The virasoro-algebra tag has no usage guidance.

**11**

votes

**1**answer

253 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 ...

**1**

vote

**1**answer

269 views

### A subalgebra of the Virasoro algebra

Let $L_n$ ($n\in\mathbb{Z}$) and $c$ be the standard generators of the Virasoro algebra ${\rm Vit}$. In the literature one usually considers the involutive authomorphism given by $\tau(L_n)=-L_{-n}$, $...

**2**

votes

**1**answer

189 views

### Link between Virasoro algebra and Heisenberg algebra

I'm reading these notes on infinite-dimensional Lie algebras.
On page 5, author defines Heisenberg algebra and shows that certain infinite sums of elements of Heisenberg algebra (I'm being a little ...

**7**

votes

**0**answers

243 views

### The space-time dimension of the N-superstring theory?

Let $\mathfrak{W}$ be the Lie algebra generated by $d_{n} = ie^{in\theta}\frac{d}{d\theta}$ and $\mathfrak{Vir} = \mathfrak{W} \oplus C \mathbb{C}$ its central extension:
$$
[L_m,L_n]=(m-n)L_{m+n}+\...

**8**

votes

**1**answer

339 views

### Are there exactly solvable CFTs?

I am wondering if there are CFTs such that n-point correlation functions in them of the fields (may be the primaries or of some notion of twist fields) is exactly known.
Are there such?
Aren't ...

**12**

votes

**1**answer

870 views

### Is this error in this paper of Langlands fixable?

The FQS criterion for the Virasoro algebra was discovered by Friedan, Qiu and Shenker (1), but the mathematicians found their proof insufficient, so that, FQS (2) and Langlands (3), published in the ...

**11**

votes

**2**answers

876 views

### What happens to Virasoro at c=25?

The Virasoro algebras $Vir_c$ are a family of infinite dimensional Lie *-algebras parametrized by a real number $c$, called the central charge.¹
I hear that there exist two critical values of the ...

**14**

votes

**3**answers

2k views

### Motivation of Virasoro algebra

I have a question on definition/motivation of Virasoro algebra. Recall that Virasoro algebra is an infinite Lie algebra generated by elements $L_n$ $(n\in \mathbb{Z})$ and $c$ over $\mathbb{C}$ with ...

**4**

votes

**1**answer

180 views

### Why is there a discrepancy between the normalizations of the central terms for the commutation relations of the Virasoro versus Neveu-Schwarz Lie algebras?

Following the standard conventions in the literature, the commutation relations of the Virasoro Lie algebra are given by
$$[L_m,L_n]=(m-n)L_{m+n}+\delta_{m,-n}\frac1{12}(m^3-m)c,$$
$$[c,L_n]=0.$$
...

**4**

votes

**1**answer

423 views

### Representations of infinite dimensional Lie algebras as vector fields on manifolds

Suppose I have e.g. the Witt algebra,
$\left[l_n,l_m \right] = -(n-m)l_{n+m}$.
I want to realize the $l_n$ as vector fields on some manifold. The classical example is when the $l_n$ span the Lie ...

**14**

votes

**2**answers

909 views

### I'm looking for a Virasoro-module whose character is 1+ 240q+ 2160q^2+ 6720q^3…

Let $E_4(q)=1+ 240q+ 2160q^2+ 6720q^3+\ldots $ be the Eisenstein series of weight 4,
also known as the theta-series of the $E_8$-lattice.
I'm looking for a $\mathbb N$-graded vector space $V$ of ...

**37**

votes

**3**answers

2k views

### Why is there such a close resemblance between the unitary representation theory of the Virasoro algebra and that of the Temperley-Lieb algebra?

For those who aren't familiar with the Virasoro or Temperley-Lieb algebras, I include some definitions:
• The (universal envelopping algebra of the) Virasoro algebra is the $\star$-algebra $...

**8**

votes

**1**answer

437 views

### How many embeddings are there of super-Virasoro into n Fermions?

What is the space of N=1 super-Virasoro vertex superalgebras inside the c=n/2 free fermion vertex superalgebra? [Said differently, how many Neveu-Schwartz vectors are there in n fermions?] Answers ...