# Number of Lepton Generations in string theory

• JustinLevy
In summary: People are confident in the existence of three generations, but they are also seriously considering a very heavy fourth generation, or "sterile neutrinos" and the like.
JustinLevy
Is the number of lepton generations in string theory restricted to 3? Or is this "landscape dependent"?

I don't really see what could limit the number of eigenmodes on a continuous object like the string.

I've heard that the study of the neutrino oscilations proves that there are exactly 3 generations

I thought that by various brane configurations, one could construct almost arbitrary combinations of gauge groups in string theory, including the standard model. This would mean that in String Theory a lepton generation number could be constructed to be 3, but also (almost?) any other value. Am I mistaken here?

Hi Justin---

It depends on which string theory you are working in, but in general the number of generations is topological. In other words, the geometry of the compact dimensions regulates the numbers of generations that you observe. In this sense, it is "landscape dependent".

In general, Orbb is correct when dealing with Type II model building, where you can make branes intersect. In other types of models, there are constraints on the types of gauge groups and matter that you can get. None of these constraints require three generations, but they can make it very difficult to see how one gets a gauge group that is larger than E8, for example.

BenTheMan said:
In other types of models, there are constraints on the types of gauge groups and matter that you can get. None of these constraints require three generations, but they can make it very difficult to see how one gets a gauge group that is larger than E8, for example.
Don't some string theories have multiple copies of E8?
If so, would that mean those theories predict more than 3 generations?

JustinLevy said:
Don't some string theories have multiple copies of E8?
If so, would that mean those theories predict more than 3 generations?

Well, yes to the first question and no to the second.

To the first, the multiple copies of E8 don't really talk to each other, except via gravity. One E8 is typically "hidden" from the other.

To the second, you have to work out the details, as this is a very model dependent question. Everything depends on the compact manifold.

BenTheMan said:
To the first, the multiple copies of E8 don't really talk to each other, except via gravity. One E8 is typically "hidden" from the other.
Ah, okay. I didn't realize those were "hidden sector" theories.

BenTheMan said:
To the second, you have to work out the details, as this is a very model dependent question. Everything depends on the compact manifold.
Are people confident enough that there are only three generations to use it as a constraint on the topology of the compact dimensions? Or are people still seriously considering a very heavy fourth generation, or "sterile neutrinos" and the like?

## What is string theory?

String theory is a theoretical framework that attempts to unify all of the fundamental forces of nature, including gravity, into one consistent mathematical model. It proposes that the smallest building blocks of the universe are not particles, but tiny vibrating strings.

## What is the significance of the number of lepton generations in string theory?

The number of lepton generations in string theory is significant because it affects the number of fundamental particles in the universe. In string theory, the number of lepton generations is determined by the number of compact dimensions in the universe, which in turn affects the number of fundamental particles that can exist.

## How many lepton generations are predicted by string theory?

String theory predicts that there are exactly three lepton generations in the universe. This is consistent with our current understanding of the number of lepton generations through experimental evidence and observations.

## Why is the number of lepton generations fixed in string theory?

The number of lepton generations is fixed in string theory because it is a consequence of the mathematics and symmetries of the theory. This number cannot be changed without drastically altering the underlying framework and predictions of string theory.

## What is the evidence for the number of lepton generations in string theory?

Currently, there is no direct experimental evidence for the number of lepton generations predicted by string theory. However, the predictions of string theory are consistent with experimental results and observations, providing support for the idea of three lepton generations.

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