In the Woods of M-Theory

TL;DR

This paper investigates BPS states in M-theory compactified on Calabi-Yau manifolds, focusing on M2-brane spectra, computing Euler characteristics of moduli spaces, and exploring discrepancies with mirror symmetry predictions to suggest the existence of extra moduli.

Contribution

It introduces a novel approach to counting M2-brane states via Euler characteristics and proposes the existence of additional moduli, supported by new calculations and conjectures.

Findings

Discrepancy with local mirror symmetry predictions.

Evidence for extra moduli of M2-branes, including flat U(1) connections.

Conjecture on higher genus curve counting using second quantized Penner model.

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.