On quantum corrections to spinning strings and Bethe equations

By N. Beisert, A. Tseytlin. 2005

171 citations recorded by the source corpus.

Abstract Recently, it was demonstrated that one-loop energy shifts of spinning superstrings on AdS 5 × S 5 agree with certain Bethe equations for quantum strings at small effective coupling. However, the string result required artificial regularization by zeta-function. Here we show that this matching is indeed correct up to fourth order in effective coupling; beyond, we find new contributions at odd powers. We show that these are reproduced by quantum corrections within the Bethe ansatz. They might also identify the “three-loop discrepancy” between string and gauge theory as an order-of-limits effect.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/5e2d6b3f2079568e370518a2e29da308035900fb

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In Nuclear and High Energy Physics

1. S. Frolov
2. G. Arutyunov
3. A. Tseytlin
4. N. Beisert
5. Romuald A. Janik
6. R. Roiban
7. M. Staudacher
8. M. Zamaklar

Citations in the corpus

• A Crossing-Symmetric Phase for AdS5 x S5 Strings (2006, unknown): “2) are known to first order at strong coupling [4,27,17,28].”
• Quantum spinning strings in AdS_4 x CP^3: testing the Bethe Ansatz proposal (2008, methodology): “As discussed in [26] in the context of string theory in AdS5×S(5), in this limit the sum over modes receives contributions from two distinct regions: (I) n≪ ω: here the sum remains discrete (II) n/ω = x =fixed: here the sum may be replaced by an integral over x These two regimes are compatible; whil”
• Logarithmic corrections to higher twist scaling at strong coupling from AdS/CFT (2006, methodology): “Thus the coefficient of the lnS term is encoded as a limit of the full string 1-loop correction determined from the string Bethe ansatz [25, 13, 21] by the BDS [12] part as well as by the 1-loop phase of [26, 27].”
• The AdS 5 ×S 5 superstring worldsheet S matrix and crossing symmetry (2006, background): “The structure of the dressing factor on the string theory side appears to be quite complicated with 1/ √ λ deviations [21, 22, 23] from the strong coupling expression [19].”
• Four-loop perturbative Konishi from strings and finite size effects for multiparticle states (2008, background): “The specific form of the dressing factor is now believed to be known through a series of works [16, 17, 18, 19, 20, 21] and the first nontrivial coefficient at weak coupling was checked by a direct perturbative evaluation [22].”
• Integrability and transcendentality (2006, unknown): “Let us in particular investigate the dressing factor of the (approximate, see [44, 45, 46]) string(9) Bethe ansatz of [43].”
• The AdS5xS5 Superstring in Light-Cone Gauge and its Bethe Equations (2006, background): “Review of the Superstring on AdS5 × S5 6 2.1 Superalgebra psu(2, 2|4) 7 2.2 Lagrangian and Coset Element 9”
• Finite-size effects from giant magnons (2006, background): “It is worth noting that H has no dependence on λ, and the dependence of the gauge-fixed action on P+ comes only through the integration limits ±r .”
• Quantum corrections to the string Bethe ansatz (2006, background): “In accordance with these results, it was proposed in [29] that agreement with the sum over frequencies (3), including non-analytic terms, could be restored by generalizing the phase (2) to”
• Foundations of the AdS5 × S5 superstring: I (2009, methodology): “The general method for determining the one-loop correction to the dressing phase has been developed in [132] and used to obtain the one-loop correction to the coefficient c2,3 in eq.”
• On string S-matrix, bound states and TBA (2007, result): “Recently, a physically relevant solution to the crossing relation, which interpolates between the weak (gauge) and strong (string) coupling regimes was conjectured [13, 14], building on the previous work [15]-[18].”
• The analytic Bethe ansatz for a chain with centrally extended symmetry (2006, background): “Indeed, the leading orders of the function S 12 extracted from perturbative string theory [8, 37] do have branch cuts and are consistent with the crossing relation [38, 22].”
• The Zamolodchikov-Faddeev Algebra for AdS5 x S5 Superstring (2006, result): “A physically relevant solution of the crossing relation, which successfully reproduces the known string theory data was conjectured in [10], building on the previous work [11]-[14].”
• Wrapping interactions and a new source of corrections to the spin-chain/string duality (2005, background): “However, as mentioned earlier, in string sigma model loop corrections one has found contributions to string energies involving half integer powers of λ′ as well as contributions of of the form e−1/ √ λ′ [28, 29, 30], see also [31].”