论文标题
巨大的M理论
Monstrous M-theory
论文作者
论文摘要
在$ 26+1美元的时空维度中，我们引入了一种重力理论，当怪物组降低至$ 25+1 $尺寸时，怪物组可以采取无数频谱。该理论在许多方面概括了M理论，我们将其命名为可怕的M理论或M $^{2} $ - 理论。在kaluza-klein减少到$ 25+1 $尺寸后，m $^{2} $ - 理论频谱不可约束地将$ \ mathbf {1} \ oplus \ oplus \ mathbf {196,883} $，其中$ \ m i \ mathbf {1} $ iS $ iS;怪物最小的非平凡表示的维度。 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子部门。以$ so_ {24} $的代表为角度，以$ 25+1 $ $ 25+1 $的形式表示，由Witten的极怪scft的分区函数系数分解提供了进一步的证据；所涉及的$ so_ {24} $的纯粹骨性质可以追溯到$ 24 $尺寸的独特功能，这允许对$ 8 $尺寸的试验性持有的非平凡概括。最后但并非最不重要的一点是，当与$ 26+1 $的rarita-schwinger无数领域相连时，M $^{2} $ - 理论的某个子部门表现出相同数量的Bosonic和Fermionic自由度；我们不禁会猜想存在可能的$ \ Mathcal {n} = 1 $ supergravity理论，$ 26+1 $时空维度。
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.
