• 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
5,075 questions , 2,226 unanswered
5,347 answers , 22,749 comments
1,470 users with positive rep
818 active unimported users
More ...

  Question on Hori, Iqbal and Vafa's 'D-branes and Mirror Symmetry'

+ 1 like - 0 dislike

In the paper mentioned above, on page 19, the physics of A-type supersymmetry is related to a Lagrangian submanifold $\gamma$ of a Kaehler manifold $X$. In particular, the phrase "...holomorphic components of normal and tangent of $\gamma$..." is used.

What does one mean by the holomorphic component of a tangent vector of a Lagrangian submanifold? A Lagrangian submanifold does not necessarily have complex structure, and does not even need to be even-dimensional, so how can a tangent vector of the Lagrangian submanifold have a holomorphic component?

This post imported from StackExchange MathOverflow at 2017-04-08 22:34 (UTC), posted by SE-user Mtheorist
asked Mar 31, 2017 in Theoretical Physics by Mtheorist (100 points) [ no revision ]
retagged Apr 8, 2017
Because it says "normal and tangent", does it mean the fiber $T_p X \otimes_\mathbb{R} \mathbb{C}$ for $p \in L \subset X$? Just from the ambient complexified tangent bundle.

This post imported from StackExchange MathOverflow at 2017-04-08 22:34 (UTC), posted by SE-user AHusain

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