String theory on complex spacetime, twistor string

[kodama]

bosonic string theory requires 26 dimensions
superstring theory requires 10, 9 spatial 1 dimension of time

Witten has researched twistor string theory

has there been any serious research with (super) string theory written on 4 complex -valued dimensions of spacetime?

the additional dimensions consists both of imaginary space and imaginary time, something Stephen hawking wrote of, but 4 real dimensions, and 4 or more imaginary dimensions, or give rise to 4 real dimensions

are there any kaluza klein theories in which the extra dimensions of space and time are imaginary, i ?

 

[Urs Schreiber]

are there any kaluza klein theories in which the extra dimensions of space and time are imaginary, i ?

For that question to be contentful one needs to say something about how the field theory is meant to depend on the given complex structure.

One well-studied example is compactifications on complex Calabi-Yau varieties, which I am sure you have heard of.

Another well-studied case of something sort of like a KK-compactification (a little different though) is F-theory, where the compactification is on a complex torus/complex elliptic curve. Here this is the geometrization of S-duality in type II string theory.- This in turn relates to the compactification of the msterious 6d (2,0)-superconformal QFT on a complex torus, which now governs the electric-magnetic duality of supersymmetric 4d Yang-Mills theory.

 

[kodama]

Hi Urs thanks for sharing

I would imagine the "simplest" complex spacetime consistent with physics, would simply be that for each spatial dimension and time dimension, there is also a corresponding imaginary part, in standard 3+1 so that if string theory could be written on such a spacetime consistently, with anomaly cancellation, there would be no landscape. the dimensions of space length width breadth has both a real part and an imaginary degree of freedom, and same with time.

another possibility is how it would affect the properties of supersymmetry on such a spacetime, on complex spacetime.
perhaps supersymmetry is exact and unbroken, much like matter-antimatter, superpartners have the same mass as SM particlers, but written on complex spacetime the superpartners have imaginary mass, and SM have real mass. if possible it could simply superstring theory, by reducing the need for extra real dimensions and possibly simplifying supersymmetry by eliminating a need to have a hidden sector to break it

 

[Urs Schreiber]

I would imagine the "simplest" complex spacetime consistent with physics, would simply be that for each spatial dimension and time dimension, there is also a corresponding imaginary part, in standard 3+1 so that if string theory could be written on such a spacetime consistently, with anomaly cancellation, there would be no landscape.

What? Now you are rambling.

You know, you seem to be seriously interested in understanding something, on the other hand you seem not to spend time to deal with the little steps that lead to true understanding of anything.

What is your background? What physics are you comfortable with?

You should go back to that point and then slowly work your way forward. In the end that will allow you to gain actual control over what you are after. In the long run this will be more satisfactoy then throwing around wild questions far ahead of what you really understand.