• Register
PhysicsOverflow is a next-generation academic platform for physicists and astronomers, including a community peer review system and a postgraduate-level discussion forum analogous to MathOverflow.

Welcome to PhysicsOverflow! PhysicsOverflow is an open platform for community peer review and graduate-level Physics discussion.

Please help promote PhysicsOverflow ads elsewhere if you like it.


PO is now at the Physics Department of Bielefeld University!

New printer friendly PO pages!

Migration to Bielefeld University was successful!

Please vote for this year's PhysicsOverflow ads!

Please do help out in categorising submissions. Submit a paper to PhysicsOverflow!

... see more

Tools for paper authors

Submit paper
Claim Paper Authorship

Tools for SE users

Search User
Reclaim SE Account
Request Account Merger
Nativise imported posts
Claim post (deleted users)
Import SE post

Users whose questions have been imported from Physics Stack Exchange, Theoretical Physics Stack Exchange, or any other Stack Exchange site are kindly requested to reclaim their account and not to register as a new user.

Public \(\beta\) tools

Report a bug with a feature
Request a new functionality
404 page design
Send feedback


(propose a free ad)

Site Statistics

205 submissions , 163 unreviewed
5,054 questions , 2,207 unanswered
5,347 answers , 22,726 comments
1,470 users with positive rep
818 active unimported users
More ...

  Can we have supersymmetry using real scalar instead of complex scalars?

+ 2 like - 0 dislike

I am aware that a suersymmetric theories containing a complex scalar a Weyl fermion and an auxiliary field exist.

I was wondering if we can have something analogous using real and not complex scalar fields, and some kind of real Weyl fermions (if such a thing does indeed exist).

asked Aug 15, 2015 in Theoretical Physics by Dmitry hand me the Kalashnikov (735 points) [ no revision ]

1 Answer

+ 3 like - 0 dislike

A spinor satisfying a reality condition is a Majorana spinor and the question is about the existence of a Majorana-Weyl spinor. But in four spacetime dimensions (in Lorentzian signature), no Majorana-Weyl spinor exists, the Weyl spinor is the smallest and so the minimal supersymmetry in four dimensions has four real supercharges and the scalar superpartner of a Weyl spinor has to be a complex scalar.

It is possible to find something analogous in three spacetime dimensions. In this case, the smallest spinor is a Majorana spinor, with two real components, and so the minimal supersymmetry in three dimensions has two real supercharges (half the number of the minimal supersymmetry in four dimensions) and the scalar superpartner of a Majorana spinor in three dimensions is a real scalar.

answered Aug 15, 2015 by 40227 (5,140 points) [ no revision ]

A hands-on (but not rigorous and definitive) approach would be to investigate the supermultiplets (irreducible representations) arising in the $N=1$ superfield. There, the chiral and antichiral superfields completely cover the scalar+fermion degree of freedom and what is left is only the vector+bispinor degrees of freedom (which is what you get from the "real superfield" under the Wess-Zumino gauge). I am not sure, however, whether it is not possible to get a longitudinal component of the vector field ($\sim$ spin 0 because $\partial_\mu \phi \leftrightarrow A_\mu$) from an appropriately constructed Lagrangian of the "real superfield". @silvrfuck 

Your answer

Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead.
To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL.
Please consult the FAQ for as to how to format your post.
This is the answer box; if you want to write a comment instead, please use the 'add comment' button.
Live preview (may slow down editor)   Preview
Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:
Then drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds).
Please complete the anti-spam verification

user contributions licensed under cc by-sa 3.0 with attribution required

Your rights