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Here is my rough understanding. In a TCFT we have chains on moduli spaces $\widetilde{M}$ of Riemann surfaces with parameterized boundary acting (in the sense of operads, PROPs, whatever) on a chain c …

CFT/QFT/TFT/etc. is a huge subject... Here are some random references off the top of my head... Segal, "The definition of conformal field theory". Costello, "Topological conformal field theories an …

Here is my impression ... (I am very much a non-expert in the physics (and probably the mathematics too) so I may well be wrong about some of these things.) Algebraic geometry sometimes enters the p …

There is a "folk theorem" (alternatively, a fun and easy exercise) which asserts that a 2D TQFT is the same as a commutative Frobenius algebra. Now, to every compact oriented manifold $X$ we can assoc …

What do Gromov-Witten invariants (of say a Calabi-Yau 3-fold) represent, or what are they supposed to represent, in terms of string theory? When I compute GW invariants, am I actually computing some i …

In (for example) Semisimple Frobenius structures at higher genus (section 1.2) and Gromov-Witten invariants and quantization of quadratic Hamiltonians (section 6.8), Givental gives a conjectural formu …

Let X be a compact symplectic manifold. There is an idea, I think probably originally due to Kontsevich, that we should be able to get Gromov-Witten invariants of X out of the Fukaya category of X. On …

In his answer to this question, Scott Carnahan mentions "mirror symmetry mod p". What is that? (Some kind of) Gromov-Witten invariants can be defined for varieties over fields other than $\mathbb{C} …

I do not know very much about quantum field theory, but I have seen, in my reading, that stable graphs can appear in QFT in the form of, I think, Feynman diagrams. By stable graph I mean a "graph with …

Indeed matrix factorizations come up in string theory. I don't know if there are good survey articles on this stuff, but here is what I can say about it. There might be an outline in the big Mirror Sy …

What is Chern-Simons theory? I have read the wikipedia entry, but it's pretty physics-y and I wasn't really able to get any sense for what Chern-Simons theory really is in terms of mathematics. Chern …

I've found the following articles useful in the past: Segal's notes: http://www.cgtp.duke.edu/ITP99/segal/ Atiyah's paper "Topological quantum field theories"

Why, from a string theory perspective, is it natural to consider the Deligne-Mumford (resp. Kontsevich) compactification of the moduli of curves (resp. maps [from curves to a target space X]) rather t …

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 …