# A Non-relativistic holography

1. Sep 19, 2016

### haushofer

Dear all,

I'm a bit confused about non-relativistic applications of holography, like e.g. in

https://arxiv.org/pdf/0812.0530v1.pdf

and

https://arxiv.org/abs/1306.0638

In these papers people try to connect holographically non-relativistic condensed matter systems, like the Quantum Hall Effect, to backgrounds in the bulk exhibiting non-relativistic isometries or non-relativistic theories of gravity, like Newton-Cartan. But in the AdS/CFT correspondence we have a duality between strongly coupled and weakly coupled theories. Shouldn't one expect to describe non-relativistic condensed matter systems by ultra-relativistic theories of gravity and vice versa? It probably has to do something with the fact that the correspondence involves the 't Hooft coupling. Can anyone comment on my confusion? Many thanks!

Last edited: Sep 19, 2016
2. Sep 19, 2016

### haushofer

Also, the explicit embedding in string theory in these examples is not known, so one does not have an explicit relation between the two couplings. But still my confusion stands.

3. Sep 19, 2016

### haushofer

Take e.g. a particle in free fall in a Newtonian gravitational field. Non-relativistic means than v/c << 1, which implies a weak gravitational coupling, right?

4. Sep 19, 2016

### ShayanJ

Are you associating strongly-coupled with ultra-relativistic and weakly-coupled with non-relativistic? If yes, that's not correct!

It seems to me that a non-relativistic Gauge/Gravity correspondence can be achieved by taking the $\frac v c \to 0$ limit of both theories, among other limits. But I don't know how to actually do it!

5. Sep 19, 2016

### haushofer

I could of course move very slowly in a strong gravitational field, but then I would not be in free fall (not moving on a geodesic). So in that sense i see that "strongly coupled" does not necessarily imply "non-relativistic". Something similar can be formulated in a field-theoretical (instead of particle) context. So I guess this is what a strongly coupled but non-relativistic field theory should look like.