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Reparameteri zations generated by Virasoro operators.

(a) Consider the string at r = 0. Which of the combinations in ( 12.151) reparameterizes the a coordinate of the string while keeping r = O? When r = 0 is preserved, the world-sheet reparameterization is actually a string reparameterization. Show that the generators of these reparameterizations form a subalgebra of the Virasoro algebra.

(b) Describe the general world-sheet reparameterization that leaves the midpoi nt a = lf / 2 of the r = 0 open string fixed. Express this reparameterization usi ng an infinite set of constrai ned parameters.

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