Virasoro algebra

Unitarity means the inner product in the space of states is positive definite
A state with negative norm is called a ghost.
If a ghost is found on any level the represetation cannot occur in a unitary theory

They are classified by c>1 and c<1 case.
- c<1 case = discrete representations
- Kac determinant formula

\(m= 2, 3, 4.\cdots\)

\(c = 1-{6\over m(m+1)} = 0,\quad 1/2,\quad 7/10,\quad 4/5,\quad 6/7,\quad 25/28, \ldots\)

\(h_{r,s}(c) = {((m+1)r-ms)^2-1 \over 4m(m+1)}\)

\(r = 1, 2, 3,\cdots,m-1\)

\(s= 1, 2, 3,\cdots, r\)

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