We study the semiclassical spectrum of excitations around a long spinning string in AdS 3 .In addition to the usual small fluctuations, we find the spectrum contains a branch of solitonic excitations of finite energy. We determine the dispersion relation for these excitations. This has a relativistic form at low energies but also matches the dispersion relation for the "holes" of the dual gauge theory spin chain at high energies. The low-energy behaviour is consistent with the hypothesis that the solitonic excitations studied here are continuously related to the elementary excitations of the string.
We analyse semiclassical strings in AdS in the limit of one large spin. In this limit, classical string dynamics is described by a finite number of collective coordinates corresponding to spikes or cusps of the string. The semiclassical spectrum consists of two branches of excitations corresponding to "large" and "small" spikes respectively. We propose that these states are dual to the excitations known as large and small holes in the spin chain description of N = 4 SUSY Yang-Mills. The dynamics of large spikes in classical string theory can be mapped to that of a classical spin chain of fixed length. In turn, small spikes correspond to classical solitons propagating on the background formed by the large spikes. We derive the dispersion relation for these excitations directly in the finite gap formalism.
We propose a correspondence between strings with cusps which approach the boundary in AdS and energetic partons in the dual gauge theory on S3. In particular, the momenta of individual quanta on S3 are identified with certain collective coordinates associated with the cusps. We check the correspondence by studying the known exact string solutions, as well as a large class of approximate solutions, in the limit of large AdS angular momentum.
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