Go to previous page Go up Go to next page

3.1 The special case: w1 = w2

It is instructive to first discuss the particularly simple special case of a circular string, where w1 = w2 and (21View Equation) does not apply. This will turn out to be a limiting case of the q > 1 scenario. For w21 = 0 the equation of motion for y(s) (19View Equation) immediately yields
'' y = 0 ==> y(s) = n s (25)
with n being the integer winding number of this circular string y(s + 2p) = y(s) + 2p n. In this case, the Virasoro constraints (6View Equation) yield k = V~ n2-+-w12-. A little bit of algebra quickly shows that the energy E may be reexpressed as a function of J1 = J2 and reads
V~ ------2-- E = 2J 1 + -n-c- (26) 1 4 J12
which is analytic in c J12! This amounts to an all-loop prediction for the dual gauge theory scaling dimension in the BMN limit J1-- > oo with c/J12 fixed, quite similar to the result for the plane-wave superstring discussed above. Let us now discuss the folded and circular string solutions in turn.
  Go to previous page Go up Go to next page