Umbral Moonshine and String Theory on K3


Paquette, N. (2016). Umbral Moonshine and String Theory on K3. Perimeter Institute. https://pirsa.org/16040090


Paquette, Natalie. Umbral Moonshine and String Theory on K3. Perimeter Institute, Apr. 22, 2016, https://pirsa.org/16040090


          @misc{ pirsa_16040090,
            doi = {},
            url = {https://pirsa.org/16040090},
            author = {Paquette, Natalie},
            keywords = {Quantum Fields and Strings},
            language = {en},
            title = {Umbral Moonshine and String Theory on K3},
            publisher = {Perimeter Institute},
            year = {2016},
            month = {apr},
            note = {PIRSA:16040090 see, \url{https://pirsa.org}}


The mathematical notion of moonshine relates the theory of finite groups with that of modular objects. The first example, 'Monstrous Moonshine', was clarified in the context of two dimensional conformal field theory in the 90's. In 2010, interest in moonshine in the physics community was reinvigorated when Eguchi et. al. observed representations of the finite group M24 appearing in the elliptic genus of nonlinear sigma models on K3. In 2013, Cheng, Duncan, and Harvey provided a uniform construction of 23 new examples of moonshine, called 'umbral moonshine', of which M24 moonshine is a special case. 

In this talk, I will describe recent work studying the symmetries of certain Landau-Ginzburg orbifold theories that flow in the IR to c=6 N=(4, 4) superconformal field theories on the moduli space of K3 sigma models. We show that discrete symmetries of the UV theory implicate all 23 instances of umbral moonshine, not just M24 moonshine, in symmetries of K3 CFTs. I will then discuss a particular string theory compactification to three dimensions where we find a precise connection to all 23 umbral groups and type IIA string theory on K3.