6 votes
Accepted

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 ...
  • 938
6 votes
Accepted

The use of Schur's lemma for Lie algebras in physics (CFT)

Let $\mathfrak{g}$ be a complex Lie algebra with a distinguished nonzero central element $x$, and let $V$ be an irreducible representation of $\mathfrak{g}$. The usual proof of Schur's lemma can be ...
  • 43.5k
5 votes

Equivariant cohomology of $\text{Diff}S^1/ S^1$ and Virasoro

For any group $G$ and subgroup $K$, there is an isomorphism $$ H^*_G(G/K)= H^*_K(pt) $$ So the cohomology in question is $H^*_{S^1}(pt)=\mathbb Z[x]$, and it does not seem to be very related to the ...
3 votes

GKO (or coset) construction - all possible highest weights $h$

The terminology is explained earlier on that page and the previous page in the paper. On the same page, we see that they set $\mathfrak{g} = \mathfrak{su}(2) \times \mathfrak{su}(2)$, and let the ...
  • 43.5k
3 votes

Poisson vertex algebra

This is an exercise problem and it is more proper to ask it on stack exchange. Your problem is that you do not know how to evaluate $Y_{-}(a\cdot b,z)$ for arbitrary $a,b$ in the Poisson vertex ...
  • 31
3 votes

Two questions on Zuber's "KdV and W-flows"

As for $I_4$ and $I_j$ for all $j\geqslant 4$ up to overall sign factors, see e.g. equation (1.9) of these lecture notes with $u=-r$. Also you may wish to look at this link. Regarding the bracket at ...
3 votes

Link between Virasoro algebra and Heisenberg algebra

This construction comes out of string theory. You can find it described in your favorite string theory textbook. Green, Schwarz and Witten and Polchinski are standard references.
  • 5,191
2 votes

A subalgebra of the Virasoro algebra

In the boundary state approach to D-brane states in closed string theory one has two copies of Virasoro , $L_n$ and $\tilde L_n$ and boundary states $|B \rangle$ are annihilated by $L_n+\tau(\tilde ...
  • 5,191
1 vote
Accepted

Indecomposable modules for Virasoro algebra whose weights are bounded

Yes there are other indecomposable modules where $L_0$ is bounded from below. Logarithmic theories provide many examples. The simplest example I can think of: take a Verma module generated by a ...
1 vote

Zhu's algebra for the Virasoro VOA

Since the question got at least one upvote, perhaps I should post my own answer instead of deleting the question. It can be proved by induction that $(L_0 + L_{-1})b \in O'(M_c)$, i.e., $(L_0+L_{-1})b$...
  • 193
1 vote

Are there exactly solvable CFTs?

Indeed, as José said, one can get exact formulas for correlations using the Coulomb gas method introduced by Feigin, Fuchs, Dotsenko and Fateev. I don't know how explicit or simple the formulas ...

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