Quantum strings and the AdS4/CFT3 interpolating function

Abstract

The existence of a nontrivial interpolating function h(λ) is one of the novel features of the new AdS 4 /CFT 3 correspondence involving ABJM theory. At strong coupling, most of the investigation of semiclassical effects so far has been for strings in the AdS 4 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.

Perturbative and Non-perturbative Approaches to String Sigma-Models in AdS/CFT

“…While at one loop we confirm the result of [57,403,404], the two-loop correction provides a new important information that, once combined with a proposal based on the Bethe Ansatz [124] and the correction to the effective string tension [58], gives information on the two-loop coefficient in the expansion of the interpolating function h(λ) of the AdS 4 CF T 3 duality.…”

“…We also note that the first subleading correction − log 2 (2π) to h(λ ABJM ), on which some debate existed [413], can be analogously computed from the scaling function at one loop [57,175,403,404,[414][415][416][417][418][419][420][421][422] in sigma-model perturbation theory as the energy of closed spinning strings in the large-spin limit or similar means. An interesting observation that only descends from our two-loop computation (6.9) is the fact that the two-loop correction to h(λ ABJM ) is exclusively due to the "anomalous" correction −1 24 in (1.9).…”

Near BMN dynamics of the AdS 3 × S 3 × S 3 × S 1 superstring

“…We plan to return to this question in the future. Another interesting line of research would be to calculate one-loop corrections to the energy along the lines of [71].…”

Exact Bremsstrahlung functions in ABJM theory

“…Whereas such relation turns out to be trivial for N = 4 SYM, this is not the case for its three-dimensional relative N = 6 super Chern-Simons theory with matter, known as ABJM theory [16]. In the latter case, a conjectured expression for h(λ) [17] agrees with weak [18][19][20][21][22][23] and strong [24][25][26][27] coupling perturbative computations (see also [28] for the generalization to ABJ theory), but an exact derivation is still missing.…”