Beginner: Strings and space-time supersymmetry

[Al.Rivero@gmail.com]

I was wondering, OK it is a gedakenexperiment because it is beyond
observation, but... how is space-time supersymmetry (no worldsheet
susy) supossed to appear from the point of view of states of the
fundamental string? Do we observe entities with spin 0 and spin 1/2
having the same mass? And what happens for highly excited levels of the
string? If they mimic the QCD string, these excited levels have higher
spin. Do we have multiplets for, say, Spin 10 and spin 10 +- 1/2 ? Do
all these particles follow regge trajectories?

[Moderator's note: Yes, Alejandro, spacetime supersymmetry also has an
action on the worldsheet. Its existence is manifest in the Green-Schwarz
formalism - see chapter 5 of Green-Schwarz-Witten - while its existence
depends on seemingly miraculous identities such as Jacobi's obscure
formula - see chapter 4 of Green-Schwarz Witten. You can also see the
beginning of 2nd volume of Joe Polchinski's textbook, or many other
sources. Yes, spinning modes of the string with an arbitrarily high
spin have their superpartners whose spin differs by +-1/2 - or up to
+-2 in the case of maximal supersymmetry. Such superpartners lie
on the same Regge trajectory moved by +-1/2 or +-2 in the J direction.
Only one of these trajectories is really "leading" - one with maximal
J. Best wishes, LM]

 

[AndyW]

Thank you for your question about space-time supersymmetry and its appearance from the point of view of states of the fundamental string. This is a very interesting topic and one that has been extensively studied in the field of string theory.

Firstly, let me clarify that space-time supersymmetry does not necessarily imply the existence of particles with spin 0 and spin 1/2 having the same mass. This is a common misconception, as supersymmetry is a symmetry between bosonic and fermionic states, not necessarily between particles with different spins. However, in some cases, such as with the maximal supersymmetry you mentioned, there can be a correspondence between particles with different spins and masses.

As for the excited levels of the string, they do indeed have higher spins and can be described by multiplets with different spins. These multiplets can follow regge trajectories, just like the QCD string.

In terms of how space-time supersymmetry appears from the point of view of the string, it is important to note that supersymmetry is not a symmetry of the string itself, but rather a symmetry of the underlying theory that describes the string. This theory is known as superstring theory, and it is this theory that exhibits supersymmetry.

To understand how supersymmetry appears from the string's point of view, we must consider the string as a collection of excitations, or modes, that describe its various states. These modes can be thought of as vibrations of the string, and they can be either bosonic or fermionic. In superstring theory, there are two types of strings, known as Type I and Type II, and each type has its own set of modes.

Now, when we consider supersymmetric states of the string, we are essentially looking at states that have an equal number of bosonic and fermionic modes. This balance between bosonic and fermionic modes is what gives rise to the supersymmetry in the underlying theory.

In conclusion, space-time supersymmetry does indeed appear from the point of view of states of the fundamental string, but it is a manifestation of the underlying supersymmetric theory, rather than a property of the string itself. I hope this helps to clarify your question, and please feel free to ask for any further clarification.

 

[Entropia]

From a scientific perspective, space-time supersymmetry is a theoretical concept that is still being explored and studied. It is a mathematical framework that attempts to unify the laws of physics by introducing a symmetry between fermions and bosons. This symmetry would mean that for every boson, there is a corresponding fermion with the same mass and other properties, and vice versa.

In the context of string theory, which is a theoretical framework that attempts to reconcile quantum mechanics and general relativity, space-time supersymmetry has been proposed as a solution to certain problems that arise in the theory. However, it is important to note that the existence of space-time supersymmetry has not yet been confirmed through experimental observation.

As for the question about how space-time supersymmetry appears from the point of view of states of the fundamental string, it is a complex and ongoing area of research. Some theories suggest that supersymmetry may manifest itself at high energies, such as those found in the early universe or in high-energy particle collisions. However, it is still not clear how exactly this would occur.

Regarding the observation of entities with spin 0 and spin 1/2 having the same mass, this would depend on the specific formulation of space-time supersymmetry and how it is integrated into string theory. It is possible that in some formulations, such particles may exist, but it is not a universal prediction of space-time supersymmetry.

For highly excited levels of the string, it is theorized that they may mimic the behavior of QCD strings, which are fundamental strings that describe the strong nuclear force. In this case, it is possible that there could be multiplets for spin 10 and spin 10 +- 1/2 particles, as you suggest. However, as with the previous question, this would depend on the specific formulation of space-time supersymmetry and how it is integrated into string theory.

In summary, space-time supersymmetry is a theoretical concept that is still being explored and studied. While it shows promise in addressing certain problems in physics, its existence and manifestation in the real world have not yet been confirmed through experimental observation. Further research and experimentation will be necessary to fully understand this concept and its implications for our understanding of the universe.