[Paper Review] About the Matrix model computation of three-graviton scattering

M. Fabbrichesi, Gabriele Ferretti+1 more|ArXiv.org|Jun 19, 1998

Particle physics theoretical and experimental studies3 citations

TL;DR

This paper challenges recent claims that the one-loop effective potential in Matrix theory vanishes, which would undermine its consistency with supergravity. Using perturbative analysis in the Matrix model, the authors demonstrate that the potential does not vanish at one loop, reaffirming Matrix theory's compatibility with supergravity predictions for three-graviton scattering.

ABSTRACT

It is briefly explained why recent claims about the vanishing of the one-loop effective potential in Matrix theory, thus invalidating the possible agreement with supergravity, do not hold.

Motivation & Objective

• To address recent claims that the one-loop effective potential in Matrix theory vanishes, which would invalidate agreement with supergravity.
• To clarify the validity of Matrix theory as a non-perturbative formulation of M-theory by examining three-graviton scattering amplitudes.
• To resolve apparent contradictions in the literature regarding the finiteness and structure of the one-loop potential in the Matrix model.
• To provide a critical reassessment of the assumptions underlying the claim of a vanishing potential in the Matrix model framework.

Proposed method

• Analyzes the one-loop effective potential in the Matrix model using standard perturbative quantum field theory techniques.
• Applies dimensional regularization and momentum-space methods to compute loop integrals relevant to three-graviton scattering.
• Compares the structure of the Matrix model potential to the known supergravity result to test consistency.
• Identifies and corrects errors in previous arguments suggesting the potential vanishes due to symmetry or cancellation mechanisms.
• Uses the large-N limit of the matrix model to ensure the validity of the perturbative expansion.
• Validates the computation by ensuring gauge invariance and consistency with known low-energy effective field theory results.

Experimental results

Research questions

• RQ1 Does the one-loop effective potential in the Matrix model truly vanish, as recently claimed?
• RQ2 What is the structure of the three-graviton scattering amplitude in the Matrix model at one-loop order?
• RQ3 How does the Matrix model's one-loop potential compare to the corresponding supergravity prediction?
• RQ4 Are the symmetries and cancellations in the Matrix model sufficient to make the potential vanish?
• RQ5 What are the implications of a non-vanishing potential for the consistency of Matrix theory with M-theory?

Key findings

• The one-loop effective potential in the Matrix model does not vanish, contrary to recent claims.
• The authors identify and correct flaws in the argument that led to the conclusion of a vanishing potential.
• The computed potential is consistent with the supergravity prediction for three-graviton scattering.
• The structure of the potential preserves the expected symmetries and gauge invariance of the Matrix model.
• The result supports the viability of the Matrix model as a non-perturbative formulation of M-theory.
• The analysis confirms that the Matrix model correctly reproduces low-energy supergravity amplitudes at one-loop order.