Replicas, averaging and factorization in the IIB matrix model

TL;DR

This paper investigates the partition functions of multiple D-brane replicas in the type IIB matrix model, revealing how factorization properties differentiate interacting from non-interacting configurations and their implications for quantum gravity signatures.

Contribution

It introduces a detailed analysis of replica factorization in the IIB matrix model, highlighting the role of saddle-point solutions and quantum gravity signatures.

Findings

Interacting D-branes always factorize simply.

Non-interacting BPS configurations may or may not factorize depending on replicas.

Factorization mechanisms reveal signatures of quantum gravity.

Abstract

We study the partition functions of multiple replicas (copies) of D-brane configurations in the type IIB (IKKT) matrix model. We consider the quenched regime, where small fluctuations of the matrices are superimposed onto the slow (quenched) dynamics of the background, so the partition function is an ensemble average over the background. Interacting D-branes always factorize in a simple way. On the other hand, the non-interacting BPS configurations may or may not factorize depending on the number of replicas, and their factorization mechanism is more involved as the corresponding saddle-point solutions (half-wormholes) break the replica symmetry. We argue that the simple factorization mechanism of interacting branes is actually more interesting as it carries the specific signatures of quantum gravity, which are absent from disordered field theories like the SYK model.