# Tag Info

### $H^4$ of the Monster

In arXiv:1707.08388, I calculate that the cohomology class you described has order 24 and that it is not a characteristic class in the ordinary sense.
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### What's the supersymmetric analogue of the Monster group?

There is a super analog constructed just as you describe with the Conway group $Co_0$ replacing the Monster and commuting with the superconformal algebra. The construction is described in detail in: ...
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### 71, the Monster, and c = 24 CFTs

Schellekens' enumeration is exhaustive in the following sense: the degree 1 subspace of the meromorphic CFT/vertex algebra is naturally a Lie algebra, and it is known that this Lie algebra must be one ...
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### Why "holomorphic" vertex algebra?

Those in a hurry can skip to the bottom. Those with some leisure time can read the details. To explain the answer, it is helpful to remember what vertex algebras are. Suppose you have a quantum field ...
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### Why are VOA characters modular forms (geometrically)?

I'm sure someone here can handwave the intuition behind these statements much better than me. This handwaving version goes like this, one is interested in computing vacuum 1-point functions on a torus,...
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### What are advantages of chiral algebras over vertex algebras?

Some comments: It is not necessarily true that chiral algebras are essentially conformal vertex algebras, as chiral algebras are allowed to vary over the curve in a way that vertex algebras are not. ...
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### Chiral homology for the Virasoro algebra and/or affine Lie algebra

There isn't much written up on how to compute the higher chiral homology of vertex algebras. Besides the original work of Beilinson and Drinfeld that covers in particular the universal cases of ...
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### What are braided vertex algebras?

For the case of vector spaces graded by an abelian group (with braiding determined by an abelian 3-cocycle following Joyal-Street), this was done by Dong and Lepowsky in their 1993 book "Generalized ...
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### Factorization and vertex algebra cohomology

If $X$ is taken to a be a formal disc $D$, then we obtain a vertex algebra. I believe in this case the above construction produces the vertex algebra cohomology (with coefficients in the adjoint ...
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### Do we have a braided tensor category for vertex algebra modules by using conformal blocks on an arbitary compact Riemann Surface?

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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### The proof that a vertex algebra can lead to a Wightman QFT

You might find "An Introduction to Conformal Field Theory" by M. Gaberdiel (arXiv:hep-th/9910156v2) useful. He has a brief discussion of how in some cases chiral algebras can be assembled into ...
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### $\text{Rep}(D(G))$ as representation category of a vertex operator algebra

A lot has happened in the last four years, and we now have lots of positive results. The current state of knowledge is given in Evans-Gannon, "Reconstruction and Local Extensions for Twisted Group ...
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### q-Virasoro and q-Heisenberg algebras

The main sources are Awata et al or Frenkel-Reshetikhin. In http://arxiv.org/pdf/q-alg/9507034v5.pdf section 4, you can see the q,t case. You can also look at http://arxiv.org/pdf/q-alg/9505025v1.pdf ...
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### Annihilation operators in a vertex algebra

Suppose there exists $v,w \in V(d)$ such that $v_{(d)}w \neq 0$. And now consider $(Tv)_{(d)}w = -2d \,v_{(d)}w \neq 0$. Notice also that by skew-symmetry your condition being true for $d>n$ ...
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### Linear independence of genus-one correlation functions

A proof of this property can be found in Proposition 2.2 of Huang's paper Vertex operator algebras and the Verlinde conjecture. This proof actually uses Zhu's algebras to simplify the discussions (...
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