• 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 ...

  Background and references for topological string theory

+ 3 like - 0 dislike

Where would one start to learn about topological string theory knowing no string theory? What are the general prerequisites and what kind of background in QFT is needed? Is a conventional book like Becker or Zwiebach good or are there better routes?

asked May 26, 2016 in Resources and References by kalle44 (0 points) [ no revision ]
recategorized May 26, 2016 by Dilaton

1 Answer

+ 3 like - 0 dislike

Well, in order to understand topological strings in depth the question is more like what are the mathematical prerequisites you need.

The starting point, for a physicist, is a 2d non-linear sigma model, thus you should have some small familiarity with 2d quantum field theories. If you have studied all basics of quantum field theory you should be fine. It is assumed you know what the stress-energy tensor is, how to make field variations etc. At the same time you should know what "normal" string theory is about, why we use Calabi-Yau manifolds (and thus all basics of the geometry associated to them). Then you need to know some representation theory in order to understand how the topological twists works to get the A and the B model and it should be in principle ok to get up to the free energy of topological strings.

Topological strings are a vast subject with incredibly rich mathematical structure. I would say that knowing basics of algebraic topology (for example cohomology) and basics of algebraic geometry (for example toric varieties, sheaf cohomology) is extremely useful and at some point unavoidable. It also depends a lot on what you want to do with topological strings. If you want to study moduli spaces you have to go even more formal and at least to me any connection with "proper" physics is in a grey area. To understand homological mirror symmetry, which is some sort of duality between the A and the B model, you need to understand category theory on top of other very abstract mathematical constructions. Or, you could be interested in the (refined) topological vertex and see how to compute topological partition function via the vertex and what is the relation to the corresponding SCFT's, i.e. the relation to a 5d or 4d Nekrasov partition function.

Vonk's and Collinuci's lectures (the first hits on Google) are very good places to begin learning some stuff. For a lot more info the yellow bible (not Di Francesco's CFT) of Hori et. al. "Mirror Symmetry" is pretty awesome. I warn you for a high level of mathematical abstractness (unless you are a mathematician which should be fine). There are some nice recorded videos of Ooguri as well here and here.

answered May 26, 2016 by conformal_gk (3,625 points) [ revision history ]
edited May 26, 2016 by conformal_gk

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