Quantum mechanical sectors in thermal super-Yang–Mills on

Abstract

We study the thermodynamics of U (N ) N = 4 Super Yang-Mills (SYM) on R × S 3 with non-zero chemical potentials for the SU (4) R-symmetry. We find that when we are near a point with zero temperature and critical chemical potential, N = 4 SYM on R × S 3 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 SU (2) and SU (2|3) sectors of N = 4 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 N = 4 SYM on R × S 3 essentially reduces to the ferromagnetic XXX 1/2 Heisenberg spin chain. We find furthermore a limit in which this relation becomes exact.

Refined counting of necklaces in one-loop N = 4 $$ \mathcal{N}=4 $$ SYM

“…The first line agrees with [14] when ξ = 1,ω 1 = 0, and with [17] when ξ = 1. 13 13 Note that (1.2) of [14] is the Hagedorn temperature of the entire N = 4 SYM.…”

“…The Hagedorn transition in the pp-wave/BMN limit was studied in [15,16]. The grand partition function with a one-parameter family of chemical potential was given in [17], and the phase space near the critical chemical potentials was studied in [18].…”

Phase transitions of largeNorbifold gauge theories

“…27 It might be useful to make use of the Penrose limit [41] to examine the intermediate regime. See [50,51] for the comparison of the Hagedorn temperature.…”

A note on the universality of the Hagedorn behavior of pp-wave strings

“…Circumventing this difficulty is quite nontrivial and was only recently accomplished by identifying an altogether different decoupling limit of thermal SU(N), N = 4 SYM in which the physics of the gauge theory is exactly captured by a ferromagnetic XXX1 Heisenberg spin chain [11]. The Hagedorn temperature is then computed from well-known thermodynamic properties of the spin chain and matches excellently with the string theory result.…”

“…Armed with the latest in AdS/CFT technology, it was suggested in the series of works [11] that this problem may be (at least partially) resolved by a new decoupling limit of the correspondence. In the gauge theory, this decoupling corresponds to low temperatures and near-critical chemical potentials while decoupling in the string theory takes place in the large µ limit of a particular compactified pp-wave background with a flat direction.…”