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Two definitions of conformal inclusion

The answer is no: it is possible to have a vertex algebra map between vertex operator algebras of equal central charge that does not take preserve the distinguished conformal vectors. Given a vertex …
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Do we have a braided tensor category for vertex algebra modules by using conformal blocks on...

In general, you won't get a vertex tensor category, because you don't get well-defined unit behavior when you use conformal blocks on higher genus surfaces. Huang-Lepowsky assume the vertex operator …
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7 votes
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Verlinde Formula and Theta Function Identities

For any integer lattice $L$, you can write a theta function $\theta_L$ as a generating function for lattice vectors of a given norm. That is, $$\theta_L(\tau) = \sum_{a \in L} q^{(a,a)/2}.$$ The quot …
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5 votes
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What happens to Virasoro at c=25?

I have an incomplete understanding of this, but I will try to say what I know. For each $c \in \mathbb{C}$, we define $Verma_c$ to be the category whose objects are Verma modules $V_{h,c}$ of central …
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2 votes

Vertex operator algebras and isomorphism of graded vector spaces

This was answered by Marcel Bischoff in a comment. For any vertex operator algebra, there is an invariant called the "character" or "graded dimension", that captures precisely the isomorphism type of …
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coset of affine Lie algebra

This is typically given by the commutant, or coset construction. You take the vector subspace of $\mathcal{R}_\text{vac}[\mathfrak{g}_k]$ spanned by vectors $v$ satisfying $Y(u,z)v \in \mathcal{R}_\t …
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8 votes

Conformal blocks in genus zero

Well, the claim is bogus, so you can't expect the proof to hold much water. On the other hand, it may be instructive to try filling in details to see why it fails. First of all, we can't define conf …
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5 votes
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When two vertex (operator) algebras can be patched-up to a full CFT on a genus 0 surface?

If your VOA $V$ is not rational, then it is quite unlikely that its category of representations is a modular tensor category. That is, you can safely conclude that Theorem 3 contains an unstated assu …
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Analogues of the Monster for central charges different from 24

As others have mentioned, there are many CFTs, but we can narrow down our list by looking at conditions that select for interesting automorphism groups. Perhaps the easiest is to consider holomorphic …
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5 votes

The Chern-Simons/Wess-Zumino-Witten correspondence

You are unlikely to find a proof of these claims, because Chern-Simons theory, as a quantum field theory in 3 dimensions, has not been precisely formulated mathematically. You can find some partial r …
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2 votes
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Why is there a discrepancy between the normalizations of the central terms for the commutati...

As far as I can tell, a $\sigma$-model with $d$ dimensional target space will have Virasoro central charge $d$ with bosonic strings, and $3d/2$ with supersymmetric strings. I believe the normalizatio …
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11 votes
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Character of parity-twisted supersymmetric VOA module -- question inspired by the Stolz-Teic...

Such an object is described in Dixon, Ginsparg, Harvey, Beauty and the Beast: superconformal symmetry in a monster module Comm. Math. Phys. Volume 119, Number 2 (1988), 221-241. A reasonably explicit …
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4 votes

Example for non equivalent rational full CFTs with same modular invariant (partition function)

I'm going to try to connect the language of Jeff Harvey's answer to the language of your question. It seems to give an answer to your title question, but not to the question you asked in the main tex …
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5 votes

Even lattices and binary codes

I don't have any references (e.g., Conway-Sloane) in front of me, so this will be rather basic. For all non-negative integers $n$, the set of even lattices $L$ satisfying $(2\mathbb{Z})^n \subseteq L …
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29 votes
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$H^4$ of the Monster

There is some evidence from characters that $H^4(M,\mathbb{Z})$ contains $\mathbb{Z}/12\mathbb{Z}$. In particular, the conjugacy class 24J (made from certain elements of order 24) has a character of …
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