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Motivated by the appearance of penumbral moonshine, and by evidence that penumbral moonshine enjoys an extensive relationship to generalized monstrous moonshine via infinite products, we establish a general construction in this work which uses singular theta lifts and a concrete construction at the level of modules for a finite group to translate between moonshine in weight one-half and moonshine in weight zero. This construction serves as a foundation for a companion paper in which we explore the connection between penumbral Thompson moonshine and a special case of generalized monstrous moonshine in detail. 

The monster sporadic group is the automorphism group of a central charge $c=24$ vertex operator algebra (VOA) or meromorphic conformal field theory (CFT). In addition to its $c=24$ stress tensor $T(z)$, this theory contains many other conformal vectors of smaller central charge; for example, it admits $48$ commuting $c=\frac12$ conformal vectors whose sum is $T(z)$. Such decompositions of the stress tensor allow one to construct new CFTs from the monster CFT in a manner analogous to the Goddard-Kent-Olive (GKO) coset method for affine Lie algebras. We use this procedure to produce evidence for the existence of a number of CFTs with sporadic symmetry groups and employ a variety of techniques, including Hecke operators and modular linear differential equations, to compute the characters of these CFTs. Our examples include (extensions of) nine of the sporadic groups appearing as subquotients of the monster, as well as the simple groups ${}^2\tsl{E}_6(2)$ and $\tsl{F}_4(2)$ of Lie type. Many of these examples are naturally associated to McKay's $\widehat{E_8}$ correspondence, and we use the structure of Norton's monstralizer pairs more generally to organize our presentation. 

The emerging study of fractons, a new type of quasi‐particle with restricted mobility, has motivated the construction of several classes of interesting continuum quantum field theories with novel properties. One such class consists offoliated field theorieswhich, roughly, are built by coupling together fields supported on the leaves of foliations of spacetime. Another approach, which we refer to asexotic field theory, focuses on constructing Lagrangians consistent with special symmetries (like subsystem symmetries) that are adjacent to fracton physics. A third framework is that ofinfinite‐component Chern‐Simons theories, which attempts to generalize the role of conventional Chern‐Simons theory in describing (2+1)D Abelian topological order to fractonic order in (3+1)D. The study of these theories is ongoing, and many of their properties remain to be understood. Historically, it has been fruitful to study QFTs by embedding them into string theory. One way this can be done is via D‐branes, extended objects whose dynamics can, at low energies, be described in terms of conventional quantum field theory. QFTs that can be realized in this way can then be analyzed using the rich mathematical and physical structure of string theory. In this paper, we show that foliated field theories, exotic field theories, and infinite‐component Chern‐Simons theories can all be realized on the world‐volumes of branes. We hope that these constructions will ultimately yield valuable insights into the physics of these interesting field theories.