We compute the meson spectrum of an N = 2 super Yang-Mills theory with fundamental matter from its dual string theory on AdS 5 × S 5 with a D7-brane probe [1]. For scalar and vector mesons with arbitrary R-charge the spectrum is computed in closed form by solving the equations for D7-brane fluctuations; for matter with non-zero mass m q it is discrete, exhibits a mass gap of order m q / √ g s N and furnishes representations of SO(5) even though the manifest global symmetry of the theory is only SO(4). The spectrum of mesons with large spin J is obtained from semiclassical, rotating open strings attached to the D7-brane. It displays Regge-like behaviour for J ≪ √ g s N , whereas for J ≫ √ g s N it corresponds to that of two non-relativistic quarks bound by a Coulomb potential. Meson interactions, baryons and 'giant gauge bosons' are briefly discussed.

Heavy ion collision experiments recreating the quark-gluon plasma that filled the microseconds-old universe have established that it is a nearly perfect liquid that flows with such minimal dissipation that it cannot be seen as made of particles. String theory provides a powerful toolbox for studying matter with such properties. This book provides a comprehensive introduction to gauge/string duality and its applications to the study of the thermal and transport properties of quark-gluon plasma, the dynamics of how it forms, the hydrodynamics of how it flows, and its response to probes including jets and quarkonium mesons. Calculations are discussed in the context of data from RHIC and LHC and results from finite temperature lattice QCD. The book is an ideal reference for students and researchers in string theory, quantum field theory, quantum many-body physics, heavy ion physics and lattice QCD.

We use holographic techniques to study SU (N c ) super Yang-Mills theory coupled to N f ≪ N c flavours of fundamental matter at finite temperature and baryon density. We focus on four dimensions, for which the dual description consists of N f D7-branes in the background of N c black D3-branes, but our results apply in other dimensions as well. A non-zero chemical potential µ b or baryon number density n b is introduced via a nonvanishing worldvolume gauge field on the D7-branes. Ref.[1] identified a first order phase transition at zero density associated with 'melting' of the mesons. This extends to a line of phase transitions for small n b , which terminates at a critical point at finite n b . Investigation of the D7-branes' thermodynamics reveals that (∂µ b /∂n b ) T < 0 in a small region of the phase diagram, indicating an instability. We comment on a possible new phase which may appear in this region.

The holographic dual of a finite-temperature gauge theory with a small number of flavours typically contains D-brane probes in a black hole background. We have recently shown that these systems undergo a first order phase transition characterised by a 'melting' of the mesons. Here we extend our analysis of the thermodynamics of these systems by computing their free energy, entropy and energy densities, as well as the speed of sound. We also compute the meson spectrum for brane embeddings outside the horizon and find that tachyonic modes appear where this phase is expected to be unstable from thermodynamic considerations.E. Holographic Renormalization of the D4-brane 54 4 No black brane geometry exists for a Euclidean D(-1)-brane. 5 Above, we pointed out that our present analysis does not apply to Dp/Dq systems T-dual to D0/D8branes. Systems T-dual to D0/D0 systems would be trivial for the present purposes as n = 0. Hence those T-dual to the D0/D4 or D3/D7 system are the only other possibility with a supersymmetric limit. A.1 High temperatures (black hole embeddings)Consider the limit T /M ≫ 1. This corresponds to black hole embeddings with m =M /T ≪