Arkady A. Tseytlin

Type-IIB string theory on AdS 3 × S 3 × T 4 with Ramond–Ramond flux as the near-horizon limit of the D1-D5 solution is expected to be dual to a (4, 4) supersymmetric 2D conformal field theory (CFT) parametrized by the integers Q 1 , Q 5 , and other moduli. It is related by T-duality to type-IIA string theory in the near-horizon limit of the D2-D4 solution, which admits an uplift to the 11D AdS 3 × S 3 × T 5 background which is the near-horizon limit of the M2-M5 solution. We point out that this relation allows one to use the quantum M2-brane description to probe “nonplanar” corrections in the dual 2D CFT, in close analogy with the Aharony-Bergman-Jafferis-Maldacena (ABJM) theory case (described by M-theory on AdS 4 × S 7 / Z k ). We consider an analog of a supersymmetric Wilson loop (line defect) expectation value represented by a type-IIA string partition function expanded around an AdS 2 ⊂ AdS 3 minimal surface. Its M-theory analog is the M2-brane partition function expanded near AdS 2 × S 1 . We compute the one-loop contribution Z 1 to the M2-brane partition function and find that in contrast to the ABJM case in arXiv:2303.15207 [where Z 1 = ( 2 sin 2 π k ) − 1 = k 4 π + π 6 k + ⋯ contains an infinite series of higher-genera string corrections, k − 1 ∼ g s T ], here it is given solely by the leading string theory contribution Z 1 = κ 2 π , where κ ∼ Q 5 plays a role analogous to k . We also discuss a generalization to the mixed-flux case which is straightforward from the 11D perspective.

We consider the S-matrix of transverse scalar excitations on an infinite D = 10 GS superstring and D = 11 supermembrane in flat target space. We compute the 4-particle scattering amplitude in the 2-loop approximation and demonstrate that, like in the Nambu string case, the D = 10 GS string S-matrix does not contain non-trivial 2d UV divergences (UV pole not accompanied by terms with logarithms of momenta is an artifact of dimensional regularization). This is consistent with underlying integrability of this model which is maintaining by adding appropriate local counterterms. In the supermembrane case there are no 1-loop divergences but we find a genuine 2-loop UV pole. This demonstrates non-finiteness of the world-volume S-matrix of the M2 brane theory.

Planar parts of conformal dimensions of primary operators in U _k (N) × U _−k (N) ABJM theory are controlled by integrability. Strong coupling asymptotics of planar dimensions of operators with large spins can be found from the energy of semiclassical strings in AdS₄ × CP³ but computing non-planar corrections requires understanding higher genus string corrections. As was pointed out in arXiv:2408.10070, there is an alternative way to find the non-planar corrections by quantizing M2 branes in AdS₄ × S ⁷/ℤ _k which are wrapped around the 11d circle of radius 1/k = λ/N and generalize spinning strings in AdS₄ × CP³. Computing the 1-loop correction to the energy of M2 brane that corresponds to the long folded string with large spin S in AdS₄ allowed to obtain a prediction for the large λ limit of non-planar corrections to the cusp anomalous dimension. Similar predictions were found for non-planar dimensions of operators dual to M2 branes that generalize the “short” and “long” circular strings with two equal spins J ₁ = J ₂ in CP³. Here we consider two more non-trivial examples of 1-loop M2 brane computations that correspond to: (i) long folded string with large spin S in AdS₄ and orbital momentum J in CP³ whose energy determines the generalized cusp anomalous dimension, and (ii) circular string with spin S in AdS₄ and spin J in CP³. We find the leading terms of the expansion of the corresponding 1-loop M2 brane energies in 1/k. We also discuss similar semiclassical 1-loop M2 brane computation in flat 11d background and comment on possible relation to higher genus corrections to energies in 10d string theory.

As was shown in Giombi and Tseytlin (2023 Phys. Rev. Lett. 130 201601), the leading large N, fixed k correction in the localization result for the expectation value of the 1 2 BPS circular Wilson loop in U ( N ) k × U ( N ) − k ABJM theory given by the ( sin ⁡ 2 π k ) − 1 factor can be reproduced on the dual M-theory side as the one-loop correction in the partition function of M2 brane in AdS 4 × S 7 / ℤ k with AdS 2 × S 1 world volume. Here we prove, following the suggestion in Giombi et al (2024 J. High Energy Phys. JHEP11(2024)056), that the analogous fact is true also for the corresponding correction B 1 = − 1 2 π k cot 2 π k in the localization result for the Bremsstrahlung function associated with the Wilson loop with a small cusp in either AdS₄ or CP 3 . The corresponding M2 brane is wrapped on the 11d circle and generalizes the type IIA string solution in AdS 4 × CP 3 ending on the cusped line. We show that the one-loop term in the M2 brane partition function reproduces the localization expression for B ₁ as the coefficient of the leading term in its small cusp expansion.

A bstract: We consider two supersymmetric M5 brane probe solutions in AdS ₇ × S ⁴ and one in AdS ₄ × S ⁷ that all have the AdS ₃ × S ³ world-volume geometry. The values of the classical action of the first two M5 probes (with S ³ in AdS ₇ or in S ⁴ ) are related to the leading N ² parts in the anomaly b-coefficient in the (2,0) theory corresponding to a spherical surface defect in symmetric or antisymmetric SU ( N ) representations. We present a detailed computation of the corresponding one-loop M5 brane partition functions finding that they vanish (in a particular regularization). This implies the vanishing of the order N ⁰ part in the b-anomaly coefficients, in agreement with earlier predictions for their exact values. It remains, however, a puzzle of how to reproduce the non-vanishing order N terms in these coefficients within the semiclassical M5-brane probe setup.