Boundary Conformal Field Theory (BCFT) emerges when Conformal Field Theory (CFT) is defined on manifolds with boundaries. In such configurations, a part of the conformal symmetry persists, providing a rich area for theoretical exploration. BCFTs have significant applications ranging from condensed matter systems, to the worldsheet dynamics of open strings, among others. Moreover, BCFT plays a role in the holographic duality on Anti-de Sitter (AdS) spacetime, giving rise to the AdS/BCFT correspondence.

Recently, extensive research has focused on CFTs defined on Carrollian manifolds, that are non-Riemannian manifolds arising when a limit of vanishing light speed ($c\to 0$) is taken on (pseudo)-Riemannian manifolds. Carrollian structures are naturally found on null hypersurfaces and hence have a wide range of applications in flatspace holography, tensionless/null string theory, among others. However, CFTs defined on a Carrollian manifold with boundaries have not been explored until very recently. The transition from relativistic to Carrollian symmetries in ($c\to 0$) limit occurs through an In\"on\"u-Wigner group contraction, by which the Carroll algebra emerges from the Poincaré algebra. In 2d CFT, the infinite dimensional Virasoro algebra transitions into 2d CCA, which is isomorphic to the 3d Bondi-Metzner-Sachs (BMS$_3$) algebra. In our recent work we discovered the part of 2d Carrollian Conformal Algebra (CCA) which survives once a boundary is introduced on a Carrollian manifold and demonstrates that it naturally appears in the description of tensionless open strings. The tensionless regime of string theory represents the opposite limit of the well-explored point-particle limit and is expected to probe the ultra-high-energy sector of string theory. In flat spacetimes, this limit corresponds to strings with a null worldsheet (null strings), the one-dimensional extended analog of massless point particles.

Our proposed project aims to delve deeper into the study of Carrollian symmetries with boundaries and their application to null open strings. A primary objective is to construct higher-spin extensions of the recently discovered BCCA, for which we pursue two alternative approaches. The first begins with a higher-spin extension of the $BMS_3$ algebra and introduces boundaries to obtain the corresponding higher-spin BCCA. The second approach performs a Carrollian contraction on a single copy of a boundary W-algebra to achieve the same goal from an alternative perspective. In addition we plan to explore the supersymmetric extension of the BCCA employing both intrinsic construction and limiting procedures. Finally, building on our recent construction of classical open null strings, we aim to initiate the quantization of tensionless open strings, thereby taking the first steps toward a full quantum description of such objects.