Outputs (21)

Pure connection formalism and Plebanski’s second heavenly equation (2025)
Journal Article
Krasnov, K., & Lipstein, A. (2025). Pure connection formalism and Plebanski’s second heavenly equation. Journal of High Energy Physics, 2025(3), Article 152. https://doi.org/10.1007/jhep03%282025%29152

Plebanski’s second heavenly equation reduces the problem of finding a self-dual Einstein metric to solving a non-linear second-order PDE for a single function. Plebanski’s original equation is for self-dual metrics obtained as perturbations of the fl... Read More about Pure connection formalism and Plebanski’s second heavenly equation.

Kerr metric from two commuting complex structures (2025)
Journal Article
Krasnov, K., & Shaw, A. (2025). Kerr metric from two commuting complex structures. Classical and Quantum Gravity, 42(6), Article 065013. https://doi.org/10.1088/1361-6382/adb531

The main aim of this paper is to simplify and popularise the construction from the 2013 paper by Apostolov, Calderbank, and Gauduchon, which (among other things) derives the Pleba´nskiPleba´nski-Demia´nskiDemia´nski family of solutions of GR using id... Read More about Kerr metric from two commuting complex structures.

Geometry of Spin(10) symmetry breaking (2024)
Journal Article
Krasnov, K. (2024). Geometry of Spin(10) symmetry breaking. Journal of Mathematical Physics, 65(8), Article 082302. https://doi.org/10.1063/5.0210073

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 GSM ⊂ Spin(10) is the group that stabilises a pure spinor Ψ1 and projec... Read More about Geometry of Spin(10) symmetry breaking.

Area-metric gravity revisited (2024)
Journal Article
Borissova, J. N., Dittrich, B., & Krasnov, K. (2024). Area-metric gravity revisited. Physical Review D, 109(12), Article 124035. https://doi.org/10.1103/physrevd.109.124035

Area metrics are an intriguing generalization of length metrics which the generalization in several quantum-gravity approaches. We describe the space of diffeomorphism-invariant area-metric actions quadratic in fluctuations and derivatives. A general... Read More about Area-metric gravity revisited.

Lorentzian Cayley form (2024)
Journal Article
Krasnov, K. (2024). Lorentzian Cayley form. Journal of Geometry and Physics, 201, Article 105211. https://doi.org/10.1016/j.geomphys.2024.105211

Cayley four-form Φ on an eight-dimensional manifold M is a real differential form of a special algebraic type, which determines a Riemannian metric on M as well as a unit real Weyl spinor. It defines a Spin(7) structure on M, and this Spin(7) structu... Read More about Lorentzian Cayley form.

Higher-spin self-dual Yang-Mills and gravity from the twistor space (2023)
Journal Article
Herfray, Y., Krasnov, K., & Skvortsov, E. (2023). Higher-spin self-dual Yang-Mills and gravity from the twistor space. Journal of High Energy Physics, 2023, Article 158. https://doi.org/10.1007/jhep01%282023%29158

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 their twistor formulation is not in the projective, but in the full twistor space, which... Read More about Higher-spin self-dual Yang-Mills and gravity from the twistor space.

Spin(11, 3), particles, and octonions (2022)
Journal Article
Krasnov, K. (2022). Spin(11, 3), particles, and octonions. Journal of Mathematical Physics, 63(3), Article 031701. https://doi.org/10.1063/5.0070058

The fermionic fields of one generation of the Standard Model (SM), including the Lorentz spinor degrees of freedom, can be identified with components of a single real 64-dimensional semi-spinor representation S+ of the group Spin(11, 3). We describe... Read More about Spin(11, 3), particles, and octonions.

One-loop same helicity YM amplitudes from BG currents (2022)
Journal Article
Chattopadhyay, P., & Krasnov, K. (2022). One-loop same helicity YM amplitudes from BG currents. Journal of High Energy Physics, 2022(3), Article 191. https://doi.org/10.1007/JHEP03%282022%29191

We propose and prove a new formula for the one-loop all same helicity Yang-Mills amplitudes. These amplitudes are seen to arise as a sum of products of two tree-level Berends-Giele currents connected by an effective propagator. To make sense of the p... Read More about One-loop same helicity YM amplitudes from BG currents.

Pure Lorentz spin connection theories and uniqueness of general relativity (2021)
Journal Article
Krasnov, K., & Mitsou, E. (2021). Pure Lorentz spin connection theories and uniqueness of general relativity. Classical and Quantum Gravity, 38(20), Article 205009. https://doi.org/10.1088/1361-6382/ac25e3

General relativity (GR) can be reformulated as a diffeomorphism invariant gauge theory of the Lorentz group, with Lagrangian of the type f(F ∧ F), where F is the curvature two-form of the spin connection. A theory from this class with a generic f is... Read More about Pure Lorentz spin connection theories and uniqueness of general relativity.

Deformations of GR, geometrodynamics and reality conditions (2021)
Journal Article
Krasnov, K., & Mitsou, E. (2021). Deformations of GR, geometrodynamics and reality conditions. Classical and Quantum Gravity, 38(8), Article 085009. https://doi.org/10.1088/1361-6382/abe756

In four dimensions complexified general relativity (GR) can be non-trivially deformed: there exists an (infinite-parameter) set of modifications all having the same count of degrees of freedom. It is trivial to impose reality conditions that give ver... Read More about Deformations of GR, geometrodynamics and reality conditions.