In the Woods of M-Theory

Abstract

We study BPS states which arise in compactifications of M-theory on Calabi-Yau manifolds. In particular, we are interested in the spectrum of the particles obtained by wrapping M2-brane on a two-cycle in the CY manifold X. We compute the Euler characteristics of the moduli space of genus zero curves which land in a holomorphic four-cycle $S\subset X$. We use M. Kontsevich's method which reduces the problem to summing over trees and observe the discrepancy with the predictions of local mirror symmetry. We then turn this discrepancy into a supporting evidence in favor of existence of extra moduli of M2-branes which consists of the choice of a flat U(1) connection recently suggested by C. Vafa and partially confirm this by counting of the arbitrary genus curves of bi-degree (2,n) in $\IP^1 \times \IP^1$ (this part has been done together with Barak Kol). We also make a conjecture concerning the counting of higher genus curves using second quantized Penner model and discuss possible applications to the string theory of two-dimensional QCD.

harvmac, 14 pp., v2. references added, typos corrected

References in corpus (3)

• Counting higher genus curves in a Calabi-Yau manifold
• Instanton sums and five-dimensional gauge theories
• Localization of virtual classes

Cited by in corpus (1)

• Local Mirror Symmetry at Higher Genus