Quantum mechanical sectors in thermal image super-Yang–Mills on image Original Research Article

We study the thermodynamics of image image super-Yang–Mills (SYM) on image with non-zero chemical potentials for the image R-symmetry. We find that when we are near a point with zero temperature and critical chemical potential, image SYM on image reduces to a quantum mechanical theory. We identify three such critical regions giving rise to three different quantum mechanical theories. Two of them have a Hilbert space given by the image and image sectors of image SYM of recent interest in the study of integrability, while the third one is the half-BPS sector dual to bubbling AdS geometries. In the planar limit the three quantum mechanical theories can be seen as spin chains. In particular, we identify a near-critical region in which image SYM on image essentially reduces to the ferromagnetic image Heisenberg spin chain. We find furthermore a limit in which this relation becomes exact.