• 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
5,079 questions , 2,229 unanswered
5,348 answers , 22,758 comments
1,470 users with positive rep
819 active unimported users
More ...

  Flux compactifications and the scalar potential

+ 2 like - 0 dislike

Does the scalar potential:

$$V=e^K(K^{I \bar{J}})D_IW D_{\bar{J}}\bar{W}-3|W|^2$$

arise **because** of the presence of fluxes? 

If the fluxes are "turned off", does this mean $F_3=0$ and $H_3=0$, or that the integral of these field strengths over a particular cycle is zero (_i.e._ there are no non-trivial sources available in the theory)? 

I usually see the $F_3$ and $H_3$ referred to as fluxes but I always thought these were field strengths.

To be specific this whole confusion arises from studying [*The Effective Action of $\mathcal{N}= 1$ Calabi-Yau orientifolds*][1]. Footnote $9$ says not having fluxes would result in not having the $V$ potential in the $4$D action; wouldn't also the kinetic terms for the field strength vanish?

  [1]: https://arxiv.org/abs/hep-th/0403067

asked Dec 2, 2016 in Theoretical Physics by anonymous [ no revision ]

1 Answer

+ 3 like - 0 dislike

$F_3$ and $H_3$ are indeed the field strengths of 2-form gauge fields (respectively in the RR and in the NS-NS sectors). According to Maxwell equations for abelian p-form gauge fields, a vacuum configuration is obtained by taking the field strength to be an harmonic form. On a compact manifold, there is a unique harmonic representative in each cohomology class and so one can identify a vacuum configuration of the gauge field with a cohomology class for the field strength. This cohomology class is determined (up to some subtleties) by the integrals of the field strength through non-trivial cycles. These integrals are classically called fluxes and a non-trivial vacuum configurations of gauge fields is generally called "with fluxes".

Fluxes "turned off" means $F_3=H_3=0$, which is equivalent to the vanishing of all the fluxes, i.e. integrals over all the 3-cycles. If we consider $IIB$ on a Calabi-Yau 3-fold, without fluxes and without branes, the 4d effective theory in the non-compact dimensions has $\mathcal{N}=2$ SUSY and so there is no superpotential: $V=0$.

answered Dec 2, 2016 by 40227 (5,140 points) [ revision history ]
So, also the kinetic terms for the gauge fields will vanish right? Is it ok for this to happen?

I don't really understand this question. The condition fluxes "turned off" is a condition on the vacuum/background configuration of IIB superstring theory on $\mathbb{R}^{1,3} \times X$, where $X$ is the compact Calabi-Yau 3-fold. The dynamics of the string theory will involve excitations above this background and in particular, it is possible to have kinetic terms describing excitations of the gauge field even if the background configuration has zero field strength (which by the way is what happens in usual gauge theory on flat space without non-trivial topology to have fluxes). Moreover, in the 4d effective action, the gauge fields come by dimensional reduction from the 4-form gauge field of IIB in 10 dimensions and not from the 2-form gauge fields related to $F_3$ and $H_3$ (in fact, the (self-dual) field strength of the 4-form field strength has automatically zero flux because there is no non-trivial 5-cycles in general in a Calabi-Yau 3-fold).

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