BPS-saturating.
• These vortex configurations are shown to correspond to physical graviton states in the Matrix theory description.
• The refined effective field theory provides a consistent mechanism for graviton production from tachyon condensation.
• The analysis improves the understanding of non-perturbative dynamics in Matrix theory, particularly the emergence of gravity from tachyonic instabilities.