[HEG] Integrability and Conformal Blocks for Gukov-Witten Surface Defects in N=4 SYM

Who: Hiroki Kawai  (UCSB)
Title: Integrability and Conformal Blocks for Gukov-Witten Surface Defects in N=4 SYM

Abstract: I will present some recent discoveries on the aspects of the Gukov-Witten type surface defect operators in N = 4 SYM based on work with Adolfo Holguin (arXiv: 2503.09944) and some other related works. There are two types of branches of the defect moduli: "generic" and "rigid". For the generic defects, I discuss the use of superconformal symmetry to fix the form of one-point and two-point functions of half-BPS operators and solve the superconformal Ward identities in terms of superconformal blocks, emphasizing the role of the broken rotational symmetry transverse to the defects. I introduce the quantization of this defect background and demonstrate that the superconformal block expansion can be verified by the leading-order perturbative calculation for the two-point functions. I also discuss the integrability condition of the defect CFT in the planar limit from the spin chain perspective and argue that the integrability is broken for the generic defects but restored in the specific subspace of the rigid branch.