Week 16.11.2014 – 22.11.2014

We study the form factor of a generic gauge-invariant local composite operator in N=4 SYM theory. At tree-level and for a minimal number of external fields, the form factor exactly realises the spin-chain picture of N=4 SYM theory in the language of scattering amplitudes. Via generalised unitarity, we obtain the cut-constructible part of the one-loop correction to the minimal form factor of a generic operator. Its UV divergence yields the complete one-loop dilatation operator of the theory. We also compute the complete two-loop correction to the two-point form factor of the Konishi operator via unitarity and obtain the two-loop Konishi anomalous dimensions from it. For the Konishi operator as well as other non-protected operators, important subtleties arise which require an extension of the method of unitarity. Moreover, since the inclusion of non-protected operators into the action renders it formally non-supersymmetric, the form factors of these operators share many features with quantities in QCD, such as the occurrence of rational terms. The talk is based on the recent works 1410.6309 and 1410.8485.

In its most general formulation the gauge/string duality may be used to build models of various strongly coupled systems in condensed matter. One of these is high-temperature d-wave superconductor. The holographic model of d-wave superconductor includes the dynamics of spin-2 charged field on top of the curved AdS geometry. In the probe approximation the model may be formulated consistently and exhibits a number of interesting physical phenomena. The important task is to classify all possible ground states of the model, which will correspond to the various phases of the dual system, and study the resulting phase diagram. In this talk I will discuss the recently found ground state which exhibits the stripes of charge density, violates the translation symmetry spontaneously and may be associated with the pseudogap state in high-Tc superconductors.

We discuss entanglement and Renyi entropies in two-dimensional conformal field theories with extended symmetry algebras of W-type, in the semiclassical (large-c) limit. From the CFT perspective, the computation of these non-local observables involves the study of semiclassical conformal blocks in theories with additional conserved currents beyond the stress tensor. From an AdS perspective, the problem can be tackled using recent holographic proposals in terms of Wilson lines in the dual three-dimensional higher spin theories. We discuss non-trivial examples exhibiting the agreement between bulk and boundary computations.