Exploring the Complexities of Space-time Supersymmetry and Supergravity

In summary, Space-time Supersymmetry is a global symmetry, while Supergravity is a theory that describes how the commutators of space-time supersymmetry charges are generators of the Poincare algebra.
  • #1
wam_mi
81
1
Hi there,

What is the difference between Space-time Supersymmetry and Supersymmetry?
Is Space-time Supersymmetry the same thing as Supergravity? What is Supergravity...

All these terms make me very confused...

Thanks a lot!
 
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  • #2
Hi,

I think this distinction comes in the context of string theory.

In string theory one has a string (duh), and on this string you define oscillator modes. The simplest string theories are just bosonic. You can also add fermionic degrees of freedom to your string in order to be able to describe fermions. However, these are degrees of freedom on your worldsheet. So you need to distinguish between supersymmetry on your worldsheet (turning bosonic degrees of freedom into fermionic ones) and supersymmetry in spacetime! Ofcourse, it turns out that fermionic and bosonic degrees of freedom on the worldsheet can be interpreted as bosons and fermions in spacetime, but this is not trivial! These particles are in a representation of the Poincaré group and it's not trivial that your worldsheet degrees of freedom neatly fit into these Poincare representations.

Now, space-time supersymmetry is the ordinary supersymmetry you encounter when you don't talk about strings. This is not the same as supergravity! Space-time supersymmetry is a global symmetry; the transformation parameters don't depend on coordinates. However, if you gauge this space-time symmetry, you can show that you introduce diffeomorphism invariance in the theory. A gauge theory with diffeomorphism invariance necessarily contains a dynamical metric, a graviton and hence describes gravity: Supergravity! (I believe this has to do with the fact that as soon as you start to quantize a spin-2 gauge theory you need diffeomorphism invariance to avoid negative-norm states, and the other way around can also be shown).

Hope this helps, but I'm not an expert on this, so maybe I say things which are not entirely true :P
 
  • #3
Typically in QM and in QFT for each symmetry you have a set of generators. Angular momentum operators generate rotations, for example. They are a subset of the Poincare algebra which consists of rotations, boosts and translations (space- and timelike).

These generators are conserved quantities due to the Noether theorem:
Lagrangian with symmetry (*) => conserved charge dQ/dt=0 => charge operator => qm generator of the symmetry (*)

Now you have such conserved charges which act as generators of SUSY. These charges do not transform as Lorentz-scalars but as Lorentz spinors! And the commutators of these charges are generators of the well-known Poincare algebra.
 
  • #4
tom.stoer said:
Typically in QM and in QFT for each symmetry you have a set of generators. Angular momentum operators generate rotations, for example. They are a subset of the Poincare algebra which consists of rotations, boosts and translations (space- and timelike).

These generators are conserved quantities due to the Noether theorem:
Lagrangian with symmetry (*) => conserved charge dQ/dt=0 => charge operator => qm generator of the symmetry (*)

Now you have such conserved charges which act as generators of SUSY. These charges do not transform as Lorentz-scalars but as Lorentz spinors! And the commutators of these charges are generators of the well-known Poincare algebra.

Hi there,

Where can I find some review articles about space-time supersymmetry?

Cheers!
 
  • #5
The notes by Aitchison or Bilal are very nice, I think :)
 
  • #6
Last edited by a moderator:

1. What is the concept of space-time supersymmetry?

Space-time supersymmetry is a theoretical framework that combines the concepts of space-time and supersymmetry. It suggests that for every fundamental particle in the universe, there exists a partner particle with different spin properties. This symmetry between particles and their partners is thought to exist at the most fundamental level of our universe.

2. How does space-time supersymmetry relate to the theory of relativity?

Space-time supersymmetry is an extension of the theory of relativity. It suggests that space and time are not separate entities, but are intertwined in a 4-dimensional continuum. This concept is known as space-time and is a fundamental element in the theory of relativity.

3. What evidence supports the existence of space-time supersymmetry?

Currently, there is no direct evidence for the existence of space-time supersymmetry. However, it is a key component in many theories that attempt to unify the four fundamental forces of nature (gravity, electromagnetism, strong and weak nuclear forces). Additionally, some predictions of supersymmetry, such as the existence of dark matter particles, have been supported by observational data.

4. What are the potential implications of proving the existence of space-time supersymmetry?

If space-time supersymmetry is proven to exist, it would have significant implications for our understanding of the universe. It could help explain the nature of dark matter, provide a more complete picture of the fundamental forces, and potentially lead to the development of new technologies and applications.

5. How are scientists currently researching and testing the concept of space-time supersymmetry?

Scientists are using a variety of methods to research and test the concept of space-time supersymmetry. These include experiments at particle accelerators, such as the Large Hadron Collider, and theoretical calculations using mathematical models. Additionally, astronomers are studying the effects of dark matter and the structure of the universe to look for potential evidence of supersymmetric particles.

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