We propose a new method to consider D-brane probes in thermal backgrounds. The method builds on the recently developed blackfold approach to higher-dimensional black holes. While D-brane probes in zero-temperature backgrounds are well-described by the Dirac-Born-Infeld (DBI) action, this method addresses how to probe thermal backgrounds. A particularly important feature is that the probe is in thermal equilibrium with the background. We apply our new method to study the thermal generalization of the BIon solution of the DBI action. The BIon solution is a configuration in flat space of a D-brane and a parallel anti-D-brane connected by a wormhole with F-string charge. In our thermal generalization, we put this configuration in hot flat space. We find that the finite temperature system behaves qualitatively different than its zero-temperature counterpart. In particular, for a given separation between the D-brane and anti-D-brane, while at zero temperature there are two phases, at finite temperature there are either one or three phases available.
We match the Hagedorn/deconfinement temperature of planar N = 4 super Yang-Mills (SYM) on R × S 3 to the Hagedorn temperature of string theory on AdS 5 × S 5 . The match is done in a near-critical region where both gauge theory and string theory are weakly coupled. The near-critical region is near a point with zero temperature and critical chemical potential. On the gauge theory side we are taking a decoupling limit found in hep-th/0605234 in which the physics of planar N = 4 SYM is given exactly by the ferromagnetic XXX 1/2 Heisenberg spin chain. We find moreover a general relation between the Hagedorn/deconfinement temperature and the thermodynamics of the Heisenberg spin chain and we use this to compute it in two distinct regimes. On the string theory side, we identify the dual limit for which the string tension and string coupling go to zero. This limit is taken of string theory on a maximally supersymmetric pp-wave background with a flat direction, obtained from a Penrose limit of AdS 5 × S 5 . We compute the Hagedorn temperature of the string theory and find agreement with the Hagedorn/deconfinement temperature computed on the gauge theory side.
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.
We investigate the thermodynamics of the recently obtained finite temperature BIon solution of arXiv:1012.1494, focusing on two aspects. The first concerns comparison of the free energy of the three available phases for the finite temperature brane-antibrane wormhole configuration. Based on this we propose a heuristic picture for the dynamics of the phases that involves a critical temperature below which a stable phase exists. This stable phase is the finite temperature analogue of the thin throat branch of the extremal brane anti-brane wormhole configuration. The second aspect that we consider is the possibility of constructing a finite temperature generalization of the infinite spike configuration of the extremal BIon. To this end we identify a correspondence point at the end of the throat where the thermodynamics of the D3-F1 blackfold configuration can be matched to that of k non-extremal black fundamental strings.Comment: 19 pages, 7 figure
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 nonrelativistic 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.
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