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23
A nexttoleading Lüscher formula
"... We propose a nexttoleading Lüscherlike formula for the finitesize corrections of the excited states energies in integrable theories. We conjecture the expressions of the corrections for both the energy and the particles ’ rapidities by interpreting the excited states as momentadependent defect ..."
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We propose a nexttoleading Lüscherlike formula for the finitesize corrections of the excited states energies in integrable theories. We conjecture the expressions of the corrections for both the energy and the particles ’ rapidities by interpreting the excited states as momentadependent defects. We check the resulting formulas in some simple relativistic model and conjecture those for the AdS5/CFT4 case. ar X iv
Multiple zeta functions and double wrapping in planar N = 4 SYM
, 2013
"... Using the FiNLIE solution of the AdS/CFT Ysystem, we compute the anomalous dimension of the Konishi operator in planar N=4 SYM up to eight loops, i.e. up to the leading double wrapping order. At this order a nonreducible EulerZagier sum, ζ1,2,8, appears for the first time. We find that at all ord ..."
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Using the FiNLIE solution of the AdS/CFT Ysystem, we compute the anomalous dimension of the Konishi operator in planar N=4 SYM up to eight loops, i.e. up to the leading double wrapping order. At this order a nonreducible EulerZagier sum, ζ1,2,8, appears for the first time. We find that at all orders in perturbation, every spectraldependent quantity of the Ysystem is expressed through multiple Hurwitz zeta functions, hence we provide a Mathematica package to manipulate these functions, including the particular case of EulerZagier sums. Furthermore, we conjecture that only EulerZagier sums can appear in the answer for the anomalous dimension at any order in perturbation theory. We also resum the leading transcendentality terms of the anomalous dimension at all orders, obtaining a simple result in terms of Bessel functions. Finally, we demonstrate that exact Bethe equations should be related to an absence of poles condition that becomes especially nontrivial at double wrapping. Keywords: Ysystem, FiNLIE, integrability, perturbative quantum field theory,
PREPARED FOR SUBMISSION TO JHEP On the oneloop curvature function in the sl(2) sector of N = 4 SYM
"... ABSTRACT: We consider twist J operators with spin S in the sl(2) sector of N = 4 SYM. The small spin expansion of their anomalous dimension defines the socalled slope functions. Much is known about the linear term, but the study of the quadratic correction, the curvature function, started only ver ..."
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ABSTRACT: We consider twist J operators with spin S in the sl(2) sector of N = 4 SYM. The small spin expansion of their anomalous dimension defines the socalled slope functions. Much is known about the linear term, but the study of the quadratic correction, the curvature function, started only very recently. At any fixed J, the curvature function can be extracted at all loops from the Pµsystem formulation of the Thermodynamical Bethe Ansatz. Here, we work at the oneloop level and follow a different approach. We present a systematic double expansion of the Bethe Ansatz equations at large J and small winding number. We succeed in fully resumming this expansion and obtain a closed explicit simple formula for the oneloop curvature function. The formula is parametric in J and can be evaluated with minor effort for any fixed J. The result is an explicit series in oddindex ζ values. Our approach provides a complete reconciliation between the Pµsystem predictions and the large J approach. ar X iv
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"... Abstract: We describe a qualitative feature of the AdS5 × S5 string spectrum which is not captured by the asymptotic Bethe ansatz. This is reflected by an enhanced discrete symmetry in the asymptotic limit, whereby extra energy degeneracy enters the spectrum. We discuss how finite size corrections s ..."
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Abstract: We describe a qualitative feature of the AdS5 × S5 string spectrum which is not captured by the asymptotic Bethe ansatz. This is reflected by an enhanced discrete symmetry in the asymptotic limit, whereby extra energy degeneracy enters the spectrum. We discuss how finite size corrections should lift this degeneracy, through both perturbative (Lüscher) and nonperturbative approaches (the Mirror TBA), and illustrate this explicitly on two such asymptotically degenerate states. ar X iv