# Exploring Symmetry in Extra Dimensions: SO(n,1) & SO(3,1)xG

• timb00
In summary, the conversation discusses the common approach of starting theories with a space time symmetry given by SO(n,1) (n>4) and then compactifying the spectrum to SO(3,1)xG. The speaker questions if there are other groups that can also have SO(3,1) as a subgroup, and suggests looking at larger groups such as SO(p,q) to allow for more symmetry. They also mention the finite amount of groups and using dynkin diagrams to find a group containing SO(3,1).
timb00
Hi how,

in my master project I am working on extra dimensions and I am asking my self
why is it common to start most of the theories with a space time symmetry given by
SO(n,1) (n>4) and then compactify the obtained spectrum to SO(3,1)xG (where G is an abitrary symmetry group).

Because I think there might be other groups which have the SO(3,1) as subgroup as well?

In my question I said that "most of the theories" working in such a way. This means that all models I have seen, working in that fashion.

I hope you understand my question, otherwise ask and i will do my best to explain my
question further.

best regards,

timb00

P.s. : sorry for my bad English.

Because then you start out with having Lorentz symmetry in the whole space. What kind of spacetime symmetries in the whole space would you propose? :)

Because there is a finite amount of groups and the bigger they get the more symmetries they contain. They usually look at SO(p,q) bigger than S0(3,1) in spatial dimensions because the conformal group doesn't have enough symmetry hence moving to a bigger rotation group will allow for more symmetry and then you can compactify the extra spatial dimensions to get around that. Also going back to what I said about a finite amount of groups you can look at dynkin diagrams to show you this hence finding a group that contains S0(3,1) is not unique.

## 1. What is the significance of exploring symmetry in extra dimensions?

Exploring symmetry in extra dimensions can help us better understand the fundamental laws of nature and potentially reveal new insights into the structure of the universe. It also allows us to investigate the possibility of extra dimensions beyond the three spatial dimensions that we are familiar with.

## 2. What is SO(n,1) & SO(3,1)xG?

SO(n,1) and SO(3,1)xG are mathematical groups that represent symmetries in higher-dimensional spaces. SO(n,1) is a group of rotations and reflections in n+1 dimensions, while SO(3,1)xG is a group of symmetries in 4-dimensional spacetime.

## 3. How does symmetry in extra dimensions relate to string theory?

String theory is a theoretical framework that attempts to reconcile the theories of general relativity and quantum mechanics. In string theory, extra dimensions are necessary to make the equations consistent, and symmetry in these extra dimensions plays a crucial role in the theory.

## 4. Can we observe these extra dimensions?

Currently, there is no experimental evidence for the existence of extra dimensions. However, some theories, such as string theory, suggest that these dimensions may be compactified and too small for us to detect with our current technology. Others propose that extra dimensions may manifest themselves through effects that we can observe, such as deviations from the laws of gravity.

## 5. How does this research contribute to the field of theoretical physics?

Exploring symmetry in extra dimensions is a crucial aspect of theoretical physics, as it allows us to develop new theories and models that can potentially explain phenomena that cannot be explained by our current understanding of the universe. It also pushes the boundaries of our knowledge and helps us uncover new insights and connections between seemingly unrelated concepts.

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