Branes with any number "n" of dimensions and laws of physics?

In summary, a brane, short for membrane, is a theoretical construct in physics that represents a higher-dimensional surface or object in a higher-dimensional space. It can have any number of dimensions, depending on the theory being studied, and is believed to play a significant role in shaping the laws of physics in our universe. While there are currently no direct real-world applications, research in this area could potentially lead to a better understanding of the fundamental forces of nature. Scientists study branes and higher dimensions through mathematical models, complex calculations, and experiments.
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Suekdccia
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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)?
 
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I can provide some insights into these questions based on my understanding of the paper and current research in this field.

1. In this paper, the authors consider the possibility of branes existing in any number of dimensions. This means that branes could potentially exist in 0, 1, 2, 3, and so on up to infinitely many dimensions. However, it is important to note that the concept of branes is still a theoretical construct and has not been experimentally proven. So, the exact number of dimensions in which branes can exist is still a matter of ongoing research and debate.

2. The concept of multiple universes or multiverse is a popular topic in theoretical physics, but it is still a highly debated and speculative idea. In this paper, the authors propose a model where branes can represent different universes with different physical laws. However, as mentioned before, this is still a theoretical construct and has not been confirmed by any experimental evidence.

Regarding the number of possible universes with different laws of physics, it is difficult to say for sure as it is highly dependent on the specific model and assumptions being made. The estimates you mentioned are based on certain assumptions about string theory and compactification of dimensions, which may not necessarily apply in this model.

As for the fundamental laws of physics changing between universes, it is again a matter of debate and speculation. Some theories propose the idea of varying fundamental constants between universes, while others suggest that the fundamental laws may remain the same but the effective laws may vary. It is also worth mentioning that the concept of a fundamental law of physics itself is still being explored and understood, and it is possible that our current understanding may change in the future.

In summary, the concept of branes and multiple universes is still a highly speculative and theoretical area of research. While this paper presents an interesting model, it is important to keep in mind that it is still a work in progress and requires further investigation and experimentation.
 

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