In this talk I will describe co-dimension 2 and 4 defects in 6d (2,0) theories in several points of view: 3d SL(N,C) Chern-Simons theory (state-integral model, cluster algebra), 3d N=2 field theory, 5d N=2 super Yang-Mills, and AdS4 holographic dual. This leads to quantitative consistency checks of different approaches, as well as new predictions for a variety of partition functions.

I will discuss knot-like defects in CS theory with complex gauge group SL(N), in the context of its connection with 3d N=2 theory (the so-called 3d-3d correspondence). I am hoping to discuss this problem from a number of different perspectives, including cluster algebras, state-integral models, 3d N=2 non-Abelian gauge theories, 5d N=2 SYM, and holographic dual, and discuss the consistency checks as well as new predictions/implications. This talk is mostly based on my recent papers with D. Gang, N. Kim and M. Romo.