Spiky strings and giant holes

Abstract

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.

From weak coupling to spinning strings

“…At leading order in spin the result ∼ 3 2 f (g) agrees with the energy scaling of spikystrings [31,32] that consist of three arcs, each of them contributing a factor of 1 2 , see [33,34]. At finite order the results differ [29,35].…”

Multi-spike strings in AdS3 with mixed three-form fluxes

“…The same dispersion relation obtained from an integrable SL(2) spin chain was reported in [18]. The spin chain description of such spiky strings were explored in detail in the series of works [19][20][21][22]. The other much discussed form of gauge-gravity duality comes in the form of strings in AdS 3 × S 3 × M 4 and the two dimensional CFTs.…”

Moduli dynamics of AdS3strings

“…Our next task is to establish a relationship between the Lax pairs (3.13)- (3.16) found in the sigma model and the standard Lax pair of the sinh-Gordon theory 20) which satisfies the Dirac equations…”

“…A different attempt to generalize Kruczenski's static solution was presented recently in [20] through 'gluing'. In this construction, which is based on a static picture, the equations of motion appear not to be satisfied at the locations of spikes.…”