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**1 - 9**of**9**### arXiv:0803.4222 Vibrating Giant Spikes and the large-winding sector

, 2008

"... Abstract: The single spike is a rigidly rotating classical string configuration closely related to the giant magnon. We calculate bosonic and fermionic modes of this solution, from which we see that it is not supersymmetric. It can be viewed as an excitation above a hoop of string wound around the e ..."

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Abstract: The single spike is a rigidly rotating classical string configuration closely related to the giant magnon. We calculate bosonic and fermionic modes of this solution, from which we see that it is not supersymmetric. It can be viewed as an excitation above a hoop of string wound around the equator, in the same sense that the magnon is an excitation above an orbiting point particle. We find the operator which plays the role of the Hamiltonian for this sector, which compared to the magnon’s ∆ − J has the angular momentum replaced by a winding charge. The single spike solution is unstable, and we use the modes to attempt a semi-classical computation of its lifetime. 1

### Quantum Wrapped Giant Magnon

, 801

"... Understanding the finite-size corrections to the fundamental excitations of a theory is the first step towards completely solving for the spectrum in finite volume. We compute the leading exponential correction to the quantum energy of the fundamental excitation of the light-cone gauged string in Ad ..."

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Understanding the finite-size corrections to the fundamental excitations of a theory is the first step towards completely solving for the spectrum in finite volume. We compute the leading exponential correction to the quantum energy of the fundamental excitation of the light-cone gauged string in AdS5 × S 5, which is the giant magnon solution. We present two independent ways to obtain this correction: the first approach makes use of the algebraic curve description of the giant magnon. The second relies on the purely field-theoretical Lüscher formulas, which depend on the world-sheet S-matrix. We demonstrate the agreement to all orders in (∆ / √ λ) −1 of these approaches, which in particular presents a further test of the S-matrix. We comment on generalizations of this method of computation to other string configurations. 1 Introduction and Summary In the AdS/CFT correspondence we find ourselves at the point where the S-matrix of [1, 2, 3, 4, 5] is believed to accurately describe the infinite-volume theory, albeit it fails to capture some finite-size effects [6, 7, 8, 9, 10]. The first step towards understanding a theory in finite volume is to compute the leading correction to the dispersion relation of its fundamental excitations.

### unknown title

"... Understanding finite-size effects is one of the key open questions in solving planar AdS/CFT. In this paper we discuss these effects in the AdS5 ×S 5 string theory at one-loop in the world-sheet coupling. First we provide a very general, efficient way to compute the fluctuation frequencies, which al ..."

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Understanding finite-size effects is one of the key open questions in solving planar AdS/CFT. In this paper we discuss these effects in the AdS5 ×S 5 string theory at one-loop in the world-sheet coupling. First we provide a very general, efficient way to compute the fluctuation frequencies, which allows to determine the energy shift for very general multi-cut solutions. Then we apply this to two-cut solutions, in particular the giant magnon and determine the finite-size corrections at subleading order. The latter are then compared to the finite-size corrections from

### Imperial-TP-AT-2011-2 Superstrings in AdS2 × S2 × T 6

"... We consider the type IIB Green-Schwarz superstring theory on AdS2 × S2 × T 6 sup-ported by homogeneous Ramond–Ramond 5–form flux and its type IIA T–duals. One motivation is to understand the solution of this theory based on integrability. This background is a limit of a 1/4 supersymmetric supergravi ..."

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We consider the type IIB Green-Schwarz superstring theory on AdS2 × S2 × T 6 sup-ported by homogeneous Ramond–Ramond 5–form flux and its type IIA T–duals. One motivation is to understand the solution of this theory based on integrability. This background is a limit of a 1/4 supersymmetric supergravity solution describing four in-tersecting D3–branes and represents a consistent embedding of AdS2 × S2 into critical superstring theory. Its AdS2 × S2 part with corresponding fermions can be described by a classically integrable PSU(1, 1|2)/SO(1, 1) × U(1) supercoset sigma–model. We point out that since the RR 5–form field has non–zero components along the 6–torus direc-tions one cannot, in general, factorize the 10d superstring theory into the supercoset part plus 6 bosons and 6 additional massless fermions. Still, we demonstrate that the full superstring model (i) is classically integrable, at least to quadratic order in fermions, and (ii) admits a consistent classical truncation to the supercoset part. Following the analogy with other integrable backgrounds and starting with the finite-gap equations of the PSU(1, 1|2)/SO(1, 1)×U(1) supercoset we propose a set of asymptotic Bethe ansatz equations for a subset of the quantum string states.

### Quantum Strings and the AdS4/CFT3 Interpolating Function

, 2010

"... The existence of a nontrivial interpolating function h(λ) is one of the novel features of the new AdS4/CFT3 correspondence involving ABJM theory. At strong coupling, most of the investigation of semiclassical effects so far has been for strings in the AdS4 sector. Several cutoff prescriptions have b ..."

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The existence of a nontrivial interpolating function h(λ) is one of the novel features of the new AdS4/CFT3 correspondence involving ABJM theory. At strong coupling, most of the investigation of semiclassical effects so far has been for strings in the AdS4 sector. Several cutoff prescriptions have been proposed, leading to different predictions for the constant term in the expansion h(λ) = λ/2 + c +.... We calculate quantum corrections for giant magnons, using the algebraic curve, and show by comparing to the dispersion relation that the same prescriptions lead to the same values of c in this CP 3 sector. We then turn to finite-J effects, where a comparison with the Lüscher F-term correction shows a mismatch for one of the three sum prescriptions. We also compute some dyonic and higher F-terms for future comparisons.