The Topological Vertex (original) (raw)

ADS

;

• Klemm, Albrecht ;
• Mariño, Marcos ;
• Vafa, Cumrun

Abstract

We construct a cubic field theory which provides all genus amplitudes of the topological A-model for all non-compact toric Calabi-Yau threefolds. The topology of a given Feynman diagram encodes the topology of a fixed Calabi-Yau, with Schwinger parameters playing the role of Kähler classes of the threefold. We interpret this result as an operatorial computation of the amplitudes in the B-model mirror which is the quantum Kodaira-Spencer theory. The only degree of freedom of this theory is an unconventional chiral scalar on a Riemann surface. In this setup we identify the B-branes on the mirror Riemann surface as fermions related to the chiral boson by bosonization.

Publication:

Communications in Mathematical Physics

Pub Date:

March 2005

DOI:

10.1007/s00220-004-1162-z

10.48550/arXiv.hep-th/0305132

arXiv:

arXiv:hep-th/0305132

Bibcode:

2005CMaPh.254..425A

Keywords:

• Neural Network;
• Statistical Physic;
• Field Theory;
• Complex System;
• Nonlinear Dynamics;
• High Energy Physics - Theory;
• Mathematics - Algebraic Geometry

E-Print:

70 pages, 16 figures, harvmac