Factorization of the Effective Action in the IIB Matrix Model

TL;DR

This paper demonstrates that the low-energy effective action of the IIB matrix model can be factorized into sums of diffeomorphism-invariant functionals, enabling a multiverse interpretation with wormhole connections.

Contribution

It shows the effective action can be expressed as a sum of products of local diffeomorphism-invariant functionals, revealing a new structure in the IIB matrix model's low-energy limit.

Findings

Effective action factorizes into sums of invariant functionals

Each functional is a local scalar operator integral

Multiverse interpretation with wormhole connections

Abstract

We study the low-energy effective action of the IIB matrix model in the derivative interpretation, where the diffeomorphism invariance is manifest and arbitrary manifolds are described by matrices. We show that it is expressed as a sum of terms, each of which is factorized into a product of diffeomorphism invariant action functionals: $S=\sum_{i}c_is_i+\sum_{i,j}c_{ij}s_is_j+\sum_{i,j,k}c_{ijk}s_is_js_k+\...$. Each action functional $s_i$ is an ordinary local action of the form $s_i=\int d^Dx\sqrt{-g} O_i(x)$, where $O_i(x)$ is a scalar operator. This is also true for the background consisting of block diagonal matrices. In this case, the effective action can be interpreted as describing a multiverse where the universes described by the blocks are connected by wormholes.