Speaker: Sandeep Suresh Cranganore (Universität zu Köln)

Title: Sugawara model with canonical spin currents and energy-momentum currents

Abstract: The Standard model of physics (Strong, Weak \& EM interactions - Yang-Mills theories) has a gauge group of $SU(3)_C \otimes SU(2)_L \otimes U(1)_Y$. Gravity, on the other hand fails to be accommodated in the standard model because Einstein's general relativity (GR) is not a gauge theory. Although, gravity can be shown to be a gauge theory by gauging the Poincaré group (set of translations and rotations+boosts) and leads to the Einstein-Cartan theory (EC) with a Riemann-Cartan (RC) spacetime as the underlying arena (manifold) containing both curvature and torsion. The Noether currents (sources) of the theory are the mass-energy distribution which is encapsulated in the canonical energy-momentum currents (translational currents) as the source of curvature, and also the intrinsic angular momentum of quantum particles encapsulated in the spin currents (rotations+boosts currents) as the source of torsion (curvature + torsion = deformations of spacetime = gravity). In 1968, H. Sugawara found an interesting model for strong-interactions by solely using hadronic vector-axial vector currents to construct the symmetric (Hilbert) energy-momentum tensor. Through the Sugawara construction and current algebra techniques, we extend the model to include the canonical spin currents by showing that they are composed of the hadronic vector-axial vector currents and thus uniting the gravitational gauge theories with the Yang-Mills gauge theories. This also leads to a topological nature of spin. As an ancillary, we also discuss how the Lorentz algebra of chiral Weyl Fermions contains quantum corrections due its interactions with an external electromagnetic field in a background Riemann-Cartan (RC) spacetime.