Monstrous M-theory

Abstract

In $26+1$ space-time dimensions, we introduce a gravity theory whose massless spectrum can be acted upon by the Monster group when reduced to $25+1$ dimensions. This theory generalizes M-theory in many respects and we name it Monstrous M-theory, or M$^{2}$-theory. Upon Kaluza-Klein reduction to $25+1$ dimensions, the M$^{2}$-theory spectrum irreducibly splits as $\mathbf{1}\oplus\mathbf{196,883}$, where $\mathbf{1}$ is identified with the dilaton, and $\mathbf{196,883}$ is the dimension of the smallest non-trivial representation of the Monster. This provides a field theory explanation of the lowest instance of the Monstrous Moonshine, and it clarifies the definition of the Monster as the automorphism group of the Griess algebra, by showing that such an algebra is not merely a sum of unrelated spaces, but descends from massless states for M$^{2}$-theory, which includes Horowitz and Susskind's bosonic M-theory as a subsector. Further evidence is provided by the decomposition of the coefficients of the partition function of Witten's extremal Monster SCFT in terms of representations of $SO_{24}$, the massless little group in $25+1$; the purely bosonic nature of the involved $SO_{24}$-representations may be traced back to the unique feature of $24$ dimensions, which allow for a non-trivial generalization of the triality holding in $8$ dimensions. Last but not least, a certain subsector of M$^{2}$-theory, when coupled to a Rarita-Schwinger massless field in $26+1$, exhibits the same number of bosonic and fermionic degrees of freedom; we cannot help but conjecture the existence of a would-be $\mathcal{N}=1$ supergravity theory in $26+1$ space-time dimensions.