Kirill Krasnov


Contact Information


Publications in INSPIRE   Google Scholar Profile


Research Interests

I am interested in different formulations of General Relativity. The aspects of most interest to me are how non-renormalisability of perturbative quantum gravity manifests itself in different formulations, and how different formulations suggest different paths towards unification of gravity with other interactions. I am also interested in the relation "Gravity is the square of Yang-Mills theory" that is visible in the scattering amplitudes of both theories, and implications this relation has for the UV divergences in quantum gravity.

I am interested in the geometry of 3-forms in 6 and 7 dimensions, and thus in aspects of geometry of manifolds of exceptional holonomy. These geometrical structures are central to the idea that 4D General Relativity arises as the dimensional reduction of a certain diffeomorphism invariant theory of differential forms in higher dimensions. This idea is what I am currently developing.

A good overview of my current interests can be formed by looking at my most recent papers on the arxiv. See also slides of some of my talks below.


Some Talks

  • Deformations of General Relativity Perimeter Institute, May 2010
  • Renormalized Volume of Hyperbolic 3-Manifolds Teichmüller Theory and its Interactions in Mathematics and Physics, Bellaterra, June 2010
  • Moduli space of shapes of a tetrahedron and SU(2) intertwiners Moduli spaces in Mathematics and Physics, Strasbourg, September 2010
  • Gravity as a diffeomorphism invariant Gauge Theory Lorentz geometry in Mathematics and in Physics, Strasbourg, June 2011
  • Gauge Theory Approach to Gravity EPFL seminar, September 2011
  • Gauge Theory Approach to Gravity Saclay/Bad Honnef/Utrecht talk, January-March 2012
  • Gravity as Gauge Theory Brussels/IHES/York/Oxford talk, December 2012-February 2013
  • Gravity as Gauge Theory Munich talk, July 2013
  • Diffeomorphism invariant gauge theories Loops 2013 talk, July 2013, Perimeter Institute, Canada
  • Perturbative Quantum Gravity Luxembourg talk, September 2013
  • Diffeomorphism invariant gauge theories Oxford Geometry and Analysis seminar, November 2013
  • One-loop beta-function for an infinite parameter family of gauge theories Probing the Fundamental Nature of Spacetime with the Renormalization Group, Nordita Workshop, March 2015
  • Gravity vs. Yang-Mills theory XXXV Max Born Symposium, Wroclaw, Poland, 7 - 12 September 2015
  • Colour/Kinematics Duality and the Drinfeld Double of the Lie algebra of Diffeomorphisms QCD meets gravity workshop, Higgs Center, Edinburgh, April 4-8, 2016
  • 3D/4D Gravity as the Dimensional Reduction of a theory of 3-forms in 6D/7D International Loop Quantum Gravity Seminar, February 21, 2017
  • Quantising Gravitational Instantons GARYFEST: Gravitation, Solitons and Symmetries, March 22-24, 2017
  • SO(7,7) structure of the SM fermions Perimeter Institute, February 2019

  • Series of lectures on formulations of General Relativity

    In February 2019 I gave four lectures on "Formulations of General Relativity" at Perimeter Institute, Canada.

  • Lecture 1: Motivations, metric and related formulations (Einstein-Hilbert, Palatini, Eddington-Schoedinger), first half of the presentation of tetrad formulations, including discussion of soldering and finishing with Einstein-Cartan action.
  • Lecture 2: Tetrad related formulations (Einstein-Cartan, Teleparallel, MacDowel-Mansouri, Stelle-West), followed by the presentation of BF-type formulations, including the discussion of the pure spin connection formulation.
  • Lecture 3: Discussion of the BF-type formulations finished, followed by the presentation of chiral formalisms for GR in four spacetime dimensions. Discussion of the self-dual/anti-self-dual decomposition of the Riemann curvature. Chiral Einstein-Cartan action. Chiral description of the Yang-Mills theory.
  • Lecture 4: Spinor form of the chiral Einstein-Cartan, chiral pure connection formulation to second order. Encoding the metric into knowledge of which forms are self-dual. Geometry of Plebanski formulation of GR. Chiral pure connection action in closed form. Chiral formulations of BF plus potential for the two-form field type. Summary and conclusions.


  • Slides for all the lectures are contained below in 4 pdf-files.

  • Introductory slides
  • Parts I,II
  • Part III
  • Part IV