We consider finite-size corrections in the SU(2)×SU(2) sector of type IIA string theory on AdS4×CP3, which is the string dual of the recently constructed N=6 superconformal Chern–Simons theory of Aharony, Bergman, Jafferis and Maldacena (ABJM theory). The string states we consider are in the R×S2×S2 subspace of AdS4×CP3 with an angular momentum J on CP3 being large. We compute the finite-size corrections using two different methods, one is to consider curvature corrections to the Penrose limit giving an expansion in 1/J, the other by considering a low energy expansion in λ′=λ/J2 of the string theory sigma-model, λ being the 't Hooft coupling of the dual ABJM theory. For both methods there are interesting issues to deal with. In the near-pp-wave method there is a 1/J interaction term for which we use zeta-function regularization in order to compute the 1/J correction to the energy. For the low energy sigma-model expansion we have to take into account a non-trivial coupling to a non-dynamical transverse direction. We find agreement between the two methods. At order λ′ and λ′2, for small λ′, our results are analogous to the ones for the SU(2) sector in type IIB string theory on AdS5×S5. Instead at order λ′3 there are interactions between the two two-spheres. We compare our results with the recently proposed all-loop Bethe ansatz of Gromov and Vieira and find agreement

We study the strong coupling behaviour of 1/4-BPS circular Wilson loops (a family of “latitudes”) in \( \mathcal{N}=4 \) Super Yang-Mills theory, computing the one-loop corrections to the relevant classical string solutions in AdS₅ ×S⁵. Supersymmetric localization provides an exact result that, in the large ’t Hooft coupling limit, should be reproduced by the sigma-model approach. To avoid ambiguities due to the absolute normalization of the string partition function, we compare the ratio between the generic latitude and the maximal 1/2-BPS circle: any measure-related ambiguity should simply cancel in this way. We use the Gel’fand-Yaglom method with Dirichlet boundary conditions to calculate the relevant functional determinants, that present some complications with respect to the standard circular case. After a careful numerical evaluation of our final expression we still find disagreement with the localization answer: the difference is encoded into a precise “remainder function”. We comment on the possible origin and resolution of this discordance.

We study worldsheet instantons in holographic type IIA backgrounds directly in string theory. The first background is a dimensional reduction of AdS₇ × S⁴ and is dual to the maximally supersymmetric Yang-Mills theory on S⁵. The second background is AdS₄ × CP³ dual to ABJM in the type IIA limit. We compute the one-loop partition function of the fundamental string in these backgrounds and show that the result is in exact agreement with field theory predictions. We argue that for higher rank instantons, the string partition function takes a product form of the single instanton partition function times the contribution of two orbifolds on the worldsheet. We determine the orbifold factor to be n^−3/2 where n is the instanton rank. With this result, we reproduce the series of non-perturbative corrections in α^′ to the planar S⁵ free energy. When studying the worldsheet instanton partition function on CP³, we encounter twelve fermionic and twelve bosonic zero modes. By deforming the ABJM theory, the zero-modes are lifted and consequently the tower of worldsheet instantons can be evaluated and matched to known results in the QFT. As a by-product, we determine a series of higher rank instanton corrections to the free energy of the mass-deformed and orbifolded ABJ(M) theory.