Topological Strings And (Almost) Modular Forms
The B-model topological string theory on a Calabi-Yau threefold X has a symmetry group {Lambda}, 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{sup 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 {Lambda}. 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 IP{sub 2} and IP{sub 1} x IP{sub 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{sub 3}/ZZ{sub 3}.
- Research Organization:
- Ernest Orlando Lawrence Berkeley NationalLaboratory, Berkeley, CA (US)
- Sponsoring Organization:
- USDOE
- DOE Contract Number:
- AC02-05CH11231
- OSTI ID:
- 928577
- Report Number(s):
- LBNL--61944; BnR: YN0100000
- Journal Information:
- Communications in Mathematical Physics, Journal Name: Communications in Mathematical Physics Journal Issue: 3 Vol. 277; ISSN 0010-3616; ISSN CMPHAY
- Country of Publication:
- United States
- Language:
- English
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