Topological field theory and rational curves

@article{Aspinwall1993TopologicalFT,
  title={Topological field theory and rational curves},
  author={Paul S. Aspinwall and David R. Morrison},
  journal={Communications in Mathematical Physics},
  year={1993},
  volume={151},
  pages={245-262}
}
We analyze the quantum field theory corresponding to a string propagating on a Calabi-Yau threefold. This theory naturally leads to the consideration of Witten's topological non-linear σ-model and the structure of rational curves on the Calabi-Yau manifold. We study in detail the case of the world-sheet of the string being mapped to a multiple cover of an isolated rational curve and we show that a natural compactification of the moduli space of such a multiple cover leads to a formula in… Expand
Holomorphic anomalies in topological field theories
We study the stringy genus-one partition function of N = 2 SCFTs. It is shown how to compute this using an anomaly in decoupling of BRST trivial states from the partition function. A particular limitExpand
COUNTING CURVES WITH MODULAR FORMS
We consider the type IIA string compactified on the Calabi-Yau space given by a degree 12 hypersurface in the weighted projective space P4(1,1,2,2,6). We express the prepotential of the low-energyExpand
Quantum K-theory of Calabi-Yau manifolds
Abstract The disk partition function of certain 3d N = 2 supersymmetric gauge theories computes a quantum K-theoretic ring for Kähler manifolds X. We study the 3d gauge theory/quantum K-theoryExpand
String Quantum Symmetries from Picard Fuchs Equations and Their Monodromy
Local and global properties of the moduli space of Calabi--Yau type compactifications determine the low energy parameters of the string effective action. We show that the moduli space geometry isExpand
Calabi-Yau four-folds for M- and F-theory compactifications
We investigate topological properties of Calabi-Yau four-folds and consider a wide class of explicit constructions in weighted projective spaces and, more generally, toric varieties. Divisors whichExpand
Target space duality of Calabi-Yau spaces with two moduli
In the context of superstring compactifications on Calabi-Yau threefolds, we consider the Picard-Fuchs equations that are obeyed by the periods of the holomorphic three-form. We review, focusing onExpand
Counting higher genus curves in a Calabi-Yau manifold
We explicitly evaluate the low energy coupling Fg in a d = 4, N = 2 compactification of the heterotic string. The holomorphic piece of this expression provides the information not encoded in theExpand
A note on E-strings
We study BPS states in type IIA string compactification on a local Calabi-Yau 3-fold which are related to the BPS states of the E-string. Using Picard-Lefshetz transformations of the 3-cycles on theExpand
All Genus Topological String Amplitudes and 5-brane Webs as Feynman Diagrams
A conjecture for computing all genus topological closed string amplitudes on toric local Calabi-Yau threefolds, by interpreting the associated 5-brane web as a Feynman diagram, is given. A propagatorExpand
0 D ec 1 99 3 Rational Curves on Calabi – Yau Threefolds
In the conformal field theory arising from the compactification of strings on a Calabi–Yau threefold X, there naturally arise fields corresponding to harmonic forms of types (2, 1) and (1, 1) on XExpand
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 39 REFERENCES
Duality in {Calabi-Yau} Moduli Space
We describe a duality in the moduli space of string vacua which pairs topologically distinct Calabi-Yau manifolds and shows that the yield isomorphic conformal theories. At the level of theExpand
Topological quantum field theory
A twisted version of four dimensional supersymmetric gauge theory is formulated. The model, which refines a nonrelativistic treatment by Atiyah, appears to underlie many recent developments inExpand
Quantum algebraic geometry of superstring compactifications
We investigate the algebrao-geometric structure which is inherent in 2-dimensional conformally invariant quantum field theories with N=2 supersymmetry, and its relation to the Calabi-Yau manifoldsExpand
Mirror symmetry and rational curves on quintic threefolds: a guide for mathematicians
We give a mathematical account of a recent string theory calcula- tion which predicts the number of rational curves on the generic quintic three- fold. Our account involves the interpretation ofExpand
Topological Lagrangians and cohomology
Witten [12] has interpreted the Donaldson invariants of four-manifolds by means of a topological Lagrangian. We show that this Lagrangian should be understood in terms of an infinite-dimensionalExpand
A Pair of Calabi-Yau manifolds as an exactly soluble superconformal theory
Abstract We compute the prepotentials and the geometry of the moduli spaces for a Calabi-Yau manifold and its mirror. In this way we obtain all the sigma model corrections to the Yukawa couplings andExpand
The N matrix model and gauged WZW models
Abstract It has been shown that the N matrix model two-dimensional gravity is related to certain topological field theories obtained by twisting the N = 2 minimal models. In this paper, the latterExpand
Exactly solvable string compactifications on manifolds of SU(N) holonomy
A variety of heterotic string compactifications on the K3 surface, manifolds of SU(3) holomony, and higher holomony manifolds, are solved exactly. An example of the quintic hypersurface in CP 4 isExpand
New manifolds for superstring compactification
We construct new manifolds with SU(3) holonomy that are candidate vacua for superstring theory and give a detailed explanation of the techniques involved. Some of these manifolds have a non-abelianExpand
Some Exact Results on the Superpotential from Calabi-Yau Compactifications
Abstract We prove that certain superpotential couplings in compactified string theories are given exactly by the values calculated at sigma-model tree level. In particular, the 27 3 coupling in (2,2)Expand
...
1
2
3
4
...