Professor KIRILL KRASNOV's Outputs (26)

Dynamics of Cayley forms (2025)
Journal Article
Krasnov, K. (2025). Dynamics of Cayley forms. Pure and Applied Mathematics Quarterly, 21(5), 1959-2003. https://doi.org/10.4310/pamq.250421122254

The most natural first-order PDE's to be imposed on a Cayley 4-form in eight dimensions is the condition that it is closed. As is well-known, this implies integrability of the Spin(7)-structure defined by the Cayley form, as well as Ricci-flatness of th... Read More about Dynamics of Cayley forms.

Spinors from pure spinors (2025)
Journal Article
Bhoja, N., & Krasnov, K. (in press). Spinors from pure spinors. Quarterly Journal of Mathematics,

We propose and develop a new method to classify orbits of the spin group Spin(2d) in the space of its semi-spinors. The idea is to consider spinors as being built as a linear combination of their pure constituents. As is well-known, two pure spinors... Read More about Spinors from pure spinors.

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.

Weyl curvature evolution system for GR (2023)
Journal Article
Krasnov, K., & Shaw, A. (2023). Weyl curvature evolution system for GR. Classical and Quantum Gravity, 40(7), Article 075013. https://doi.org/10.1088/1361-6382/acc0cc

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 dynamical fields are a complex symmetric tracefree 3 × 3 matrix Ψij, which... Read More about Weyl curvature evolution system for GR.

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.

Actions for self-dual Higher Spin Gravities (2021)
Journal Article
Krasnov, K., Skvortsov, E., & Tran, T. (2021). Actions for self-dual Higher Spin Gravities. Journal of High Energy Physics, 2021, Article 76. https://doi.org/10.1007/jhep08%282021%29076

Higher Spin Gravities are scarce, but covariant actions for them are even scarcer. We construct covariant actions for contractions of Chiral Higher Spin Gravity that represent higher spin extensions of self-dual Yang-Mills and self-dual Gravity theor... Read More about Actions for self-dual Higher Spin Gravities.

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.

SO(9) characterization of the standard model gauge group (2021)
Journal Article
Krasnov, K. (2021). SO(9) characterization of the standard model gauge group. Journal of Mathematical Physics, 62(2), Article 021703. https://doi.org/10.1063/5.0039941

A recent series of works characterized the Standard Model (SM) gauge group GSM as the subgroup of SO(9) that, in the octonionic model of the latter, preserves the split O=C⊕C3 of the space of octonions into a copy of the complex plane plus the rest.... Read More about SO(9) characterization of the standard model gauge group.

Local rigidity of Einstein 4-manifolds satisfying a chiral curvature condition (2020)
Journal Article
Fine, J., Krasnov, K., & Singer, M. (2020). Local rigidity of Einstein 4-manifolds satisfying a chiral curvature condition. Mathematische Annalen, 379, 569–588. https://doi.org/10.1007/s00208-020-02097-z

Let (M, g) be a compact oriented Einstein 4-manifold. Write R+ for the part of the curvature operator of g which acts on self-dual 2-forms. We prove that if R+ is negative definite then g is locally rigid: any other Einstein metric near to g is isome... Read More about Local rigidity of Einstein 4-manifolds satisfying a chiral curvature condition.

A 4D gravity theory and G2-holonomy manifolds (2019)
Journal Article
Herfray, Y., Krasnov, K., Scarinci, C., & Shtanov, Y. (2019). A 4D gravity theory and G2-holonomy manifolds. Advances in Theoretical and Mathematical Physics, 22(8), 2001-2034. https://doi.org/10.4310/ATMP.2018.v22.n8.a5

© 2019 International Press of Boston, Inc. Bryant and Salamon gave a construction of metrics of G2 holonomy on the total space of the bundle of anti-self-dual (ASD) 2-forms over a 4-dimensional self-dual Einstein manifold. We generalise it by conside... Read More about A 4D gravity theory and G2-holonomy manifolds.

Fermions, differential forms and doubled geometry (2018)
Journal Article
Krasnov, K. (2018). Fermions, differential forms and doubled geometry. Nuclear Physics B, 936, 36-75. https://doi.org/10.1016/j.nuclphysb.2018.09.006

© 2018 The Author We show that all fermions of one generation of the Pati–Salam version of the Standard Model (SM) can be elegantly described by a single fixed parity (say even) inhomogeneous real-valued differential form in seven dimensions. In this... Read More about Fermions, differential forms and doubled geometry.

Pure-connection gravity and anisotropic singularities (2018)
Journal Article
Krasnov, K., & Shtanov, Y. (2018). Pure-connection gravity and anisotropic singularities. Physics of the Dark Universe, 4(1), Article 12. https://doi.org/10.3390/universe4010012

In four space-time dimensions, there exists a special infinite-parameter family of chiral modified gravity theories. They are most properly described by a connection field, with space-time metric being a secondary and derived concept. All these theor... Read More about Pure-connection gravity and anisotropic singularities.

General relativity from three-forms in seven dimensions (2017)
Journal Article
Krasnov, K. (2017). General relativity from three-forms in seven dimensions. Physics Letters B, 772, https://doi.org/10.1016/j.physletb.2017.06.025

We consider a certain theory of 3-forms in 7 dimensions, and study its dimensional reduction to 4D, compactifying the 7-dimensional manifold on the 3-sphere of a fixed radius. We show that the resulting 4D theory is (Riemannian) General Relativity (G... Read More about General relativity from three-forms in seven dimensions.