Questions tagged [vertex-algebras]

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11
votes
1answer
711 views

different N=2 SUSY structures on the chiral de Rham complex of a Calabi-Yau manifold?

The context In a beautiful paper, Malikov-Schechtman-Vaintrob defined a canonical sheaf of vertex algebras equipped with a differential on any manifold $X$ (either in the $C^\infty$, complex analytic ...
43
votes
2answers
3k views

$H^4$ of the Monster

The Monster group $M$ acts on the moonshine vertex algebra $V^\natural$. Because $V^\natural$ is a holomorphic vertex algebra (i.e., it has a unique irreducible module), there is a corresponding ...
10
votes
1answer
616 views

Is there a canonical map between the cohomology of orbifold Chiral de Rham on an orbifold and the cohomology of Chiral de Rham on a crepant resolution?

The two-variable elliptic genus is a topological invariant of almost-complex manifolds that takes values in power series. These power series turn out to describe weak Jacobi forms when the manifold ...
4
votes
2answers
2k views

About state-field correspondence

In the definition of vertex algebra, we call the vertex operator state-field correspondence, does that mean that it is an injective map?? Are there some physical interpretations about state-field ...
2
votes
1answer
202 views

Modular property of affine algebra and conformal vertex algebra

I wonder how modular property naturally arises in conformal theory. Is it obvious from physical viewpoint?
0
votes
1answer
285 views

About vertex algebra, mode expansion

A vertex operator is a linear map associating every state to a operator-valued distributions (quantum field) on a algebra curve, which is also called operator-state correspondence. Chose a local ...

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