We explore phases of an N = 2 super Yang-Mills theory at finite quark density by introducing quark chemical potential in a D3-D7 setup. We formulate the thermodynamics of brane embeddings and we find that the density versus chemical potential equation of state has rich structure. This yields two distinct first order phase transitions in a small window of quark density. In order words, there is a new first order phase transition in the region of deconfined quarks. In this new phase, the chemical potential is a decreasing function of the density. We suggest that this might be relevant to the difference in sQGP-wQGP phases of QCD. PACS numbers: Valid PACS appear hereIntroduction: There has been much hope that one might be able to use AdS/CFT [1] to describe the real systems after certain amount of deformations. For example, it has been suggested that the fireball in Relativistic Heavy Ion Collision (RHIC) viewed as a strongly interacting system [2,3], has been studied using dual gravity models [4][5][6][7][8]. There have been many attempts to construct models phenomenologically closer to QCD [9].More recently, there has been renewed interest in N = 2 super Yang-Mills (SYM) systems with quenched fundamental quark flavors studied by using a holographic description with probe D7-branes in the AdS 5 black hole background [10][11][12][13][14][15]. The key observation is that we have confinement of quarks even in the absence of gluon confinement or area law [10]. The phases of this theory are characterized by the brane embeddings: whether the D7-brane touches the black hole horizon (black hole embedding) or not (Minkowski embedding). Different types of embedding lead to different meson spectra.In this letter, we explore the phases of this theory at finite quark density by introducing quark chemical potential along the lines of [16,17]. We will first establish a clear formulation of the thermodynamics of brane embeddings. We find that we need to renormalize the finite chemical potential due to the divergence of the thermodynamic potentials. We will also find that apart from the type of first order phase transition described in [10,11] at zero chemical potential, there is another class of first order phase transition within the black hole embedding category: it is indicated in Fig. 1 as a hopping between two black hole embeddings.Since black hole embeddings correspond to the deconfined phase, we cautiously suggest that this new type of first order phase transitions might be relevant to the difference between sQGP-wQGP in RHIC experiments. In particular, we find that the chemical potential in this new phase is a decreasing function of the density.We emphasize that depending on whether we control the system by the chemical potential (grand canonical ensemble) or by the density (canonical ensemble), the phase diagram is different. In this letter, we present the analysis and the results for the system based on the canonical

Abstract. We generalize the translation invariant tensor-valued Minkowski Functionals which are defined on two-dimensional flat space to the unit sphere. We apply them to level sets of random fields. The contours enclosing boundaries of level sets of random fields give a spatial distribution of random smooth closed curves. We outline a method to compute the tensor-valued Minkowski Functionals numerically for any random field on the sphere. Then we obtain analytic expressions for the ensemble expectation values of the matrix elements for isotropic Gaussian and Rayleigh fields. The results hold on flat as well as any curved space with affine connection. We elucidate the way in which the matrix elements encode information about the Gaussian nature and statistical isotropy (or departure from isotropy) of the field. Finally, we apply the method to maps of the Galactic foreground emissions from the 2015 PLANCK data and demonstrate their high level of statistical anisotropy and departure from Gaussianity.

The D1/D5 system is considered in the presence of the NS B field. An explicit supergravity solution in the asymptotically flat and near horizon limits is presented. Explicit mass formulae are presented in both cases. This solution has no D3 source branes and represents a true bound state of the D1/D5 system. We study the motion of a separated D1-brane in the background geometry described above and reproduce the Liouville potential that binds the D1 brane. A gauge theory analysis is also presented in the presence of Fayet-Iliopoulos (FI) parameters which can be identified with the self-dual part of the NS B field. In the case of a single D5-brane and an arbitrary number of D1 branes we can demonstrate the existence of a bound state in the Higgs branch. We also point out the connection of the SCFT on the resolved Sym Q 1 Q 5 (T 4 ) with recent developments in non-commutative Yang-Mills theory.

We present a closed framework of AdS/CFT with finite U (1) B -charge chemical potential. We show how the gauge-invariant identification of the chemical potential with the bulk gauge field emerges from the standard AdS/CFT dictionary. Physical importance and necessity of the Minkowski embeddings within the present framework is also shown numerically in the D3-D7 systems. We point out that the D3-D7 model with only the black-hole embeddings does not have the low-temperature and lowchemical-potential region in the grand-canonical ensemble, hence it is incomplete. A physical interpretation that explains these numerical results is also proposed.