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arXiv:1111.2839v3 Real and Virtual Bound States in Lüscher Corrections for CP 3 Magnons
, 2011
"... We study classical and quantum finitesize corrections to giant magnons in AdS4 × CP 3 using generalised Lüscher formulae. Lüscher Fterms are organised in powers of the exponential suppression factor (e−∆/2h)m, and we calculate all terms in this series, matching oneloop algebraic curve results ..."
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We study classical and quantum finitesize corrections to giant magnons in AdS4 × CP 3 using generalised Lüscher formulae. Lüscher Fterms are organised in powers of the exponential suppression factor (e−∆/2h)m, and we calculate all terms in this series, matching oneloop algebraic curve results from our previous paper [1]. Starting with the second term, the structure of these terms is different to those in AdS5 × S5 thanks to the appearance of heavy modes in the loop, which can here be interpreted as twoparticle bound states in the mirror theory. By contrast, physical bound states can represent dyonic giant magnons, and we also calculate Fterms for these solutions. Lüscher µterms, suppressed by e−∆/E, instead give at leading order the classical finitesize correction. For the elementary dyonic giant magnon we recover the correction given by [2]. We then extend this to calculate the next term in 1/h, giving a oneloop prediction. Finally we also calculate Fterms for the various composite giant magnons, RP 3 and ‘big’, again finding agreement to all orders.
Strings in AdS4 × CP 3: finite size spectrum vs.
"... Abstract:We compute the first curvature corrections to the spectrum of lightcone gauge type IIA string theory that arise in the expansion of AdS4×CP 3 about a planewave limit. The resulting spectrum is shown to match precisely, both in magnitude and degeneration that of the corresponding solutions ..."
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Abstract:We compute the first curvature corrections to the spectrum of lightcone gauge type IIA string theory that arise in the expansion of AdS4×CP 3 about a planewave limit. The resulting spectrum is shown to match precisely, both in magnitude and degeneration that of the corresponding solutions of the allloop Gromov–Vieira Bethe Ansatz. The oneloop dispersion relation correction is calculated for all the single oscillator states of the theory, with the level matching condition lifted. It is shown to have all logarithmic divergences cancelled and to leave only a finite exponentially suppressed contribution, as shown earlier for light bosons. We argue that there is no ambiguity in the choice of the regularization for the selfenergy sum, since the regularization applied is the only one preserving unitarity. Interaction matrices in the full degenerate twooscillator sector are calculated and the spectrum of all two light magnon oscillators is completely determined. The same finitesize corrections, at the order 1J, where J is the length of the chain, in the twomagnon sector are calculated from the all loop Bethe Ansatz. The corrections obtained by the two completely different methods coincide up to the fourth order in λ ′ ≡ λ J2. We conjecture that the equivalence extends to all orders in λ ′ and to higher orders in 1J.
Dyonic Giant Magnons in CP 3: Strings and Curves at Finite J
, 2009
"... Abstract: This paper studies giant magnons in AdS4 × CP 3 using both the string sigmamodel and the algebraic curve. We complete the dictionary of solutions by finding the dyonic generalisation of the CP 1 string solution, which matches the ‘small ’ giant magnon in the algebraic curve, and by pointi ..."
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Abstract: This paper studies giant magnons in AdS4 × CP 3 using both the string sigmamodel and the algebraic curve. We complete the dictionary of solutions by finding the dyonic generalisation of the CP 1 string solution, which matches the ‘small ’ giant magnon in the algebraic curve, and by pointing out that the solution recently constructed by the dressing method is the ‘big ’ giant magnon. We then use the curve to compute finiteJ corrections to all cases, which for the nondyonic cases always match the AFZ result. For the dyonic RP 3 magnon we recover the S 5 answer, but for the ‘small ’ and ‘big ’ giant magnons we obtain new corrections. 1
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 finiteJ effects, where a comparison with the Lüscher Fterm correction shows a mismatch for one of the three sum prescriptions. We also compute some dyonic and higher Fterms for future comparisons.