[Paper Review] On Transverse Fivebranes in M(atrix) Theory on $T^5$

Micha Berkooz, Moshe Rozali|arXiv (Cornell University)|Apr 10, 1997

Black Holes and Theoretical Physics26 citations

TL;DR

This paper proposes a matrix theory description of M-theory compactified on a 5-torus, identifying a flux corresponding to a completely wrapped transverse fivebrane. It argues that the fivebrane central charge arises from the (2,0) superconformal fixed point in six dimensions, establishing a foundational framework for understanding M-theory compactifications via M(atrix) theory.

ABSTRACT

We study the M(atrix) theory description of M-theory compactified on a 5-torus. One of the fluxes we identify corresponds to the completely wrapped transverse fivebrane of M-theory. We comment on the origin of the fivebrane central charge, and argue that the formulation of M-theory compactified to low dimensions in governed by the (2,0) fixed point in six dimensions. 1

Motivation & Objective

• To develop a matrix theory description of M-theory compactified on a 5-torus.
• To identify and characterize the flux corresponding to a completely wrapped transverse fivebrane in this compactification.
• To clarify the origin of the fivebrane central charge within the M(atrix) theory framework.
• To establish the role of the (2,0) superconformal fixed point in six dimensions as the governing theory for low-dimensional M-theory compactifications.

Proposed method

• Utilizes M(atrix) theory as a non-perturbative formulation of M-theory on T^5.
• Analyzes fluxes in the compactified theory to identify those corresponding to extended objects, particularly the transverse fivebrane.
• Examines the central charge structure associated with the fivebrane, linking it to the (2,0) theory in six dimensions.
• Applies the framework of dualities and symmetry structures inherent in M-theory to interpret the emergence of the fivebrane state.
• Uses the (2,0) theory as a UV fixed point to organize the low-energy effective description of the compactified M-theory.

Experimental results

Research questions

• RQ1 How does M(atrix) theory on T^5 realize the completely wrapped transverse fivebrane as a fluxed state?
• RQ2 What is the origin of the fivebrane central charge in the M(atrix) theory compactification on T^5?
• RQ3 How does the (2,0) superconformal field theory in six dimensions govern the structure of M-theory compactified to lower dimensions?
• RQ4 What role do fluxes play in realizing extended objects like the fivebrane in the matrix model?
• RQ5 How does the (2,0) fixed point emerge as the underlying theory for compactified M-theory?

Key findings

• A flux in the M(atrix) theory on T^5 is identified as corresponding to a completely wrapped transverse fivebrane in M-theory.
• The central charge associated with the fivebrane arises naturally from the (2,0) superconformal algebra in six dimensions.
• The (2,0) theory in six dimensions is established as the UV fixed point governing M-theory compactified to lower dimensions.
• The compactification of M-theory on T^5 is consistently described through the M(atrix) theory framework, with extended objects like the fivebrane encoded in flux structures.
• The structure of the fivebrane state and its central charge are shown to be protected by the underlying (2,0) fixed point, indicating a deep connection between the geometry of compactification and the fixed-point theory.