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

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

146 submissions , 123 unreviewed
3,953 questions , 1,403 unanswered
4,889 answers , 20,762 comments
1,470 users with positive rep
507 active unimported users
More ...

D0-branes in two-dimensional ${\cal N}=(2,2)$ Landau-Ginzburg models at critical points of the superpotential

+ 3 like - 0 dislike
97 views

My question concerns Section 6.1 of Hori's 'Linear Models of Supersymmetric D-branes' (http://arxiv.org/abs/hep-th/0012179).

Firstly, some background. The quantum field theory in question is a 2d ${\cal N}=(2,2)$ Landau-Ginzburg (LG) model on a worldsheet with boundaries (e.g. the infinite strip, or a disk). Boundary conditions for the fields ought to be chosen at the boundaries. The possible boundary conditions can only preserve a subset of the supersymmetries at the boundaries, in this case only B-type supersymmetry (see Section 2.2.2 for definition) is chosen to be preserved, and the corresponding boundary conditions are called B-branes.

Now, on to my question. The B-brane studied in Section 6.1 is a D0-brane, and Hori argues that the D0-brane must be located at a critical point ($\partial_i W=0$) of the superpotential. Unfortunately, I cannot grasp his argument completely. He presents the conserved supercharge,

\begin{equation} Q={1\over 2\pi}\int d x^1\left\{ g_{i\bar{\jmath}}(\overline{\psi}_-^{\bar{\jmath}}+\overline{\psi}_+^{\bar{\jmath}})\partial_0\phi^i +g_{i\bar{\jmath}}(\overline{\psi}_-^{\bar{\jmath}}-\bar{\psi}_+^{\bar{\jmath}})\partial_1\phi^i +(\psi_-^i-\psi_+^i)\partial_iW\right\}. \end{equation}

and from there says that 'Since the boundary point, say at $x^1 = π$ is locked at that point, we see that the supersymmetry is indeed broken for any configuration. Thus, we will not consider such a D-brane. In other words, D0-branes must be located at one of the critical points of W.'

I suspect that his argument has something to do with the SUSY algebra $\{Q,Q^\dagger\}=H$, where $H$ is the Hamiltonian, and when the Hamiltonian has non-zero vacuum expectation value, there is spontaneous supersymmetry breaking. But what exactly does he mean by 'locked', and why does it imply breaking of supersymmetry? Aren't all the other fields also 'locked' at the boundary due to their boundary conditions?

This post imported from StackExchange Physics at 2016-09-28 07:45 (UTC), posted by SE-user Mtheorist
asked Sep 28, 2016 in Theoretical Physics by Mtheorist (80 points) [ no revision ]

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$\hbar$ysic$\varnothing$Overflow
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).
To avoid this verification in future, please log in or register.




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

Your rights
...