Spiky Strings In The Sl(2) Bethe Ansatz

We consider spiky strings in the context of the SL(2) Bethe ansatz equations. We obtain an asymmetric distribution of Bethe roots along one cut which determines the all loop anomalous dimension at leading and subleading orders in a large S expansion. At leading order in strong coupling (large lambda) the energy of such states is given, in terms of the spin S and the number of spikes n by E-S = n root lambda/2 pi (ln =4 pi S/root lambda broken vertical bar In 4/n-1) broken vertical bar O(InS/S). This result agrees perfectly with the same expansion obtained from the known spiky string classical solution. We also discuss a two cut spiky string Bethe root distribution at one-loop in the SL(2) Bethe ansatz.