Boundary symmetries and strong coupling dualities

In this doctoral thesis we study aspects of dualities that arise from string theory. We make extensive use of the Chern-Simons formulation of three-dimensional gravity and its boundary symmetries, which we review in detail using the Drinfeld-Sokolov reduction of the affine boundary symmetry algebra.
These tools are used to study a particular contraction of the identification between boundary charges of AdS3 gravity and CFT2 symmetry generators. This identification is used to motivate a duality between a nonrelativistic bulk theory of gravity and a nonconformal boundary field theory.
Additionally, we study a six-dimensional derivation of the Alday-Gaiotto-Tachikawa correspondence, which identifies observables in four-dimensional supersymmetric gauge theories and two-dimensional CFTs. The relation to the 3d-3d correspondence proposed by Córdova and Jafferis is extended and amended by including general codimension two surface defects, which leads to a proposed correspondence involving generalized Toda theories.
Finally, we consider the evolution of spatial entanglement entropy in strongly coupled CFTs after a quench of arbitrary profile. Through holography we obtain a general expression for the leading order behavior in a small region expansion.