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 Kähler potential Kleft(lambda, overline{lambda}right) on the superconformal manifold. Likewise, our results confirm the conjecture that the partition function on the supersymmetric hemisphere computes the holomorphic central charge, cΩ(λ), associated with the boundary condition Ω. The boundary entropy, given by a ratio of hemispheres and sphere, is therefore fully determined by anomalies.
Highlights
We calculate the trace and axial anomalies of N = (2, 2) superconformal theories with exactly marginal deformations, on a surface with boundary
Integration of the bulk super-Weyl anomaly shows that the sphere partition function computes the Kahler potential K(λ, λ) on the superconformal manifold
Our results confirm the conjecture that the partition function on the supersymmetric hemisphere computes the holomorphic central charge, cΩ(λ), associated with the boundary condition Ω
Summary
We begin by reviewing the results of Gomis et al [1]. We consider the U(1)V supergravity whose gauge field V μ couples to the vector-like R-symmetry, the one preserved by the. 1 8π isolation this M √gR(2) K, where R(2) is the Ricci scalar of the Riemann surface Supersymmetry relates it to the cohomologically non-trivial term ∼ δσ|∂λ|2, so that N = 2 invariant counterterms cannot remove it. The importance of eq (2.8) stems from the fact that the sphere partition function can be sometimes obtained exactly by localization of the functional integral [3, 4] (as pioneered in [26], see [27, 28] for recent reviews) This is a powerful new method for computing the quantum Kahler potential on the moduli space of Calabi-Yau threefolds, which does not rely on mirror symmetry. It would be impossible to find a regularization scheme, valid everywhere in M , for such sigma models To avoid this embarrassing situation one must demand that M have vanishing Kahler class, a non-trivial restriction on superconformal manifolds
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