Posters may be viewed at: http://categorified.net/WIMTP/

**Sabine Harribey**, CPHT Ecole Polytechnique - Heidelberg University

*Melonic quantum field theory*

Tensors models exhibit a melonic large N limit, simpler that the planar limit of random matrices but richer that the limit of vector models. In d dimensions, they give rise to a new family of conformal field theories and provide interesting examples of the renormalization group flow from a free theory in the UV to a melonic large N CFT in the IR. In this poster, I will present some applications of these properties from random geometry to conformal field theories.

**Eilind Karlsson**, TU München

*Dualizability in higher Morita categories - steps towards proving a conjecture about (n+1)-dualizability in the higher Morita category Alg_n*

**Philine van Vliet**, DESY Hamburg

*Conformal defects and emergent supersymmetry. *

The conformal bootstrap is a powerful, nonperturbative method to study (supersymmetric) conformal field theories ((S)CFTs). Advancements in especially the numerical bootstrap have led to extremely precise results for the computation of critical exponents in various (S)CFTs, and the conformal bootstrap has gained a lot of attention in recent years. (S)CFTs can be generalized by adding extended objects. These extended objects break the (super-)conformal symmetry group into a smaller (super-)conformal subgroup, and the resulting defect theory can be studied with the defect bootstrap. Defect theories appear in many places in theoretical physics: from Wilson lines in high-energy string theory, to boundary CFTs found in low-energy condensed matter physics. In recent work we studied three-dimensional boundary CFTs with N=2 supersymmetry, which have possible phenomenological applications in condensed matter physics as an example of emergent supersymmetry. Such theories allow two types of boundaries, on which we have studied various important observables. One of the boundaries can be analytically continued to d=4, and we bootstrapped the observables in the 4 - \epsilon expansion. The programme can be expanded to include line defects, which is work in progress.