Surface operators in the 6d N = (2, 0) theory

Abstract

This thesis presents surface operators as the ideal observables to explore the physics of the 6d N = (2, 0) SCFT. Exploiting the analogy between surface operators and Wilson loops, we adapt some of the nonperturbative tools successful in the context of Wilson loops.We construct large families of BPS surfaces by studying the possible R- symmetry breaking and count the resulting supercharges. We calculate their conformal anomaly, discuss their relation to other BPS defects through compactification of the 6d theory, and detail their holographic dual in terms of calibrated submanifolds in AdS7 × S4. We also apply the framework of defect CFT to study locally-BPS surface operators in the nonabelian theory.We discuss the insertion of local operators into the 1/2 BPS plane, an example of which is the displacement operator. By studying correlators involving also operators from the stress tensor multiplet, we obtain a number of constraints following from superconformal Ward identities that translate into linear relations between the coefficients entering the anomaly of surface operators. We also study the divergences associated with singular surfaces, and inparticular for the crease we find that the expectation value leads to a nontrivial function of two angles interpreted as the generalised potential for strings on a AdS2 × S4 background.We calculate it in the free theory, holography and using defect CFT techniques, leading to a conjecture for the BPS result at all N. These various results reveal the breadth of topics accessible to surface operators and provide an ideal playground to study the properties of the 6d N = (2, 0) theories.

Date of Award	1 Oct 2021
Original language	English
Awarding Institution	King's College London
Supervisor	Nadav Drukker (Supervisor)