In this work (which supersedes our previous preprint [1]) we determine the expectation value of the N = 4 SU(N) SYM Lagrangian density operator in the presence of an infinitely heavy static particle in the symmetric representation of SU(N), by means of a D3-brane probe computation. The result that we obtain coincides with two previous computations of different observables, up to kinematical factors. We argue that these agreements go beyond the D-brane probe approximation, which leads us to propose an exact formula for the expectation value of various operators. In particular, we provide an expression for the total energy loss by radiation of a heavy particle in the fundamental representation.

We compute the exact vacuum expectation value of circular Wilson loops for Euclidean N = 4 super Yang-Mills with G = SO(N ), Sp(N ), in the fundamental and spinor representations. These field theories are dual to type IIB string theory compactified on AdS 5 × RP 5 plus certain choices of discrete torsion, and we use our results to probe this holographic duality. We first revisit the LLM-type geometries having AdS 5 × RP 5 as ground state. Our results clarify and refine the identification of these LLM-type geometries as bubbling geometries arising from fermions on a half harmonic oscillator. We furthermore identify the presence of discrete torsion with the one-fermion Wigner distribution becoming negative at the origin of phase space. We then turn to the string world-sheet interpretation of our results and argue that for the quantities considered they imply two features: first, the contribution coming from world-sheets with a single crosscap is closely related to the contribution coming from orientable world-sheets, and second, world-sheets with two crosscaps don't contribute to these quantities.

We use supersymmetric localization to study probes of four dimensional Lagrangian N = 2 superconformal field theories. We first derive a unique equation for the eigenvalue density of these theories. We observe that these theories have a Wigner eigenvalue density precisely when they satisfy a necessary condition for having a holographic dual with a sensible higher-derivative expansion. We then compute in the saddle-point approximation the vacuum expectation value of 1/2-BPS circular Wilson loops, and the two-point functions of these Wilson loops with the Lagrangian density and with the stress-energy tensor. This last computation also provides the corresponding Bremsstrahlung functions and entanglement entropies. As expected, whenever a finite fraction of the matter is in the fundamental representation, the results are drastically different from those of N = 4 supersymmetric Yang-Mills theory.

We use the AdS/CFT correspondence to compute the energy radiated by an infinitely massive half-Bogomol'nyi-Prasad-Sommerfeld particle charged under N=4 super Yang-Mills theory, transforming in the symmetric or antisymmetric representation of the gauge group, and moving in the vacuum, to all orders in 1/N and for large 't Hooft coupling. For the antisymmetric case we consider D5-branes reaching the boundary of five-dimensional anti-de Sitter space (AdS(5)) at arbitrary timelike trajectories, while for the symmetric case, we consider a D3-brane in AdS(5) that reaches the boundary at a hyperbola. We compare our results to the one obtained for the fundamental representation, deduced by considering a string in AdS(5).

In this work we consider a heavy quark moving with constant proper acceleration in the vacuum of any four dimensional conformal field theory. We argue that the two-point function of its momentum fluctuations is exactly captured by the Bremsstrahlung function that gives the total radiated power. For the particular case of N = 4 SU(N) SYM this function is exactly known, so in this case we obtain an explicit expression for the momentum diffusion coefficient, and check that various limits of this result are reproduced by probe computations in AdS 5 . Finally, we evaluate this transport coefficient for a heavy quark accelerated in the vacuum of N = 4 SU(3) SYM, and comment on possible lessons of our results for the study of heavy quarks traversing the super Yang-Mills plasma.arXiv:1302.6991v2 [hep-th]