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Calabi-Yau manifolds are higher dimensional generalizations of elliptic curves and K3 surfaces. They can be defined as the compact complex Kähler manifolds with trivial canonical bundle, and play a central role in mirror symmetry. This tag can also be used for Calabi-Yau algebras and categories. These algebraic notions are inspired by the properties of the derived categories of coherent sheaves on Calabi-Yau manifolds.

1 vote
2 answers
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is complex moduli space of a Calabi - Yau Kahler

The complex moduli space of a Calabi-Yau manifold is a complex manifold (BTT). Is it also Kahler ?
J Verma's user avatar
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7 votes
3 answers
2k views

what is large compex structure limit of CY moduli space

What is the Large Complex Structure limit(LCL) of complex moduli space of a Calabi-Yau 3-fold and why do we need to consider LCL in Mirror symmetry.
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4 votes
1 answer
1k views

vector multiplet/hypermultiplet moduli space of String Theory

What is vector multiplet and hypermultiplet moduli space associated to IIA/B string theory (or in general to a N = 2 Supersymmetric theory) ? The vector multiplet moduli space is special Kahler while …
J Verma's user avatar
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14 votes
1 answer
3k views

Witten's topological twisting

I am reading the Witten's topological twisting for $N = 2$ Superconformal Field Theory(SCFT) http://arxiv.org/abs/hep-th/9112056 In this paper Witten constructed 2 TQFTs i.e. A-model and B-model from …
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2 votes
1 answer
691 views

Are there non-supersymmetric and/or non-Calabi-Yau topological sigma models?

I am reading some aspects of Mirror Symmetry and in mirror symmetry the $N=2$ SCFT on a Calabi Yau Manifold can be divided into two sectors each of which is a topological sigma model, A-Model and B-Mo …
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13 votes
4 answers
3k views

Calabi - Yau Manifolds

I just started reading about Calabi-Yau manifolds and most of the sources I came across defined Calabi-Yau manifold in a different way. I can see that some of them are just same and I can derive one f …
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16 votes
1 answer
3k views

Donaldson-Thomas Invariants in Physics

First of all, I am sorry for there are a bunch of questions (though all related)and may not be well framed. What are the DT invariants in physics. When one is computing DT invariants for a Calabi-Yau …
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