Semiclassical quantization of spinning strings in AdS₄× ℂℙ³

Abstract

Abstract:We derive the one-loop correction to the space-time energy of a folded string in AdS 4 × CP 3 carrying spin S in AdS 4 and angular momentum J in CP 3 in the long string approximation. From this general result in the limit J ≪ log S we obtain the one-loop correction to the cusp anomalous dimension which turns out to be − 5 log 2 2π . This value appears to be in conflict with the prediction from the recently conjectured all-loop Bethe ansatz.

Dualities for loop amplitudes of N = 6 Chern-Simons matter theory

“…We note that there already exists evidence that the quantum corrections of the two theories are closely connected. 9 Indeed it was conjectured in [40], and tested for in [41,42,43,44], that the anomalous dimensions of twist operators of ABJM theory can be obtained from N = 4 super Yang-Mills, up to normalization factors which can be easily determined, simply by substituting,…”

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

“…In the limiting φ = 0 and φ = π/2 cases, where there are no cubic terms, we see that the two-point functions are manifestly finite. Before ending this section, we should note that in order to determine the finite part of the spectrum, dimensional regularization is not a suitable regulator for the loop integrals [51], see also [52][53][54][55][56][57][58]. The reason is that in order to maintain unitarity, one should choose a cutoff such that the decay processes, originating from the cubic Lagrangian, are energetically allowed [44] (see also [59]).…”

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

“…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).…”

“…There, only the quadratic part of the fermionic Lagrangian is necessary, with a structure which is well-known in terms of the type IIA covariant derivative restricted by the background RR fluxes 3 . Here instead we will work with the string action (2.39) derived in [230,231] from the 11d membrane action based on the supercoset OSp(4 8) (SO(1, 3) × SO (7)), performing 3 Alternatively, one could still use the coset action of [126,267] -which is not suitable when strings move confined in AdS [126,282] -starting with a classical solution spinning both in AdS4 with spin S and in CP 3 with spin J, and taking on the resulting expression for the one-loop energy a smooth J → 0 limit [415]. double dimensional reduction and choosing a κ-symmetry light-cone gauge for which both light-like directions lie in AdS 4 .…”