# What can make a string massless?

• kcajrenreb
In summary: Supersymmetry is a way to make a string with negative mass squared into a tachyon by ensuring that there is a superpartner for every particle in the universe.
kcajrenreb
What makes some strings have mass, and others none? (eg. graviton vs. electron)

I am completely ignorant about string theory. However I am under the impression that the theory has not been developed to the point where anyone can answer your question.

It's determined by the energy in the vibrations, the higher the frequency, the higher the mass.

So a massless string has no vibration at all?

Kevin_Axion, you didn't really answer my question, how can a string become massless?

A string does not "become" massless. Mass is one (of several) resultant properties of a string's vibrations.

i.e.: Some strings vibrate in a fashion such that they manifest a property of mass, whereas some vibrate so that they do not manifest a property of mass.

http://superstringtheory.com/basics/basic5a.html

this should answer your questions. The basic principle is how the certain modes of the one dimensional string behave under the group symmetries such as E(8)xE(8) which allows us to identify how the different modes of the string behave as particles i.e being a fermion or a boson. The main answer basically about the mass is the group being used which is most likely these days G2's exceptional 8 x exceptional 8 built from the octonian generators.

Okay, I see now. Thanks guys.

kcajrenreb said:
So a massless string has no vibration at all?
Not really. A string with no vibration at all actually has a NEGATIVE mass squared. This perhaps counterintuitive fact can only be understood through quantum mechanics of strings. In supesymmetric string theory such a no-vibration mode of string is unphysical, so the next lowest (first physical) mode of vibration is massless.

Yeah, a string with negative mass squared is a tachyon, right? And supersymmetry was made to avoid that problem, correct?

Sorry for the delay, I was waiting for a response from a string theorist I was talking to:

"Sorry for the delayed reply, I have been trying to think of the best way to explain it. What you end up getting is what is known as a tower of excitations, simply put

$m^2 = (\frac{n\pi}{L})^2$

Where L is a length related to compactification, ie its a small number and n=0,+/- 1,+/-2... so that its the n=0 mode that gives you a massless particle in string theory. This isn't anything fundamental though.
For the next bit you will need tex the world add on for your browser.
In general we require gauge bosons to be massless, regardless if we are doing String Theory, GR, or any other field theory. Consider E&M, its Lagrangian density is

$\mathcal{L}=F ^{\mu\nu} F_{\mu\nu}$

Where F is the field strength tensor

$F_{\mu\nu}= \partial_\mu A_\nu-\partial_\nu A_\mu$

After some algebra you get

$F_{\mu\nu} F^{\nu\mu}=\partial_\mu A_\nu \partial ^\mu A ^\nu -\partial_\nu A_\mu \partial ^\mu A ^\nu$

Schematically this is just

$F ^2 = (\nabla A) ^2$

Which looks like part of the lagrangian that leads to the Klein Gordon equation. The crucial part that it is missing is the m2 A2 term. What happens if we put that in by hand? Its not good. A is the Gauge field, its the photon when we quantize the theory. Since its the gauge field it must obey gauge symmetry, for abelian fields this means that the lagrangian must be invariant under the transformation

$A_\mu\rightarrow A_\mu -\partial_\mu f$

where f is an arbitrary function. When we add a mass term to our original lagrangian it loses gauge invariance, therefore all gauge fields, by definition, have to be massless. The higgs mechanism allows a way around this for low energies, but that is another discussion entirely."

Last edited:
kcajrenreb said:
Yeah, a string with negative mass squared is a tachyon, right? And supersymmetry was made to avoid that problem, correct?
Right.

## 1. What is the concept of a "massless string"?

The concept of a massless string refers to a theoretical string that has no mass, meaning it has zero weight. In physics, mass is a measure of the amount of matter in an object, so a massless string would have no physical substance or particles that make it up. It is often used as a simplifying assumption in theoretical models or calculations.

## 2. Can a string in the real world be truly massless?

No, a string in the real world cannot be truly massless. All physical objects, including strings, have some amount of mass. The concept of a massless string is purely theoretical and is used as a simplifying assumption for certain calculations and models.

## 3. What factors can affect the mass of a string?

The mass of a string can be affected by various factors, including its length, thickness, and the material it is made of. For example, a longer string will have more mass than a shorter string made of the same material. Additionally, denser materials will have a greater mass than less dense materials.

## 4. How does the mass of a string impact its physical properties?

The mass of a string can impact its physical properties in several ways. A heavier string will be able to withstand more tension and is less likely to break than a lighter string. Additionally, the mass of a string can affect its vibration and resonance properties, which is important for instruments like guitars and violins.

## 5. Can the mass of a string be reduced or eliminated?

While it is not possible to completely eliminate the mass of a string, it is possible to reduce it. This can be achieved by using lighter materials or thinner strings. However, there will always be some amount of mass present, as even the smallest particles have some mass. The concept of a massless string is purely theoretical and cannot be achieved in the real world.

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