Perturbative Corrections to Kahler Moduli Spaces

Abstract

We propose a general formula for perturbative-in-alpha' corrections to the Kahler potential on the quantum Kahler moduli space of Calabi-Yau n-folds, for any n, in their asymptotic large volume regime. The knowledge of such perturbative corrections provides an important ingredient needed to analyze the full structure of this Kahler potential, including nonperturbative corrections such as the Gromov-Witten invariants of the Calabi-Yau n-folds. We argue that the perturbative corrections take a universal form, and we find that this form is encapsulated in a specific additive characteristic class of the Calabi-Yau n-fold which we call the log Gamma class, and which arises naturally in a generalization of Mukai's modified Chern character map. Our proposal is inspired heavily by the recent observation of an equality between the partition function of certain supersymmetric, two-dimensional gauge theories on a two-sphere, and the aforementioned Kahler potential. We further strengthen our proposal by comparing our findings on the quantum Kahler moduli space to the complex structure moduli space of the corresponding mirror Calabi-Yau geometry.

28 pages; v2: discussion in section 5 extended and refs. added

References in corpus (7)

• Exact Results In Two-Dimensional (2,2) Supersymmetric Gauge Theories With Boundary
• Exact Results in Supersymmetric Field Theories on Manifolds with Boundaries
• New Methods for Characterizing Phases of 2D Supersymmetric Gauge Theories
• Linear Sigma Models With Strongly Coupled Phases -- One Parameter Models
• Real and integral structures in quantum cohomology I: toric orbifolds
• The Stringy Instanton Partition Function
• A few Ricci-flat stacks as phases of exotic GLSM's

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