Is torsion the geometrical description of the magnetic field?

Question

The low-energy effective action of the bosonic string is given by: $$S=\frac{1}{2k_0^2}\int d^{26}x\sqrt{-g}e^{-2\Phi}({\cal R}+4\partial_\mu\Phi\partial^\mu\Phi-\frac{1}{12}H_{\mu\nu\rho}H^{\mu\nu\rho}),$$ where $k_0^2\sim l_s^{24}$, $\cal R$ is the scalar curvature, $\Phi$ is the dilaton field and $$H_{\mu\nu\rho}=\partial_\mu B_{\nu\rho}+\partial_\nu B_{\rho\mu}+\partial_\rho B_{\mu\nu},$$ where $B_{\mu\nu}$ is the Kalb-Ramond field.

David Tong says in his String Theory Notes (7.2.1) that the term $H_{\mu\nu\rho}H^{\mu\nu\rho}$ plays the same role as torsion in general relativity providing an anti-symmetric component to the affine connection. I take this to mean that an objects' angular momentum vector rotates as it moves along a geodesic. Now a magnetic field makes the spin of a charged particle precess (Larmor Precession). Does this mean that the Kalb-Ramond field is related to an ordinary magnetic field in 4D spacetime?

Answer 1

Einstein's unified field theory attempted to unify gravity and electromagnetism. In its more modern formulation the torsion vector (contracted torsion tensor $T^k{}_{ik}$) is identified with the 4-potential of EM field. See e.g. this paper for details.