Monstrous M-Theory †

Abstract

In (Formula presented.) space–time dimensions, we introduce a gravity theory whose massless spectrum can be acted upon by the Monster group when reduced to (Formula presented.) dimensions. This theory generalizes M-theory in many respects, and we name it Monstrous M-theory, or M (Formula presented.) -theory. Upon Kaluza–Klein reduction to (Formula presented.) dimensions, the M (Formula presented.) -theory spectrum irreducibly splits as 1 ⊕ 196,883, where 1 is identified with the dilaton, and 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 (Formula presented.) -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 (Formula presented.), the massless little group in (Formula presented.) ; the purely bosonic nature of the involved (Formula presented.) -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 (Formula presented.) -theory, when coupled to a Rarita–Schwinger massless field in (Formula presented.), exhibits the same number of bosonic and fermionic degrees of freedom; we cannot help but conjecture the existence of a would-be (Formula presented.) supergravity theory in (Formula presented.) space–time dimensions.