In the woods of M-theory

Nikita Nekrasov

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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 ⊂ 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 ℙ1 × ℙ1 (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.

Original languageEnglish
Pages (from-to)XII-13
JournalJournal of High Energy Physics
Issue number1
Publication statusPublished - 2001
Externally publishedYes


  • M-Theory
  • Nonperturbative Effects
  • Sigma Models


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