There exist several quantum deformations of string theories, leading to different space-time geometries. In some cases it has been shown that these a priori different theories are in fact related through a “worldsheet” duality. During the project we harnessed this duality to uncover a large space of new integrable deformations, and started the investigation of their quantum properties.
These new integrable deformations can in particular be applied to AdS3 strings (string theories propagating on a space-time containing a three-dimensional AdS space). In some cases, we found that they can preserve half of the original supersymmetries, leading to a rather simple geometry that is particularly suited to explore the holographic inter. This is in contrast with other quantum deformations which usually lead to singularities in the geometry.
We also went beyond quantum groups, constructing a new elliptic deformation of AdS3 strings. To analyse the theory at the quantum level we looked at the scattering on excitations propagating on the worldsheet of the string and checked that the Yang-Baxter equation (the hallmark equation for an integrable theory) is indeed satisfied. To achieve this we adapted some of the integrability methods to account for the few manifest symmetries in the deformed theory.
Given the power of integrability to solve string theories, we also investigated the possibility of finding similar integrable structures in theories featuring higher-dimensional objects, in particular membranes. We looked at the dynamics of excitations propagating on the three-dimensional worldvolume of the membrane and found that their scattering simplifies drastically in flat D=11 dimensional space-time.
The project resulted in 8 publications, among which two reviews: one on “Exact approaches on the string worldsheet” and one on “AdS3 Integrability, Tensionless Limits, and Deformations”, available on the arXiv. The results were presented at 7 international conferences and workshops, and at 9 research seminars. An introduction to “Integrable sigma-models” lecture was given to MSc students at Imperial College London (2023), and a PhD course on “The worldsheet S-matrix” was given during the Young Researchers School in 2022.
