# Does the measure of proximity of two theories in "theory space" run?

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From reading this article, I have learned that two effective QFTs can be very close together in the "theory space" appropriate to describe for example physics at the LHC scale, whereas the corresponding points in the high energy landscape of all valid theories can be far away from each other (and vice versa).

This makes me wonder how such a thing can happen, I mean:

1) Is there some kind of "renormaization flow" or beta function, that makes the measure of proximity (or metric of "theory space"?) run when one goes from the effective energy scale to high energies at about the Plankck scale (or from the Planck scale down to the effective scale)?

2) What are the mechanisms that can explain such a "duality" between short and large distances in the corresponding "theory space" when going from the effective to the high energy scale or vice versa?

retagged Mar 17, 2014
Try arxiv.org/abs/hep-th/0505153

This post imported from StackExchange Physics at 2014-03-17 03:19 (UCT), posted by SE-user Mitchell Porter
@MitchellPorter Ill try it. Prof. Strassler usually explains stuff very well. I would appreciate it too, if you could shortly explain the main points of the paper in an answer ;-). For example I did not here about duality cascades before, but is this the correct term for what Im asking about (in my probably not precise enough wording)? Thanks anyway for the link :-)

This post imported from StackExchange Physics at 2014-03-17 03:19 (UCT), posted by SE-user Dilaton
No, but the paper explains Seiberg duality and RG flow very well, so it's good for your background knowledge. It should clarify the issues even if it doesn't answer the question.

This post imported from StackExchange Physics at 2014-03-17 03:19 (UCT), posted by SE-user Mitchell Porter

This is just a note to my admittedly rather confused question:

As I now see it, two low energy effectieve QFTs would be near each other if they are attracted by a ow energy fixed point of the RG flow, whereas they would be far away from each other for example when being repelled by a higher energy fixed point in the course of the RG flow.

The proximity or distance of the two QFTs could probably be measured by the relative entropy as shown in a new paper shortly summerized in this TRF article.

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