Topological Strings and (Almost) Modular Forms

Details Topological Strings and (Almost) Modular Forms Topological Strings and (Almost) Modular Forms

2006-07-17

arxiv.org/abs/hep-th/0607100v2

Commun.Math.Phys.277:771-819,2008

Physics

High Energy Physics

High Energy Physics - Theory

62 pages, 1 figure; v2: minor corrections

Scientific paper

10.1007/s00220-007-0383-3

The B-model topological string theory on a Calabi-Yau threefold X has a symmetry group Gamma, generated by monodromies of the periods of X. This acts on the topological string wave function in a natural way, governed by the quantum mechanics of the phase space H^3(X). We show that, depending on the choice of polarization, the genus g topological string amplitude is either a holomorphic quasi-modular form or an almost holomorphic modular form of weight 0 under Gamma. Moreover, at each genus, certain combinations of genus g amplitudes are both modular and holomorphic. We illustrate this for the local Calabi-Yau manifolds giving rise to Seiberg-Witten gauge theories in four dimensions and local P_2 and P_1 x P_1. As a byproduct, we also obtain a simple way of relating the topological string amplitudes near different points in the moduli space, which we use to give predictions for Gromov-Witten invariants of the orbifold C^3/Z_3.

Affiliated with

Also associated with

No associations

Rating

Topological Strings and (Almost) Modular Forms does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Topological Strings and (Almost) Modular Forms, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Topological Strings and (Almost) Modular Forms will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-506482