# About anti symmetric tensor $B_{ab}$ in gravity

If the symmetric tensor $g_{ab}$ represents the graviton, what particle does the anti symmetric tensor $B_{ab}$ in supergravity represent?

The antisymmetric tensor field in string theory is a sort of generalized gauge boson. It has no realization in the compactified theory, and decomposes into gauge fields under Kaluza Klein reduction.

However, if you're asking for a nice intuitive understanding of $B_{\mu\nu}$, consider a charged point particle coupled to an electromagnetic field $A_{\mu}$ in the classical theory. The action of the interaction between the point particle and the electromagnetic field is given by

$$S_{I}=q\int_{\Gamma} A_{\mu}\,\mathrm{d}x^{\mu}=q\int_{\Gamma}A,$$

where $\Gamma$ is the world-line of the point-particle. Similarly, in a string theory, we can couple a string to a two-form field as

$$S_{I}=q\int_{\Sigma} B_{\mu\nu}\,\mathrm{d}x^{\mu}\wedge\mathrm{d}x^{\nu}=q\int_{\Sigma}B,$$

where $\Sigma$ is the string world-sheet. Thus, the two-form field plays the same role in the string theory as the electromagnetic field plays in the classical point-particle theory.

I hope this helps!

• Definitely helps, but why is it there in the first place? What is the source of a B field? The interaction indicates it to the presence of some "charge" in the string. So, does this represent some kind of new charge? – sgemc Jan 30 '18 at 6:34