### Torsion Gravity from String Theory

#### Posted by Urs Schreiber

I was asked by A. Pelster, who has worked on torsion gravity together with H. Kleinert and F. Hehl, if I consider it worthwhile thinking about torsion gravity in the context of string theory.

Of course everybody knows that there is the Kalb-Ramond field in string theory whose field strength acts like a torsion in many situations. For instance in the highly important (S)WZW models the Kalb-Ramond field provides the *parallelizing torsion* of the group manifold that the string is propagating on.

Apart from that, the Kalb-Ramond field of string theory is perhaps more prominently known for its relation to noncommutative field theory, as described in the seminal paper

N. Seiberg and E. Witten, String Theory and Noncommutative Geometry .

Now A. Pelster points me to papers by Richard Hammond, who has done very detailed studies of torsion gravity in general as well as its relation to string theory in particular. The most comprehensive review article is apparently

R. Hammond, Tosion gravity.

When challenged, I realized that I couldn’t satisfactorily answer why I had heard so little about the role of the Kalb-Ramond field as providing spacetime torsion. Together with R. Hammond, A. Pelster likes to argue that, since the Kalb-Ramond field is not at order ${\alpha}^{{\textstyle \prime}}$ in the string action but on par with the gravitational terms, it should actually have measurable effects even at relatively modest enegies - shouldn’t it?

Indeed, R. Hammond, who discusses experimental signatures of torion in great detail, argues that any detection of torsion would have direct implications for the experimental verification of string theory. In his above paper he conculdes

We have seen that torsion is called on stage by many directors, from string theory to supergravity, yet the audience has not yet settled on the correct interpretation of its role. I believen any diract, or even indirect, observation of torsion would be one of the greatest breakthroughs in many decades, and would certainly help settle these questions.

I should try to better understand the big picture of torsion gravity in string theory.