Trivial and Non-trivial Defect Conformal Manifolds

Abstract

It has been known for many years that there exist families of superconformal field theories (SCFTs) connected by exactly marginal deformations. Such families are called “conformal manifolds”. In the presence of boundaries or defects, we can study the analogue construction, defect conformal manifolds. Just as exactly marginal operators parameterise the conformal manifold, the corresponding operators on conformal defects allow for their marginal deformations.

In this thesis, we consider two kinds of defect exactly marginal operators. One is “trivial” that arises from global symmetry breaking. When a defect breaks a global symmetry, there is a contact term in the conservation equation with defect exactly marginal operators. The resulting defect conformal manifold is the symmetry breaking coset and its Zamolodchikov metric is expressed as the 2-point function of the exactly marginal operators. As the Riemann tensor on the conformal manifold can be expressed as an integrated 4-point function of the marginal operators, we find an exact relation to the curvature of the coset space. We confirm this relation against previously obtained 4-point functions for insertions into the 1/2 BPS Wilson loop in N = 4 super Yang Mills, the 1/2 BPS surface operator of the 6d N = (2, 0) theory and 1/2 BPS Wilson loops in ABJM theory. We also construct the 1/3 BPS loops in ABJM and examine the relation there.

However, defect conformal manifolds do not require broken symmetries. One natural setting is in 3d, where line operators have multiple marginal couplings. We constructed many new moduli spaces of both conformal and non-conformal BPS Wilson loops in N = 4 quiver Chern-Simons-matter theory on S3, connected by continuous supersymmetric deformations. In the case of conformal BPS loops, the deformations play the role of defect exactly marginal operators which generate the “nontrivial” conformal manifolds. With the same method, we also address a longstanding question of whether ABJM theory has 1/3 BPS Wilson loop operators, where such loops are made of a large supermatrix combining two 1/2 BPS Wilson loops.

Date of Award	1 Feb 2024
Original language	English
Awarding Institution	King's College London
Supervisor	Nadav Drukker (Supervisor) & affiliated academic (Supervisor)