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# Advances in Theoretical and Mathematical Physics

## Volume 13 (2009)

### Number 3

### Form field theory on Calabi–Yau three-fold

Pages: 637 – 666

DOI: http://dx.doi.org/10.4310/ATMP.2009.v13.n3.a2

#### Authors

#### Abstract

We show how the natural Abelian duality of 2 and 3-form gravity theories on seven-dimensional manifold $CY_3 \times S^1$ leads to an S-duality between 2 and 3-form theories on simply connected $CY_3$. The massless sector of the 2-form field theory on $CY_3$ corresponds to the A model string field theory. We discuss the complex structure independence of the 2-form theory for a general Kähler manifold and derive the holomorphic anomaly equations for simply connected $CY_3$.