# Questions tagged [vertex-algebras]

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### When two vertex (operator) algebras can be patched-up to a full CFT on a genus 0 surface?

Theorem 3 of the nLab article "Full field algebra" states that Theorem 3. Two vertex operator algebras $V$ may appear as the left and right chiral halfs of a full conformal field theory precisely ...
188 views

### Fourier series of a Wightman field

From a proof that 2D Wightman CFT leads to a vertex algebra : Let $$Y(a,z):=\frac{1}{(1+z)^{2\Delta_a}}\Phi_a\left(i\frac{1-z}{1+z}\right),\quad\text{with}\quad |z|<1.$$ Here $\Delta_a\ge 0$ ...
180 views

### Closest point to a dual lattice point (in particular for root lattices!)

Given a lattice $\Lambda\subset \mathbb{R}^n$ and a point $p\in\mathbb{R}^n$ outside the lattice, then I known it is a hard question to determine the set $S\subset \Lambda$ of all lattice points with ...
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 ...
401 views

### q-Virasoro and q-Heisenberg algebras

The literature has definitions (seemingly plural, though they might be linked) of a $q$-deformed Virasoro algebra. But is there any link of these to a $q$-deformed Heisenberg algebra? (Classically ...
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^{...
771 views

### Is this a vertex algebroid?… What is vertex algebroid?

A couple of day ago, I was lamenting to a friend about the fact that I have no idea what vertex algebroids are. During our discussion, I came up with a guess of what a vertex algebroid might be. I'm ...
570 views

### properties of formal delta functions

The formal delta function is $\,\,\displaystyle\delta(x):=\sum_{n\in\mathbb Z}x^n.$ If we agree that expressions $(x+y)^n$ for $n\in\mathbb Z$ are always expanded in non-negative powers of the second ...