Finite-size Effects in Holography

We study holography in the sense of the anti-de Sitter/conformal field theory (AdS/CFT) correspondence, where the field theory lives in a compact space. We first review some aspects of the AdS/CFT duality. We then discuss our work on finite-size corrections to the drag force exerted on a quark in the quark-gluon plasma. Interestingly, the finite-size effects yield a drag force with decreased magnitude, which is opposite to what is seen in many situations with Newtonian fluids. We then turn to meson excitations in a holographic description of N=2 supersymmetric Yang-Mills theory at finite size. In contrast to other related systems reported in the literature, the first meson excitation is an SO(4) charged scalar meson instead of a vector. Intriguingly, there is also a cross-over between the vector and scalar meson spectra as a function of the system size. Finally, we discuss the extension of this system with a magnetic Kalb-Ramond field. We find intriguing new structure in the phase diagram of the system, and investigate possible causes for an apparent mass gap in the spectrum.