Fiona K. Seibold

A bstract: We construct a 1-parameter family of Ramond-Ramond fluxes supporting the elliptic AdS ₃ × S ³ × T ⁴ metric with constant dilaton and preserving 8 of the 16 supercharges of the undeformed background. On the supersymmetric locus, we compute the tree-level worldsheet S-matrix in uniform light-cone gauge up to quadratic order in fermions and find that it non-trivially satisfies the classical Yang-Baxter equation. Moreover, imposing classical integrability and symmetries, we conjecture compatible processes quartic in fermions. We also investigate different limits of interest, including trigonometric deformations and the limit to the AdS ₂ × S ² × T ⁶ superstring. Our results provide strong evidence for a supersymmetric and integrable elliptic deformation of the AdS ₃ × S ³ × T ⁴ superstring supported by Ramond-Ramond flux and a constant dilaton.

We construct families of integrable deformations that interpolate between A d S 3 × S 3 × S 3 × S 1 and either A d S 3 × S 3 × S 2 × T 2 or A d S 3 × S 2 × S 2 × T 3 . They preserve half of the supersymmetry of the original background, namely one copy of the d ( 2 , 1 ; α ) algebra. From this it follows a similar integrable interpolation between A d S 3 × S 3 × T 4 and A d S 3 × S 2 × T 5 , which also preserves half of the supersymmetry, namely a copy of the psu ( 1 , 1 | 2 ) algebra. In all cases, the interpolating backgrounds are constructed by using TsT transformations, which makes it easy to implement them in the integrability formalism in the full quantum theory. To illustrate this point, we discuss the lightcone gauge fixing of the models and compute their pp-wave Hamiltonian.

A bstract: We compute the one-loop 2 → 2 scattering amplitude of massless scalars on the world volume of an infinite D = 11 supermembrane quantized in the static gauge. The resulting expression is manifestly finite and turns out to be much simpler than in the bosonic membrane case in arXiv:2308.12189 being proportional to the tree-level scattering amplitude. We also consider the case of ℝ ^{1, 1} × S ¹ membrane with one dimension compactified on a circle of radius R and demonstrate how the supermembrane scattering amplitude reduces to the one on an infinite D = 10 Green-Schwarz superstring in the limit of R → 0.

With the aim of investigating the existence of an integrable elliptic deformation of strings on AdS₃ × S³ × T⁴, we compute the tree-level worldsheet S-matrix of the elliptically-deformed bosonic sigma model on AdS₃ × S³ in uniform light-cone gauge. The resulting tree-level S-matrix is compatible with the integrability of the model and has interesting features, including a hidden U(1) symmetry not manifest in the Lagrangian. We find that it cannot be embedded in the known exact integrable R-matrices describing deformations of the undeformed AdS₃ × S³ × T⁴ light-cone gauge S-matrix including fermions. Therefore, we construct embeddings of the deformed 6-d metric in type II supergravity with constant dilaton and homogeneous fluxes. The simplicity of these solutions suggests they are promising candidates to lead to an integrable string sigma model including fermions.

Integrable string sigma models on AdS₃ backgrounds with 16 supersymmetries have the distinguishing feature that their superisometry group is a direct product. As a result the deformation theory of these models is particularly rich since the two supergroups in the product can be deformed independently. We construct bi-η and bi-λ deformations of two classes of ℤ₄ permutation supercoset sigma models, which describe sectors of the Green-Schwarz and pure-spinor string worldsheet theories on type II AdS₃ backgrounds with pure R-R flux. We discuss an important limit of these models when one supergroup is undeformed. The associated deformed supergravity background should preserve 8 supersymmetries and is expected to have better properties than the full bi-deformation. As a step towards investigating the quantum properties of these models, we study the two-loop RG flow of the bosonic truncation of the bi-λ deformation.