Superconformal surfaces in four dimensions

Abstract

We study the constraints of superconformal symmetry on codimension two defects in four-dimensional superconformal field theories. We show that the one-point function of the stress tensor and the two-point function of the displacement operator are related, and we discuss the consequences of this relation for the Weyl anomaly coefficients as well as in a few examples, including the supersymmetric Rényi entropy. Imposing consistency with existing results, we propose a general relation that could hold for sufficiently supersymmetric defects of arbitrary dimension and codimension. Turning to N = (2, 2) surface defects in N ≥ 2 superconformal field theories, we study the associated chiral algebra. We work out various properties of the modules introduced by the defect in the original chiral algebra. In particular, we find that the one-point function of the stress tensor controls the dimension of the defect identity in chiral algebra, providing a novel way to compute it, once the defect identity is identified. Studying a few examples, we show explicitly how these properties are realized.

Central charges of 2d superconformal defects

“…Ref. [52] further provided compelling evidence for the conjecture that d 1 ∝ d 2 for 2d N = (2, 2) superconformal defects in any d. All of these results extend equally well to 2d N = (4, 4) superconformal defects. We will thus only explicitly compute b and d 2 .…”

“…One factor is the Schur index [81,82]. By appealing to a growing body of evidence from various perspectives [52,71,74,[83][84][85], we claim that the other factor is e −REc , where E c is the SUSY Casimir Energy (SCE). We propose that introducing the defect shifts E c by a term ∝ d 2 , and provide compelling evidence from our two examples.…”

“…In fact, in a 4d SCFT with a 2d N = (2, 0) superconformal defect, ref. [52] proved that the SUSY algebra requires d 1 = d 2 . Ref.…”

The superconformal equation

“…Block expansions and bootstrap equations for supersymmetric defects have also been studied and applied e.g. in [30,34,38,77,78].…”

Analytic bootstrap and Witten diagrams for the ABJM Wilson line as defect CFT1

“…Such generators have a natural normalization in the bulk theory and therefore the Ward identities (2.13) fix the physical normalization of the displacement operator, making its two-point function an important piece of defect CFT data. There is concrete evidence that in the presence of a superconformal defect this coefficient is related to the one-point function of the stress tensor operator [64][65][66]. Moreover, for the case of the Wilson line this coefficient is particularly important as it computes the energy emitted by an accelerating heavy probe in a conformal field theory [10,67], often called Bremsstrahlung function.…”