Quantcast
  • 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.

News

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

Attributions

(propose a free ad)

Site Statistics

205 submissions , 163 unreviewed
5,082 questions , 2,232 unanswered
5,353 answers , 22,789 comments
1,470 users with positive rep
820 active unimported users
More ...

  Projective superspace: why extra bosonic coordinates

+ 3 like - 0 dislike
871 views

I'm studying the projective superspace formalism for N = 4 supersymmetric $\sigma$-models in two dimensions. My question is: why do we need the extra bosonic coordinates for the manifest action?

I can see that the action (with $\sigma$ the worldsheet coordinates and $\theta$ the fermionic coordinates),

$$S = \int\mathrm{d}^{2}\sigma\mathrm{d}^{8}\theta \mathcal{L},$$

would have a Lagrangian with negative mass dimension since $[\mathrm{d}\sigma]=-1$ and $[\mathrm{d}\theta]=+1/2$ so $[\mathcal{L}]=-2$ and this would be the reason to introduce (two) extra bosonic coordinates in the superspace such that the Lagrangian would become dimensionless.

But what's wrong with a Lagrangian with negative mass dimension in this very abstract superspace? If we would reduce to normal space then there wouldn't be a problem I guess?

(My background knowledge is still very low since I'm just a master student physics so I'm looking for a simple argumentation...)


This post imported from StackExchange Physics at 2015-07-12 18:27 (UTC), posted by SE-user cherzieandkressy

asked Jul 8, 2015 in Theoretical Physics by cherzieandkressy (15 points) [ revision history ]
edited Jul 12, 2015 by Dilaton
Just for curiosity, can you tell me what references are you following? Thanks.

This post imported from StackExchange Physics at 2015-07-12 18:28 (UTC), posted by SE-user Rexcirus
Mainly arXiv:1207.1241 and old ones like sciencedirect.com/science/article/pii/0370269388908593 and sciencedirect.com/science/article/pii/0550321384905923. After some more thinking about it, I guess the main thing is that you want to describe the $\sigma$-model with your Lagrangian (just like in the N = (2,2) case where the Lagrangian is the generalised Kahler potential from which you can derive the metric and b-field). And constructing a consistent N = (4,4) Lagrangian with $[\mathcal{L}]$=-2 will be very hard I guess...

This post imported from StackExchange Physics at 2015-07-12 18:28 (UTC), posted by SE-user cherzieandkressy

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:
p$\hbar$ysicsOv$\varnothing$rflow
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
...