What is the Kalb-Ramond field?

[jcap]

All String theories include the massless bosonic fields $G_{\mu\nu}$, $B_{\mu\nu}$ and $\Phi$.

I understand that $G_{\mu\nu}$ is the spin-$2$ field of the spacetime metric and $\Phi$ is the spin-$0$ dilaton field.

The $B_{\mu\nu}$ is called the Kalb-Ramond field and is said to:

1. be analogous to the electromagnetic potential $A_\mu$ ,
2. play the same role as torsion in GR, providing an anti-symmetric component to the affine connection (spin connection?)

What are its physical effects?

Does the electromagnetic potential $A_\mu$ actually arise from $B_{\mu\nu}$ after reducing to $4$-D spacetime?

Does $B_{\mu\nu}$ cause a particle's spin to precess as the particle travels along a geodesic?

What is the spin of the $B_{\mu\nu}$ field itself?

 

[AndyW]

Thank you for your post. It is correct that $G_{\mu\nu}$ is the spin-$2$ field of the spacetime metric and $\Phi$ is the spin-$0$ dilaton field. The Kalb-Ramond field $B_{\mu\nu}$ is also a bosonic field and can be thought of as the spin-$1$ field of the Kalb-Ramond 2-form potential.

The physical effects of the Kalb-Ramond field are not fully understood yet, as it is still a subject of ongoing research. However, it is believed that it plays a role in the dynamics of string theory, possibly contributing to the generation of particles and their interactions.

The electromagnetic potential $A_\mu$ can arise from the Kalb-Ramond field $B_{\mu\nu}$ after reducing to $4$-D spacetime, as the Kalb-Ramond field contains both electric and magnetic components. This is known as the Kalb-Ramond mechanism.

There is currently no evidence to suggest that the Kalb-Ramond field causes a particle's spin to precess as it travels along a geodesic. However, this is an area of active research and may be explored in the future.

The spin of the Kalb-Ramond field itself is not well-defined, as it is a higher-dimensional object. However, it can be decomposed into its spin components in lower dimensions. Overall, the Kalb-Ramond field is an important component of string theory and its role in the physical effects of the theory is still being studied.