Abstract
We describe a model where breaking of W3 symmetry will lead to the emergence of time and subsequently of space. Surprisingly the simplest such models which lead to higher dimensional spacetimes are based on the four “magical” Jordan algebras of 3×3 Hermitian matrices with real, complex, quaternion and octonion entries, respectively. The simplest symmetry breaking leads to universes with spacetime dimensions 3, 4, 6, and 10.
Highlights
String field theory is notoriously complicated, but there is a baby version, namely non-critical string field theory [1,2,3]
The starting point is the continuum limit of 2d “causal dynamical triangulations” (CDT) [5,6], a limit which in the case of trivial spacetime topology is 2d quantum Horava–Lifshitz gravity [7]
The starting point for introducing the above mentioned model was that even the baby versions of string field theory, the noncritical string field theories, tell us surprising little about the actual creation of the universe
Summary
String field theory is notoriously complicated, but there is a baby version, namely non-critical string field theory [1,2,3]. The interaction term in the string field Hamiltonian contains products of three annihilation and creation operators. The same is true for standard non-critical string theory which is related to a special kind of W (3) symmetry which ensures that the partition function can be viewed as a τ -function of certain coupling constants [11] This led us to realize that one can obtain the CDT string field theory starting from a so-called W (3) Hamiltonian by symmetry breaking [12]. If μ > 0 a universe starting with zero (or more precisely infinitesimal) length will have a (unnormalized) wave function and a corresponding expectation value of the size of space at time T : G(L, T ).
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