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

Abstract

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

16 pages, in harvmac big

References in corpus (4)

• Large N Field Theories, String Theory and Gravity
• Non commutative gravity from the ADS/CFT correspondence
• Matrix Theory, AdS/CFT and Higgs-Coulomb Equivalence
• Unitary Representations of Noncompact Quantum Groups at Roots of Unity

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