# H-flux by any other name

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There are more than a few papers referring to H-flux and/or H-twist etc. Is there anywhere a survey relating these variants?

This post imported from StackExchange MathOverflow at 2014-08-10 09:05 (UCT), posted by SE-user Jim Stasheff
asked Oct 30, 2013
retagged Nov 21, 2014

## 1 Answer

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The $B$-field is a massless excitation present in the NS-NS spectrum of the superstring. It is a spacetime 2-form. What is generally called $H$ is the corresponding field-strength : $H=dB$, it is a (spacetime) 3-form. In the simplest situations, the condition $H=0$, i.e. $B$ closed, is a natural constraint on a string background. Nevertheless, in more complicated situations, we can have $H \neq 0$, i.e. a non-trivial "H-flux", defining a "H-twist" of the more common cases with $H=0$.

Remark: I am not sure to fully understand the meaning of the question.

answered Aug 10, 2014 by (5,120 points)

Just to point out that when using a closed 3-form H to twist de Rham cohomology (i.e. the rational image of degree-3 twisting of K-theory) it is crucial that H not be exact. The thing is that the B-field is in general only locally given by a 2-form and H is hence in general only locally exact (as every closed form is).

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