# Questions tagged [vertex-algebras]

The vertex-algebras tag has no usage guidance.

19
questions with no upvoted or accepted answers

**14**

votes

**0**answers

279 views

### The Monster Moonshine Module from the engineering or algorithmic point of view

From what I understand (see, e.g., this question), the Monster Moonshine Module is a kind if "third generation" (or "second quantization"?) after the Golay code (with automorphism group $M_{24}$) and ...

**12**

votes

**0**answers

275 views

### Vertex algebras and factorization algebras

It is often said that vertex algebras are a special case of factorization algebras. In particular, in their book "FAs in QFT" Costello/Gwilliam construct a functor from a certain class of 2d "...

**12**

votes

**0**answers

334 views

### Does the de Rham version of Cohen's theorem hold in the $\infty$-setting?

One of the first results that one needs to prove in the theory of chiral algebras is a de Rham version of Cohen's theorem on the homology of $C_n$ spaces. This is achieved in Beilinson-Drinfeld's book ...

**6**

votes

**0**answers

185 views

### $X$ with $H^*(X)=$affine Verma module?

Let $\mathfrak{g}$ be a finite dimensional simple Lie algebra over $\mathbf{C}$, and $\widehat{\mathfrak{g}}_\kappa$ the associated affine Lie algebra. It is the central extension of the loop algebra $...

**6**

votes

**1**answer

288 views

### $GL(\infty)$ group action through the boson-fermion correspondence

Every point of the Sato Grassmannian can be used to generate a tau function of the KP hierarchy. In addition, the Sato Grassmannian can be seen as a subset of the "second quantized fermion Fock space" ...

**6**

votes

**0**answers

140 views

### Orthogonality relations for characters of VOAs?

If $G$ is a finite group, the characters of its irreps satisfy
$$
\langle \chi_1,\chi_2\rangle := \frac{1}{|G|}\sum_{g\in G} \chi_1(g)\; \overline{\chi_2(g)} = \delta_{\chi_1,\chi_2}.
$$
Alexei ...

**6**

votes

**0**answers

135 views

### A single vertex operator - bare bones explanation?

There is an ocean of literature (and a sea of popular texts inside) on vertex algebras, including quite a lot of Q & A here on MO, and I am trying to read some random selections from time to time. ...

**6**

votes

**0**answers

121 views

### Functions on [0,1] with positive fractional series coefficients and symmetric under x->1-x

Suppose a function $g(x)$ has a convergent power series expansion with real (not necessarily integer or rational) exponents on $[0,1]$ of the form
$$
g(x)=\frac{1}{x^\delta}(1+\sum_{i=1}^\infty c_i x^{...

**5**

votes

**0**answers

288 views

### Reference Request: Vertex Algebras

I am currently a graduate student in mathematics with an interest in vertex algebras. I am comfortable with the algebraic aspects and would like to learn more about the geometric aspects. The issue is ...

**4**

votes

**0**answers

224 views

### Are vertex operator algebras ever conspiratorial?

I have a vertex operator algebra (VOA) $V$ with all niceness properties (unitary, rational, CFT type, etc). Its Lie algebra $\mathfrak{g} = V_1$ of spin-$1$ fields is large, and I understand how the ...

**4**

votes

**0**answers

167 views

### Arithmetic analogs of vertex algebras?

Has anyone successfully defined and studied analogs of vertex algebras where the grading of the fields is by $(\log \mathbb Q)$ rather than $\mathbb Z$? What I mean is that the usual fields
$$
a(z) = ...

**4**

votes

**0**answers

253 views

### $\mathbb Z/2$-orbifolds in Virasoro representations, CFTs, VOAs

Suppose that ${\rm Vir}_c$ is a rational Virasoro algebra with central charge $c$.
Then ${\rm Vir}_c$ has finitely many irreducible modules $M_h$, parametrised by the highest weights $h$.
Furthermore ...

**3**

votes

**0**answers

143 views

### Self-dual vertex algebras

Let $(V,Y)$ be a self-dual conformal vertex algebra. For instance, it could be the vertex algebra associated to a positive definite, even, unimodular quadratic form. I look for a formula to compute
$$
...

**3**

votes

**0**answers

223 views

### Does the following first order approximation of the Kapranov-Vasserot infinitesimal loops still do any job?

Let $X$ be a scheme over, say, a field $k$. Let us denote $\mathrm{Spec}(k[\varepsilon])$ by $T$ and its (unique) $k$-point by $0\in T$. Call the first order infinitesimal cone $C_{T,0}(X)$ over $X$ ...

**2**

votes

**0**answers

61 views

### Representation theoretic definition of wavefunctions of an integrable hierarchy?

I am reading Kac's book on infinite dimensional lie algebras. In the last chapter, he starts with a highest weight module of an affine lie algebra $\mathfrak{g}(A)$, and uses it to define tau ...

**2**

votes

**0**answers

58 views

### Free almost commutative vertex algebras

Given a commutative $k$-algebra $A$, we can freely generate a commutative vertex algebra by formally adjoining a derivation. We obtain a functor $CAlg_{k} \rightarrow CVAlg_{k} $, which I'll denote $\...

**1**

vote

**1**answer

78 views

### Vertex operator algebras and isomorphism of graded vector spaces

I have two vertex operator algebras and I would like to show that as graded vector spaces, they are isomorphic, rather than as algebras.
The issue is I have not found anything in the literature that ...

**1**

vote

**0**answers

161 views

### Wightman axioms to Vertex algebra, the inspiration for the infinitesimal translation operator T?

In section 1.1, 1.2 of Kac's book Vertex Algebras for Beginners, he deduces the axioms of vertex algebras (or more precisely, right chiral algebras) from the Wightman axioms for $2$d CFT.
Denote $\...

**1**

vote

**0**answers

174 views

### Understanding the Segal-Sugawara construction

I am trying to understand the Segal-Sugawara construction from the book "vertex algebras and algebraic curves" by Frenkel, Ben-Zvi in 3.4.8. As an absolute layman in the area of mathematical physics ...