DefIS has been conceived on purpose as a low-cost proposal (163 904 EUR) in theoretical high energy physics with very high expectations. It takes place in the arena of Integrability in Gauge and String Theory. This is a domain of research which is very active. For instance, there are at the present time three Advanced ERC Grantees (V. Kazakov, A. Tseytlin, K. Zarembo) working on this subject. The purpose of DefIS is to obtain new results related to one topic of this field. What characterises this topic is that its emergence is very recent. Furthermore, it relies on previous achievements of the members of the DefIS collaboration. Finally, interest of the community working on Integrability in Gauge and String Theory for this subject of research is expanding fast. The primary goal of DefIS is to push forward the current frontier of knowledge on integrable field theories. Few field theories have the property of being integrable. Their study has nevertheless proved to be of great importance for theoretical physics. The reason is that integrability allows for the use of specific techniques in order to compute exact results. This property has been extensively used recently in the context of Integrability in Gauge and String Theory where the dynamics is obtained from an integrable sigma-model. DefIS aims to construct the full landscape of integrable sigma-models showing up in this context and to determine its characteristics. This will be achieved by deforming integrable sigma-models while preserving their integrability. DefIS will also unravel dualities within this landscape. Consequences for the AdS/CFT correspondence and its extension will also be studied. There is no other French team devoted to the study of deformations of integrable sigma-models and its consequences for the AdS/CFT correspondence and beyond. But there is at the same time an ever increasing international competition on this line of research. Furthermore, the interest in the underlying theme of DefIS is emerging from the recent results (including one publication in Physical Review Letters) obtained by members of DefIS. Therefore, to maintain France as a prominent actor at the forefront of this competitive and emerging field, the only possibility is to strengthen this existing collaboration. This is one important motivation for proposing DefIS to ANR.