How Are Gravitons Related to Closed Strings in String Theory?

[N.J.R]

I don't know the relation of graviton and closed string.
Why the graviton is closed string? And what conditions need that?
I really want to know about it in detail.(of course including formula)

 

[selfAdjoint]

The graviton in bosonic string theory comes from the interaction of the right moving excitations and the left moving ones on the string. This requires the string to be closed; on an open string the R and L excitations would just peter out at the endpoints.

 

[R0man]

Sure, I'd be happy to help explain the relation between gravitons and closed strings. First off, a graviton is a theoretical particle that is thought to be the carrier of the force of gravity. It is predicted by the theory of quantum gravity, which aims to unify the theories of general relativity and quantum mechanics.

Now, in string theory, which is a proposed theory of quantum gravity, the fundamental objects are not point-like particles, but rather tiny strings that vibrate at different frequencies. These strings can be open or closed, meaning they have two distinct ends or they form a loop. The graviton is a closed string, meaning it has no endpoints and forms a loop.

The reason for this is because the graviton is a spin-2 particle, which means it has two units of angular momentum. This is a property that is only possible for a closed string. In contrast, open strings can only have spin-0 or spin-1.

As for the conditions needed for a graviton to be a closed string, it is important to note that in string theory, the strings vibrate in extra dimensions beyond the usual four dimensions of space and time. These extra dimensions are compactified, meaning they are curled up and invisible at large scales. The graviton must exist in a 10-dimensional spacetime in order to be a closed string.

In terms of formula, the graviton is described by the graviton field, which is a tensor field that satisfies the Einstein field equations. This field is composed of closed strings and can be represented by a sum over all possible string states.

I hope this helps to clarify the relation between gravitons and closed strings. If you have any further questions, please don't hesitate to ask.