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I stumbled about two things in GSW section 2.2.3 on Vertexoperators,

that I don't really understand.

The first one is GSW's statement just before 2.2.54, p. 88, that the

L_m's of the Virasoro algebra generate transformations like

tau -> tau -ie^{im tau}

.... From what was said on p. 65 of the generators of the residual

symmetry and on p. 72 from the Virasoro generators I know that these

should be conserved charges, thus generating some transformations with

f(sigma^+) = e^imsigma^+ and f(sigma^-) = e^imsigma^-, which is at

sigma = 0 just e^imtau. But how to get from this result to the above

transformation law?

The second one is the statement on p. 92 that for the two conditions

k_mu zeta^munu = 0 and tr zeta = 0 the tensor zeta should be a

symmetric traceless tensor. Tracelessness is clear, but how to show

that under this condition the tensor should be symmetric?

I hope that these questions are not too elementary, but as I am new

with the string stuff, many elementary things bother me most,

sometimes.

RenĂ©.

--

RenĂ© Meyer

Student of Physics & Mathematics

Zhejiang University, Hangzhou, China

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# Questions on GSW 2.2.3

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