Matrix Compactification On Orientifolds

TL;DR

This paper extends Matrix model compactification to orientifolds, describing how discrete symmetries and projective representations encode the quantum space structure in a Yang-Mills framework.

Contribution

It generalizes orbifold compactifications to orientifolds, introducing a spectral triple approach for encoding quantum space data in Matrix models.

Findings

Compactification described via discrete symmetry group G and projective representation U.

Spectral triple encapsulates all data of the quantum space.

Framework generalizes previous orbifold results to orientifolds.

Abstract

Generalizing previous results for orbifolds, in this paper we describe the compactification of Matrix model on an orientifold which is a quotient space as a Yang-Mills theory living on a quantum space. The information of the compactification is encoded in the action of the discrete symmetry group G on Euclidean space and a projective representation U of G. The choice of Hilbert space on which the algebra of U is realized as an operator algebra corresponds to the choice of a physical background for the compactification. All these data are summarized in the spectral triple of the quantum space.