Solving Supersymmetry Q: U_R(1) Symmetry & theta*Q

[alphaone]

Hi
I have a question concerning the anticommuting variable theta of the superspace manifold: For a proof of some renormalisation theorems I have seen the author make use of the transformation properties of theta under the internal U_R(1) symmetry i.e. he said theta -> exp(-i alpha)*theta ,under this symmetry. Now I would like to know where this comes from. Is it coming from the fact that the SUSY generator Q does not commute with the R-symmetry and that we want theta*Q to be invariant under this symmetry? If so why do we need theta*Q to be invarint? I would really appreciate any response and if my question is not really clear please let me know as well.

 

[nonplus]

Hi
I have a question concerning the anticommuting variable theta of the superspace manifold: For a proof of some renormalisation theorems I have seen the author make use of the transformation properties of theta under the internal U_R(1) symmetry i.e. he said theta -> exp(-i alpha)*theta ,under this symmetry. Now I would like to know where this comes from. Is it coming from the fact that the SUSY generator Q does not commute with the R-symmetry and that we want theta*Q to be invariant under this symmetry? If so why do we need theta*Q to be invarint? I would really appreciate any response and if my question is not really clear please let me know as well.

I'm not an expert, but I think it goes something like this: Before we go to the superspace formalism, we know how the R-symmetry acts on the fields. To realize this symmetry in superspace, we look at for example the chiral superfield. We know how the R-symmetry acts on the components fields, the scalar and the fermion. If we look at the scalar, there are no thetas around, and so this will tell us how the entire superfield transforms.
But this transformation is only consistent with the transformation of the component fermions as long as the superspace coordinates, theta, also transforms.

I don't know if that made things clearer, I think this is explained in f.x the BUSSTEPP lectures on supersymmetry. You can find it here:
http://www.stringwiki.org/wiki/Supersymmetry_and_Supergravity

BTW: This question would probably be more at home in "beyond the standard model".

nonplus

 

[denian]

it is important to understand the underlying principles and assumptions in any mathematical proof or theory. In this case, the use of the transformation properties of theta under the internal U_R(1) symmetry is based on the concept of supersymmetry (SUSY).

SUSY is a theoretical framework that proposes a symmetry between fermions and bosons, which are two types of fundamental particles in particle physics. This symmetry is believed to exist in nature, although it has not yet been observed.

The SUSY generator Q is a mathematical operator that transforms fermions into bosons and vice versa. It is a key component of SUSY and plays a crucial role in the theory. The R-symmetry, on the other hand, is an additional symmetry that is often included in SUSY theories to explain the different masses and charges of particles.

Now, in order for the SUSY theory to hold, the SUSY generator Q must not commute with the R-symmetry. This means that the transformation of a particle under the R-symmetry will not be the same as its transformation under SUSY.

So, to answer your question, the reason why we need theta*Q to be invariant under the R-symmetry is because it is a fundamental property of SUSY. In other words, the SUSY theory would not be consistent if theta*Q did not transform in the same way as other particles under the R-symmetry.

I hope this helps clarify the concept for you. If you have any further questions or need more clarification, please do not hesitate to ask. As scientists, it is important to always seek a deeper understanding of the theories and principles we work with.