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- TL;DR Summary
- Could branes exist in any "n" number of dimensions? How would this affect to the laws of physics?

I had a few questions about this paper by Nima Arkani-Hamed, Georgi Dvali and Savas Dimopoulos (https://arxiv.org/abs/hep-th/9907209) which is closely related to the concept of branes (https://en.wikipedia.org/wiki/Brane)

1. The authors of the paper mention that the branes in the model could exist in any n dimensions. Does it mean that these branes could range from 0 to infinitely many dimensions?

2. In Brane Cosmology, usually branes are considered as different universes. Also, branes are usually closely related with string theory. Assuming this, according to some estimates based on the compactification of the number of dimensions usually discussed in string theory, there could be around 100^500 or 100^272.000 different universes with different laws of physics.

But if we have an infinite number of possible dimensions, couldn't the number of different universes with different laws be infinitely big? Even more, could the most fundamental laws of physics change between these branes/universes? Could even the most fundamental laws of physics change between universes (i.e not only the effective laws of physics could change as cosmological inflationary models and string theory usually propose as I just mentioned before, but the most fundamental laws of physics, such as the laws of conservation, of quantum mechanics, of relativity itself...etc could radically change as well)?

1. The authors of the paper mention that the branes in the model could exist in any n dimensions. Does it mean that these branes could range from 0 to infinitely many dimensions?

2. In Brane Cosmology, usually branes are considered as different universes. Also, branes are usually closely related with string theory. Assuming this, according to some estimates based on the compactification of the number of dimensions usually discussed in string theory, there could be around 100^500 or 100^272.000 different universes with different laws of physics.

But if we have an infinite number of possible dimensions, couldn't the number of different universes with different laws be infinitely big? Even more, could the most fundamental laws of physics change between these branes/universes? Could even the most fundamental laws of physics change between universes (i.e not only the effective laws of physics could change as cosmological inflationary models and string theory usually propose as I just mentioned before, but the most fundamental laws of physics, such as the laws of conservation, of quantum mechanics, of relativity itself...etc could radically change as well)?