In studying the dynamics of large N c , SU (N c ) gauge theory at finite temperature with fundamental quark flavours in the quenched approximation, we observe a first order phase transition. A quark condensate forms at finite quark mass, and the value of the condensate varies smoothly with the quark mass for generic regions in parameter space. At a particular value of the quark mass, there is a finite discontinuity in the condensate's vacuum expectation value, corresponding to a first order phase transition. We study the gauge theory via its string dual formulation using the AdS/CFT conjecture, the string dual being the near-horizon geometry of N c D3-branes at finite temperature, AdS 5 -Schwarzschild×S 5 , probed by a D7-brane. The D7-brane has topology R 4 × S 3 × S 1 and allowed solutions correspond to either the S 3 or the S 1 shrinking away in the interior of the geometry. The phase transition represents a jump between branches of solutions having these two distinct D-brane topologies. The transition also appears in the meson spectrum.

We consider a D7-brane probe of AdS 5 × S 5 in the presence of pure gauge B-field. In the dual gauge theory, the B-field couples to the fundamental matter introduced by the D7-brane and acts as an external magnetic field. The B-field supports a 6-form Ramond-Ramond potential on the D7-branes world volume that breaks the supersymmetry and enables the dual gauge theory to develop a non-zero fermionic condensate. We explore the dependence of the fermionic condensate on the bare quark mass m q and show that at zero bare quark mass a chiral symmetry is spontaneously broken. A study of the meson spectrum reveals a coupling between the vector and scalar modes, and in the limit of weak magnetic field we observe Zeeman splitting of the states. We also observe the characteristic √ m q dependence of the ground state corresponding to the Goldstone boson of spontaneously broken chiral symmetry.

Using a ten dimensional dual string background, we study aspects of the physics of finite temperature large N four dimensional SU (N ) gauge theory, focusing on the dynamics of fundamental quarks in the presence of a background magnetic field. At vanishing temperature and magnetic field, the theory has N = 2 supersymmetry, and the quarks are in hypermultiplet representations. In a previous study, similar techniques were used to show that the quark dynamics exhibit spontaneous chiral symmetry breaking. In the present work we begin by establishing the non-trivial phase structure that results from finite temperature. We observe, for example, that above the critical value of the field that generates a chiral condensate spontaneously, the meson melting transition disappears, leaving only a discrete spectrum of mesons at any temperature. We also compute several thermodynamic properties of the plasma.

We use a ten dimensional dual string background to study aspects of the physics of large N four dimensional SU (N ) gauge theory, where its fundamental quarks are charged under a background electric field. The theory is N = 2 supersymmetric for vanishing temperature and electric field. We work in a limit where the quarks do not back-react. At zero temperature, we observe that the electric field induces a phase transition associated with the dissociation of the mesons into their constituent quarks. This is an analogue of an insulatormetal transition, since the system goes from being an insulator with zero current (in the applied field) to a conductor with free charge carriers (the quarks). At finite temperature this phenomenon persists, and the dissociation transition becomes subsumed into the more familiar meson melting transition. Here, the dissociation phenomenon reduces the critical melting temperature.

The phase structure of flavoured N = 2 SYM on a three sphere in an external magnetic field is studied. The pairing effect of the magnetic field competes with the dissociating effect of the Casimir energy, leading to an interesting phase structure of confined and deconfined phases separated by a critical curve of a first order quantum phase transition. At vanishing magnetic field the phase transition is of a third order. For sufficiently strong magnetic field, the only stable phase is the confined phase and magnetic catalysis of chiral symmetry breaking is realized. The meson spectra of the theory exhibit Zeeman splitting and level crossing and feature a finite jump at the phase transition between the confined and deconfined phases. At strong magnetic field the ground state has a massless mode corresponding to the Goldstone boson associated with the spontaneously broken U (1) R-symmetry analogous to the η meson in QCD.