This is the live session included as part of the LonTI lecture on Conformal blocks in two dimensions. Please register at https://lonti.weebly.com/registration.html to receive joining instructions for this live session which will be held via Zoom. D-branes are a remarkable set of soliton-like objects in string theory which have played a critical role in many areas of string theory. Despite being non-perturbative, they can be understood exactly using world-sheet methods through the boundary state formalism. In this lecture, I introduce the notion of a boundary state and show how to use it to extract physical information about D-branes and the open strings that live on them.

D-branes are a remarkable set of soliton-like objects in string theory which have played a critical role in many areas of string theory. Despite being non-perturbative, they can be understood exactly using world-sheet methods through the boundary state formalism. In this lecture, I introduce the notion of a boundary state and show how to use it to extract physical information about D-branes and the open strings that live on them.

I will review how integrability can be used to understand the spectral problem (including massless modes) of Type IIB string theory on AdS3 x S3 x T4 with R-R flux. I will then show how integrability emerges in the dual CFT2. This provides arguably the first non-BPS test of the planar AdS3/CFT2 correspondence in the literature and gives strong evidence in identifying particular points in the moduli space of the dual theories.

I will review the gauge/string correspondence, with particular emphasis on recent exact results based on integrable techniques.

We give a brief introduction to recent advances in the AdS/CFT correspondence with particular emphasis on the role integrable structures enter this duality.