Does Coupling Constant Evolution Reduce to Cosmological Constant?

Abstract

The great surprise of the last year was that twistor induction allows large number of induced twistor structures. SO(3) acts as moduli space for the dimensional reductions of the 6-D Kahler action defining the twistor space of space-time surface as a 6-D surface in 12-D twistor space assignable to M⁴ x CP₂. This 6-D surface has space-time surface as base and sphere S² as fiber. The action of the twistor sphere in induced twistor structure defines running cosmological constant and one can understand the mysterious smallness of cosmological constant. This in turn leads to the understanding of coupling constant evolution in terms of the flow changing the value of cosmological constant defined by the area of the twistor sphere of space-time surface for induced twistor structure. Cosmological constant effectively replaces cutoff of length of quantum field theories and the RG invariance reduces to the invariance of action and possibly also scattering amplitudes under small enough variations of the cosmological constant. Zeros of Riemann zeta are believed to related to criticality. The complex integral of zeta along curve having zero of ζ as endpoint is critical with respect to the variations of the end point, which leads to the proposal that this kind of integral serves as an argument in the expressions for running coupling constants. In the case of the S² part of 6-D dimensionally reduced Kahler action this leads to a highly unique expression of Kahler coupling constant such that critical points assignable to the zeros of zeta. Whether the S² part of the 6-D action has zeros of zeta as critical points can be tested numerically.