Spin Matrix theory: a quantum mechanical model of the AdS/CFT correspondence

• Published in: The journal of high energy physics 2014-11, Vol.2014 (11), p.1, Article 134
• Main Authors: Harmark, Troels, Orselli, Marta
• Format: Article
• Language: English
• Subjects: Classical and Quantum Gravitation; Elementary Particles; High energy physics; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; String Theory
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP11(2014)134

A bstract We introduce a new quantum mechanical theory called Spin Matrix theory (SMT). The theory is interacting with a single coupling constant g and is based on a Hilbert space of harmonic oscillators with a spin index taking values in a Lie (super)algebra representation as well as matrix indices for the adjoint representation of U( N ). We show that SMT describes N = 4 super-Yang-Mills theory (SYM) near zero-temperature critical points in the grand canonical phase diagram. Equivalently, SMT arises from non-relativistic limits of N = 4 SYM. Even though SMT is a non-relativistic quantum mechanical theory it contains a variety of phases mimicking the AdS/CFT correspondence. Moreover, the g → ∞ limit of SMT can be mapped to the supersymmetric sector of string theory on AdS 5 × S 5 . We study SU(2) SMT in detail. At large N and low temperatures it is a theory of spin chains that for small g resembles planar gauge theory and for large g a non-relativistic string theory. When raising the temperature a partial deconfinement transition occurs due to finite- N effects. For sufficiently high temperatures the partially deconfined phase has a classical regime. We find a matrix model description of this regime at any coupling g . Setting g = 0 it is a theory of N 2 + 1 harmonic oscillators while for large g it becomes 2 N harmonic oscillators.