The Mode is an enclosed, detectable manifestation of the Substance… The Substance is equipped with infinite attributes(Spinoza, Ethica, pars I)
2. Topological Tools
2.1. The Standard Version of the Borsuk–Ulam Theorem (BUT)
2.2. BUT Variants
2.3. Quantum String Axioms
- Every string has an action.
- If are antipodal, then .
- Separate strings with k features with the same description are antipodal.
- There is a set of antipodal strings for every string .
2.4. Generalized BUT (genBUT)
3. Embedding the Monster Group in Md−1
4. Of Monsters and Universes
4.1. Dimensions Reduction
- The Monster group is progressively formed starting from its subgroups, with a gradual building from blocks.
- The Monster group is the original structure giving rise to our universe.
- The Monster group, the original structure, splits in its subgroups, then one of the subgroups gives rise to our universe.
4.2. Topological Relationships between the Monster and String Theories
4.3. The Problem of Singularity
4.4. The Monster and the Spacetime
5. Quantifying Physical Monster’s Parameters
5.1. Towards the Monster’s Enthalpy
5.3. Watching the Monster: Vertex Algebra
6. Questions and Conclusions
- Where does the Monster take such a huge amount of enthalpy? It takes us in pre-, pre-Big Bang scenarios. This is the same problem with inflationist models, that do not explain where the energy of the required false vacuum comes from. A link between the Monster group and the false vacuum might be speculated.
- What is the role of the j-function in the pre Big Bang period? Does it provide energy?
- How does the Monstrous Moonshine look like? We could either imagine a timeless, immutable manifold where just the Monster Group movements take place, or as we did, a dynamical, time-dependent structure.
- Does the curvature of the Monster Module change with the passage of time? This could be a very useful information, in order to elucidate the hypothesized step from an ancient anti DeSitter hyperbolic universe to the current, flat one.
- Our universe might not arise directly from the Monster, but by one of its subgroups, e.g., the Th group (Figure 3), which is correlated with the successful superstring 10D theory. Is it possible to split the Leech lattice in which the Monster group is embedded, in order to achieve the lower dimensional E8 lattice where the Th group’s movements take place? It is central to remind that the step from an E8 lattice to the Leech lattice requires ×3 multiplication and peculiar rotations.
- The topological step from the vertex operator algebra to the Lie Monster Group requires a continuous function. Are we in front of a “super” gauge field? In other words, is there a gauge field that causes the first projection depicted at the top of Figure 3? In a topological framework, the feature that links the symmetries at a higher level with the single point at a lower level is the continuous function. If we assess two antipodal points as symmetries, and the single point as symmetry breaks and local transformations, a gauge field could be required, in order to restore the (apparently hidden) symmetry.
Conflicts of Interest
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