Boundary Weyl anomaly of $\mathcal{N}=(2,2)$ superconformal models

TL;DR

This paper computes boundary anomalies in 2D superconformal theories, linking them to partition functions and boundary entropy, and confirming conjectures about their geometric and holomorphic properties.

Contribution

It extends anomaly calculations to boundary cases in $ abla=(2,2)$ theories, connecting anomalies to partition functions and boundary entropy, and confirms related conjectures.

Findings

Sphere partition function computes the Kähler potential on the superconformal manifold.

Hemisphere partition function computes the holomorphic boundary central charge.

Boundary entropy is fully determined by anomalies.

Abstract

We calculate the trace and axial anomalies of $\mathcal{N}=(2,2)$ superconformal theories with exactly marginal deformations, on a surface with boundary. Extending recent work by Gomis et al, we derive the boundary contribution that captures the anomalous scale dependence of the one-point functions of exactly marginal operators. Integration of the bulk super-Weyl anomaly shows that the sphere partition function computes the K\"ahler potential $K(\lambda, \bar\lambda)$ on the superconformal manifold. Likewise, our results confirm the conjecture that the partition function on the supersymmetric hemisphere computes the holomorphic central charge, $c^\Omega(\lambda)$, associated with the boundary condition $\Omega$. The boundary entropy, given by a ratio of hemispheres and sphere, is therefore fully determined by anomalies.