Questions tagged [mirror-symmetry]
Use for questions about mirror symmetry in theoretical/mathematical physics.
164 questions
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compute the Kähler moduli of an elliptic curve
Say given elliptic curve $ \{ (x,y) | y^2 = (x^2-1)(x^2-k^2) \}$, what is the right form of the K$\ddot{a}$hler form and how to compute the K$\ddot{a}$hler moduli of this elliptic curve? Thank you.
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Mirror of Flop?
If two Calabi-Yau 3-folds are bi-rational to each other via a Flop , then what is the relation between their mirrors ?
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a question on Costello's theorem
Costello's theorem,"open TCFT=Calabi Yau A-infinity category",he also mentions when applied to Fukaya category we can recover Gromov-Witten theory, but I see that it needs some assumption,also even if ...
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Are the two B model constructions equivalent?
Now we have two B model constructions: Kontsevich-Baranikov (for genus 0) and Costello (for any genus). My question is, are they equal in genus 0? Or now which one is the one we want? Thanks!
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balanced curves in Calabi-Yau 3-folds
A balanced smooth rational curve in a calabi-Yau X is a smooth rational curve whose normal bundle is $O(-1)\oplus O(-1)$.
We usually like these curves because of their rigidity.
But, Is there any ...
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Shrinking Fano surfaces to a point in Calabi-Yau 3-folds
Let X be a Calabi-Yau 3-fold, and $D\subset X$, smooth,Fano divisor.
Since $K_X=0$ we have $N_D^X=K_D$. I have seen the following fact in many papers:
By deforming X within Kahler moduli, we can ...
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Mirror of local Calabi-Yau
What is the mirror manifold of the total space of the bundle $O(-1)\oplus O(-1)$ over $P^1$? I have tried to find the answer on the web but failed. Is there a good reference for this? Thanks.
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"Fourier-Mukai" functors for Fukaya categories?
I just skimmed a bit of this fresh-off-the-press paper on homological mirror symmetry for general type varieties.
One thing that intrigued me was statement (ii) of Conjecture 3.3. It suggests that, ...
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Higher genus closed string B-model
The closed string A-model is mathematically described by Gromov-Witten invariants of a compact symplectic manifold $X$. The genus 0 GW invariants give the structure of quantum cohomology of $X$, which ...
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Which part of physical B model is not rigorous?
Which part of physical B model is not rigorous? the physical theory of B model,if it is not mathematical rigorous just because the Feynman integral,but it looks like for me the space is finite ...
CommunityBot
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Understanding formula in Frenkel-Witten
I'm not the person to understand everything in Geometric Endoscopy and Mirror Symmetry, but some parts of it are reasonably clear to me.
In particular, one of the main objects, mathematically ...
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Picard-Fuchs equations
If I have the periods $$\pi_1(\lambda)=\int_0^1\frac{dx}{\sqrt{x(x-1)(x-\lambda)}}$$ and $\pi_2(\lambda)$ similarly defined of the cubic curve $$y^2z=z(x-z)(x-\lambda z)$$ Such functions will be ...
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Is the Fukaya category "defined"?
Sometimes people say that the Fukaya category is "not yet defined" in general.
What is meant by such a statement? (If it simplifies things, let's just stick with Fukaya categories of compact ...
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Singularity theory references
I am looking for some good references on singularity theory. I'm interested in singularity theory in the context of mirror symmetry, so this means I'm interested in things like Picard-Lefschetz theory,...
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