# Start a new discussion

## Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

## Discussion Tag Cloud

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeJan 31st 2014

the entry modular tensor category was lacking (among many things that it is still lacking) some pointers to literature that reviews the relation to QFT. I have added a handful, maybe the best one is this here:

• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeJul 16th 2014
• (edited Jul 16th 2014)

I see that the entry modular tensor category is full of trivial typos in the text. I am too quasi-offline now to do anything about it, though. Maybe tomorrow. That entry could generally use a bit of attention.

• CommentRowNumber3.
• CommentAuthorDavid_Corfield
• CommentTimeJul 17th 2014

Fixed some typos.

• CommentRowNumber4.
• CommentAuthorUrs
• CommentTimeJul 17th 2014

Thanks!

• CommentRowNumber5.
• CommentAuthorJoe Moeller
• CommentTimeFeb 2nd 2020
The string diagram in the definition appears to be broken.
• CommentRowNumber6.
• CommentAuthorUrs
• CommentTimeMay 23rd 2021

• Colleen Delaney, Lecture notes on modular tensor categories and braid group representations, 2019 (pdf)
• CommentRowNumber7.
• CommentAuthorUrs
• CommentTimeMay 23rd 2021

• CommentRowNumber8.
• CommentAuthorUrs
• CommentTimeMay 23rd 2021

added pointer to the original article:

• CommentRowNumber9.
• CommentAuthorUrs
• CommentTimeMay 14th 2022
• (edited May 14th 2022)

Question:

the structure of a braided tensor category (and thus also that of a modular tensor category) on [ the rep categ. of a VOA ] is entirely fixed by the genus zero conformal blocks.

(here quoted from p. 36 of Ingo Runkel’s “Algebra in Braided Tensor Categories and Conformal Field Theory”, where the evident idea is indicated).

What would be a good citation of this fact as a theorem with a proof?

(I know to sift through the canonical sources on the matter, but maybe somebody knows direct pointer to volume, page and verse where this is citably proven.)

• CommentRowNumber10.
• CommentAuthorUrs
• CommentTimeMay 15th 2022

added a brief mentioning of this statement to the entry (here)

• CommentRowNumber11.
• CommentAuthorUrs
• CommentTimeMay 16th 2022

and

and used these to slightly expand the paragraph on VOAs (here)

• CommentRowNumber12.
• CommentAuthorUrs
• CommentTimeJun 10th 2022

added further original references on the construction of MTCs as VOA-representation categories:

• Yi-Zhi Huang, Rigidity and modularity of vertex tensor categories, Communications in Contemporary Mathematics 10 supp01 (2008) 871-911 $[$arXiv:math/0502533, doi:10.1142/S0219199708003083$]$

• Yi-Zhi Huang, James Lepowsky, Lin Zhang, Logarithmic tensor category theory for generalized modules for a conformal vertex algebra, I: Introduction and strongly graded algebras and their generalized modules, In: Bai, Fuchs, Huang, Kong, Runkel, Schweigert (eds.), Conformal Field Theories and Tensor Categories Mathematical Lectures from Peking University. Springer (2014) $[$arXiv:1012.4193, doi:10.1007/978-3-642-39383-9_5$]$