Dimensional oxidization on coset space

TL;DR

This paper explores how space-time geometry can emerge from a generalized gauge symmetry algebra beyond the traditional $gl( abla)$, focusing on coset spaces and proposing a specific infinite-dimensional symmetry realization.

Contribution

It introduces a new gauge symmetry framework for emergent space-time on coset spaces, extending previous models based on $gl( abla)$ and providing a concrete gauge theory construction.

Findings

Proposes a specific infinite-dimensional gauge symmetry for coset spaces.

Shows that a 0-dimensional gauge theory with mass and Chern-Simons terms reproduces gauge theory on the coset.

Connects gauge algebra functions and Lorentzian generators to space-time geometry.

Abstract

In the matrix model approaches of string/M theories, one starts from a generic symmetry $gl(\infty)$ to reproduce the space-time manifold. In this paper, we consider the generalization in which the space-time manifold emerges from a gauge symmetry algebra which is not necessarily $gl(\infty)$. We focus on the second nontrivial example after the toroidal compactification, the coset space $G/H$, and propose a specific infinite-dimensional symmetry which realizes the geometry. It consists of the gauge-algebra valued functions on the coset and Lorentzian generator pairs associated with the isometry. We show that the $0$-dimensional gauge theory with the mass and Chern-Simons terms gives the gauge theory on the coset with scalar fields associated with $H$.