Quantum Spacetimes and Finite N Effects in 4D Super Yang-Mills Theories

TL;DR

This paper explores quantum spacetime models related to 4D super Yang-Mills theories, focusing on finite N effects and symmetries, and finds qualitative agreements with finite N gauge theory properties.

Contribution

It introduces a quantum spacetime model using $AdS^5_q imes S^5_q$ with hidden symmetries and analyzes its relation to finite N effects in $ ext{N}=4$ SYM theories.

Findings

Quantum spacetime modeled as $AdS^5_q imes S^5_q$ with $SU_q(3)$ and hidden $SO_q(6)$ symmetries.

Qualitative agreement between quantum spacetime models and finite N gauge theory properties.

Analysis of quantum space quotients as models for $Z_n$ quiver theories with broken SUSY.

Abstract

The truncation in the number of single-trace chiral primary operators of $\N=4$ SYM and its conjectured connection with gravity on quantum spacetimes are elaborated. The model of quantum spacetime we use is $AdS^5_q \times S^5_q$ for $q$ a root of unity. The quantum sphere is defined as a homogeneous space with manifest $SU_q(3)$ symmetry, but as anticipated from the field theory correspondence, we show that there is a hidden $SO_q(6)$ symmetry in the constrution. We also study some properties of quantum space quotients as candidate models for the quantum spacetime relevant for some $Z_n$ quiver quotients of the $\N=4$ theory which break SUSY to $\N=2$. We find various qualitative agreements between the proposed models and the properties of the corresponding finite $N$ gauge theories.