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Weyl Curvature Evolution System for GR
Kirill Krasnov, Adam Shaw
Starting from the chiral first-order pure connection formulation of General Relativity, we put the field equations of GR in a strikingly simple evolution system form. The two dynam…
Higher-Spin Self-Dual Yang-Mills and Gravity from the twistor space
Yannick Herfray, Kirill Krasnov, Evgeny Skvortsov
We lift the recently proposed theories of higher-spin self-dual Yang-Mills (SDYM) and gravity (SDGR) to the twistor space. We find that the most natural room for the twistor formul…
Geometry of Spin(10) Symmetry Breaking
Kirill Krasnov
We provide a new characterisation of the Standard Model gauge group GSM as a subgroup of Spin(10). The new description of GSM relies on the geometry of pure spinors. We show that G…
Notes on Spinors and Polyforms II: Quaternions and Octonions
Niren Bhoja, Kirill Krasnov
Pauli matrices are 2x2 tracefree matrices with a real diagonal and complex (complex-conjugate) off-diagonal entries. They generate the Clifford algebra Cl(3). They can be generalis…
Notes on Spinors and Polyforms I: General Case
Niren Bhoja, Kirill Krasnov
It is well-known that the Clifford algebra Cl(2n) can be given a description in terms of creation/annihilation operators acting in the space of inhomogeneous differential forms on…