- #1
giulio_hep
- 104
- 6
Homework Statement
I'd like to better understand why the central charge is assumed to be equal to the number of dimensions in the spacetime background.
Homework Equations
By definition of Virasoro algebra and its operators:
[Lm,Ln]=(m−n)Lm+n+c/12(m3−m)δm+n,0
The Attempt at a Solution
The commutator relation among the modes satisfying the string worldsheet-equation gives rise to the Virasoro relation with c=D. But I'm missing the details of exactly how it happens.
As another attempt to answer my question, I think that maybe c=D can follow from the defintion of the Vertex Operator Algebra where D is the rank of space of states (but again I'm unclear if this second approach is equivalent to the first one ... and if/how the VOA is related with the first quantization of the bosonic string theory...)
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