What role does torsion'' play in string theory?

[arroy_0205]

What role does "torsion'' play in string theory?

In general relativity we assume that connection is torsion free. However from a purely geometrical viewpoint, the concept of torsion can not be ignored (theoretically) and in string theory, it is said that "torsion" does play its role. Can anybody tell what consequences arise if torsion is taken into account?

 

[Finbar]

In general relativity we assume that connection is torsion free. However from a purely geometrical viewpoint, the concept of torsion can not be ignored (theoretically) and in string theory, it is said that "torsion" does play its role. Can anybody tell what consequences arise if torsion is taken into account?

I believe that even in gravity coupled to spinors torsion should be taken into account. That is gravity should have two sources the energy-momentum tensor and the the spinor tensor. I guess that the same would be true of string theory. So fermionic superstrings should have a non-zero spinor tensor?! That would be my guess.

 

[tom.stoer]

For me the Einstein-Cartan theory with non-vanishing torsion based on Riemann-Cartan manifolds is much more natural than the pure GR framework with its restriction to torsion-free geometries. This becomes clear if one considers gauge aspects of gravity and fermion coupling.

Einstein-Cartan theory differs from GR, but the difference is not visible experimentally since torsion is non-propagation and therefore should vanish in the vacuum. It cannot be detected.

I guess this carries over to SUGRA. I do not know about the situation in ST, but I guess it's rather similar. I would expect 10d torsion to play a role as well.

 

[crackjack]

I have seen something called "discrete torsion" in ST which comes up as a result of some arbitrariness in writing the partition function on orbifolds. This is how it was originally explained by Vafa. Later, it has acquired a geometrical explanation which I am not very sure about (ref: hep-th/9909108, hep-th/9909120). Can someone tell me if and how they are related to the torsion in Einstein-Cartan theory?

 

[arivero]

I am not expert of GR, but I think that GR does not use torsion, and string theory produces the equations of GR, so torsion is still out of the play, is it?

 

[tom.stoer]

That's correct tomy knowledge. But string theory produces SUGRA as well, and there is no reason why one should restrict to a torsion-free SUGRA.