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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.

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.

6D interpretation of 3D gravity (2017)
Journal Article
Herfray, Y., Krasnov, K., & Scarinci, C. (2017). 6D interpretation of 3D gravity. Classical and Quantum Gravity, 34(4), https://doi.org/10.1088/1361-6382/aa5727

We show that 3D gravity, in its pure connection formulation, admits a natural 6D interpretation. The 3D field equations for the connection are equivalent to 6D Hitchin equations for the Chern–Simons 3-form in the total space of the principal bundle o... Read More about 6D interpretation of 3D gravity.

Colour-kinematics duality and the Drinfeld double of the Lie algebra of diffeomorphisms (2017)
Journal Article
Fu, C.-H., & Krasnov, K. (in press). Colour-kinematics duality and the Drinfeld double of the Lie algebra of diffeomorphisms. Journal of High Energy Physics, 2017, Article 75. https://doi.org/10.1007/JHEP01%282017%29075

Colour-kinematics duality suggests that Yang-Mills (YM) theory possesses some hidden Lie algebraic structure. So far this structure has resisted understanding, apart from some progress in the self-dual sector. We show that there is indeed a Lie algeb... Read More about Colour-kinematics duality and the Drinfeld double of the Lie algebra of diffeomorphisms.