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Euclidean Twistor Unification

by Peter Woit

Submission summary

As Contributors: Peter Woit
Arxiv Link: (pdf)
Date submitted: 2021-10-18 17:26
Submitted by: Woit, Peter
Submitted to: SciPost Physics
Academic field: Physics
  • High-Energy Physics - Theory
  • Mathematical Physics
Approach: Theoretical


Taking Euclidean signature space-time with its local Spin(4)=SU(2)xSU(2) group of space-time symmetries as fundamental, one can consistently gauge one SU(2) factor to get a chiral spin connection formulation of general relativity, the other to get part of the Standard Model gauge fields. Reconstructing a Lorentz signature theory requires introducing a degree of freedom specifying the imaginary time direction, which will play the role of the Higgs field. To make sense of this one needs to work with twistor geometry, which provides tautological spinor degrees of freedom and a framework for relating by analytic continuation spinors in Minkowski and Euclidean space-time. It also provides internal U(1) and SU(3) symmetries as well as a simple construction of the degrees of freedom of a Standard Model generation of matter fields. In this proposal the theory is naturally defined on projective twistor space rather than the usual space-time, so will require further development of a gauge theory and spinor field quantization formalism in that context.

Current status:
Editor-in-charge assigned

Author comments upon resubmission

This is a heavily revised version of the original submission. I believe it addresses the issues raised by the referees.

List of changes

1. Complete reorganization of the paper, emphasizing new proposal for unification instead of trying to motivate through technical issues about defining quantum field theory for Euclidean spinor fields.
2. Additional arguments addressing the necessity of introducing a choice of imaginary time direction in Euclidean qft in order to recover a physical state space and Minkowski signature theory.
3. Clarification that the issue of how to relate a theory on Euclidean space-time to a theory in twistor space still remains to be addressed, with some explanation of the problems faced.

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