Spin Matrix Theory: A quantum mechanical model of the AdS/CFT correspondence

Abstract

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 infinite g limit of SMT can be mapped to the supersymmetric sector of string theory on AdS_5 x 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 2N harmonic oscillators.

36 pages, 3 figures. v2: Refs. added

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Cited by in corpus (20)

• Non-Relativistic Strings and Limits of the AdS/CFT Correspondence
• Aspects of Nonrelativistic Strings
• Words to describe a black hole
• Nonrelativistic Approximations of Closed Bosonic String Theory
• Spin Matrix Theory String Backgrounds and Penrose Limits of AdS/CFT
• Decoding stringy near-supersymmetric black holes
• Aspects of Non-Relativistic Quantum Field Theories
• Worldsheet Formalism for Decoupling Limits in String Theory
• Matrix Theory Reloaded: A BPS Road to Holography
• The Panorama of Spin Matrix Theory
• Spin Matrix Theory in near $\frac{1}{8}$-BPS corners of $\mathcal{N}=4$ super-Yang-Mills
• Longitudinal Galilean and Carrollian limits of non-relativistic strings
• Supersymmetric Galilean Electrodynamics
• The quantum detection of projectors in finite-dimensional algebras and holography
• From Hagedorn to Lee-Yang: Partition functions of $\mathcal{N}=4$ SYM theory at finite $N$
• Permutation symmetry in large N Matrix Quantum Mechanics and Partition Algebras
• Nonrelativistic giant magnons from Newton Cartan strings
• Notes on su$(1,2)\oplus$u$(1)$ Chern-Simons theory and Torsional Newton-Cartan gravity
• Conformal Mapping of Non-Lorentzian Geometries in SU(1,2) Conformal Field Theory
• Symmetry structure of the interactions in near-BPS corners of $\mathcal{N}=4$ super-Yang-Mills