Defining the type IIB matrix model without breaking Lorentz symmetry

TL;DR

This paper proposes a Lorentz-invariant approach to the type IIB matrix model, avoiding symmetry-breaking regularizations and enabling direct numerical simulations of emergent space-time dynamics.

Contribution

It introduces a nonperturbative gauge-fixing method that preserves Lorentz symmetry, allowing for classical behavior of observables and direct extraction of time evolution from matrix configurations.

Findings

Lorentz-invariant observables become classical without symmetry-breaking cutoffs

A new gauge-fixing method preserves Lorentz symmetry nonperturbatively

Numerical simulations can directly extract time evolution from matrices

Abstract

The type IIB matrix model is a promising nonperturbative formulation of superstring theory, which may elucidate the emergence of (3+1)-dimensional space-time. However, the partition function is divergent due to the Lorentz symmetry, which is represented by a noncompact group. This divergence has been regularized conventionally by introducing some infrared cutoff, which breaks the Lorentz symmetry. Here we point out that Lorentz invariant observables become classical as one removes the infrared cutoff and that this "classicalization" is actually an artifact of the Lorentz symmetry breaking cutoff. In order to overcome this problem, we propose a natural way to "gauge-fix" the Lorentz symmetry in a fully nonperturbative manner. This also enables us to perform numerical simulations in such a way that the time-evolution can be extracted directly from the matrix configurations.