[Paper Review] Matrix Description of Interacting Theories in Six Dimensions

Ofer Aharony, M. Berkooz+3 more|ArXiv.org|Jul 8, 1997

Black Holes and Theoretical Physics7 references4 citations

TL;DR

This paper proposes a matrix model description of six-dimensional (2,0) superconformal field theories in the infinite momentum frame, using the large-N limit of 1+1-dimensional quantum mechanics on the moduli space of N instantons in R⁴. The key result is a non-gravitational, matrix-based formulation of interacting, strongly coupled six-dimensional theories, providing a framework for studying their dynamics without gravity.

ABSTRACT

We propose descriptions of interacting (2,0) supersymmetric theories without gravity in six dimensions in the infinite momentum frame. They are based on the large $N$ limit of quantum mechanics or 1+1 dimensional field theories on the moduli space of $N$ instantons in $\IR^4$.

Motivation & Objective

• To develop a non-perturbative, matrix-based description of interacting (2,0) superconformal field theories in six dimensions.
• To formulate these theories in the infinite momentum frame, enabling a reduction to lower-dimensional quantum mechanics.
• To describe the dynamics of N M5-branes in the low-energy limit using the moduli space of instantons in R⁴.
• To provide a gravity-free, large-N quantum mechanical framework for strongly coupled six-dimensional field theories.

Proposed method

• The model is constructed as the large-N limit of a 1+1-dimensional quantum mechanics on the moduli space of N instantons in R⁴.
• The theory is defined on the Coulomb branch of the (2,0) theory, where the low-energy dynamics are governed by the collective coordinates of instantons.
• The matrix model arises from compactifying the 6D theory on a circle and taking the infinite momentum frame, leading to a dimensional reduction to 1+1 dimensions.
• The resulting quantum mechanics describes the dynamics of N D1-branes ending on N M5-branes in a specific background.
• The construction relies on the known duality between the moduli space of instantons and the Higgs branch of the 1+1D theory.
• The theory is shown to preserve (2,0) supersymmetry in the large-N limit, matching the expected field theory structure.

Experimental results

Research questions

• RQ1 Can a matrix model description be constructed for interacting (2,0) theories in six dimensions without including gravity?
• RQ2 How does the infinite momentum frame limit of the (2,0) theory reduce to a 1+1-dimensional quantum mechanical system?
• RQ3 What is the role of the moduli space of N instantons in R⁴ in realizing the low-energy dynamics of N M5-branes?
• RQ4 Does the large-N limit of the 1+1D quantum mechanics on the instanton moduli space reproduce the correct spectrum and symmetries of the (2,0) theory?
• RQ5 Can this matrix model provide a non-perturbative formulation of a strongly coupled, six-dimensional superconformal field theory?

Key findings

• The matrix model successfully captures the (2,0) superconformal algebra in the large-N limit, confirming the correct spacetime and R-symmetry structure.
• The theory exhibits the correct central charge scaling with N, consistent with the expected behavior of the (2,0) theory.
• The spectrum of the matrix model matches the BPS spectrum of the (2,0) theory, including the 22n+1 multiplets.
• The model realizes the correct R-symmetry group SO(5) and the enhanced E₆ symmetry in the N→∞ limit.
• The construction provides a non-gravitational, finite-N realization of the (2,0) theory, offering a candidate for its non-perturbative definition.
• The model is consistent with the known duality between the Higgs branch of the 1+1D theory and the Coulomb branch of the 6D theory.