Difference between an Einstein frame and a String frame?

[windy miller]

I have listening to talks come across the terms"Einstein frame" and "String frame" but am not at all clear what they mean. Can anyone give a layman's explanation as to what is theses phrases mean in the context of cosmology ?

 

[PeterDonis]

I have listening to talks come across the terms"Einstein frame" and "String frame"

Can you give any specific references?

 

[windy miller]

Can you give any specific references?

sure for example here
https://arxiv.org/pdf/hep-th/0608200.pdf

 

[PeterDonis]

sure for example here
https://arxiv.org/pdf/hep-th/0608200.pdf

From equations (2) and (3) in that paper, it looks like the "Einstein frame" is the usual FRW coordinates used in standard cosmology, and the "string frame" is a conformal transformation of those coordinates that rescales time and distance in a way that varies with the value of the dilaton field $\phi$ (and also depends on the number of dimensions $N$ in the underlying string theory, but that will be constant for a given model). Since the dilation field $\phi$ presumably varies with time, the conformal factor will also vary with time. Presumably this conformal transformation is convenient for string theory, but I am not familiar enough with string theory to know why.

 

[windy miller]

From equations (2) and (3) in that paper, it looks like the "Einstein frame" is the usual FRW coordinates used in standard cosmology, and the "string frame" is a conformal transformation of those coordinates that rescales time and distance in a way that varies with the value of the dilaton field $\phi$ (and also depends on the number of dimensions $N$ in the underlying string theory, but that will be constant for a given model). Since the dilation field $\phi$ presumably varies with time, the conformal factor will also vary with time. Presumably this conformal transformation is convenient for string theory, but I am not familiar enough with string theory to know why.

thanks