Lecture notes/book on conformal nets.
$begingroup$
I am looking for introductory lecture notes or a textbook on conformal nets. It should be as self-contained as possible. I am particularly interested in learning about sectors. Preferably it would have examples of conformal nets, other than the ones associated to loop groups and vertex operator algebras. I believe one can construct a conformal net using the Clifford algebra associated to the Hilbert space $L^{2}(S^{1},mathbb{C})$, a source where this example is treated in some way would be best.
I am aware of the lecture notes by Yasuyuki Kawahigashi, but they are far from self-contained.
reference-request conformal-geometry von-neumann-algebras quantum-field-theory
edited Oct 13 '17 at 13:35
Jules Lamers
18219
asked Oct 13 '17 at 9:38
PeterPeter
1,294421
$endgroup$
add a comment |
$begingroup$
I am looking for introductory lecture notes or a textbook on conformal nets. It should be as self-contained as possible. I am particularly interested in learning about sectors. Preferably it would have examples of conformal nets, other than the ones associated to loop groups and vertex operator algebras. I believe one can construct a conformal net using the Clifford algebra associated to the Hilbert space $L^{2}(S^{1},mathbb{C})$, a source where this example is treated in some way would be best.
I am aware of the lecture notes by Yasuyuki Kawahigashi, but they are far from self-contained.
reference-request conformal-geometry von-neumann-algebras quantum-field-theory
edited Oct 13 '17 at 13:35
Jules Lamers
18219
asked Oct 13 '17 at 9:38
PeterPeter
1,294421
$endgroup$
add a comment |
$begingroup$
I am looking for introductory lecture notes or a textbook on conformal nets. It should be as self-contained as possible. I am particularly interested in learning about sectors. Preferably it would have examples of conformal nets, other than the ones associated to loop groups and vertex operator algebras. I believe one can construct a conformal net using the Clifford algebra associated to the Hilbert space $L^{2}(S^{1},mathbb{C})$, a source where this example is treated in some way would be best.
I am aware of the lecture notes by Yasuyuki Kawahigashi, but they are far from self-contained.
reference-request conformal-geometry von-neumann-algebras quantum-field-theory
edited Oct 13 '17 at 13:35
Jules Lamers
18219
asked Oct 13 '17 at 9:38
PeterPeter
1,294421
$endgroup$
I am looking for introductory lecture notes or a textbook on conformal nets. It should be as self-contained as possible. I am particularly interested in learning about sectors. Preferably it would have examples of conformal nets, other than the ones associated to loop groups and vertex operator algebras. I believe one can construct a conformal net using the Clifford algebra associated to the Hilbert space $L^{2}(S^{1},mathbb{C})$, a source where this example is treated in some way would be best.
I am aware of the lecture notes by Yasuyuki Kawahigashi, but they are far from self-contained.
reference-request conformal-geometry von-neumann-algebras quantum-field-theory
reference-request conformal-geometry von-neumann-algebras quantum-field-theory
edited Oct 13 '17 at 13:35
Jules Lamers
18219
asked Oct 13 '17 at 9:38
PeterPeter
1,294421
edited Oct 13 '17 at 13:35
Jules Lamers
18219
asked Oct 13 '17 at 9:38
PeterPeter
1,294421
edited Oct 13 '17 at 13:35
Jules Lamers
18219
edited Oct 13 '17 at 13:35
Jules Lamers
18219
edited Oct 13 '17 at 13:35
Jules Lamers
18219
18219
asked Oct 13 '17 at 9:38
PeterPeter
1,294421
asked Oct 13 '17 at 9:38
PeterPeter
1,294421
asked Oct 13 '17 at 9:38
PeterPeter
1,294421
1,294421
add a comment |
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
André Henriques has written lecture notes on the topic: "Three-tier CFTs from Frobenius algebras" (arXiv:1304.7328) as well as more extensive lecture notes on conformal field theory for a course taught at Berkeley in 2014. Although they do not cover your entire wish-list, they are nicely written and self contained. You could also take a look at the PhD thesis of his student, Shan Shah, "Bicoloured torus loop groups" (arXiv:1704.02600).
answered Oct 13 '17 at 13:24
Jules LamersJules Lamers
18219
$endgroup$
1
$begingroup$
Thank you Jules! Especially the "lecture notes on conformal field theory" look very good, and from what I can see they include a description of the conformal net that I was alluding to in the question. I will leave the question open for a bit longer, but if nothing else comes up I will accept your answer.
$endgroup$
– Peter
Oct 13 '17 at 13:38
$begingroup$
@Peter You're welcome! I hope you're enjoying Germany :)
$endgroup$
– Jules Lamers
Oct 14 '17 at 12:43
$begingroup$
@Peter PS. A next time I would recommend MathOverflow for these kind of questions
$endgroup$
– Jules Lamers
Oct 31 '17 at 19:56
add a comment |
$begingroup$
In Antony Wassermann's paper Operator algebras and conformal nets the free Fermion super conformal net was constructed using Clifford algebras. The conformal net for $LSU(N)$ was constructed as a sub-theory of free fermions.
answered Dec 15 '18 at 4:41
Bin GuiBin Gui
111
$endgroup$
add a comment |
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2470388%2flecture-notes-book-on-conformal-nets%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
André Henriques has written lecture notes on the topic: "Three-tier CFTs from Frobenius algebras" (arXiv:1304.7328) as well as more extensive lecture notes on conformal field theory for a course taught at Berkeley in 2014. Although they do not cover your entire wish-list, they are nicely written and self contained. You could also take a look at the PhD thesis of his student, Shan Shah, "Bicoloured torus loop groups" (arXiv:1704.02600).
answered Oct 13 '17 at 13:24
Jules LamersJules Lamers
18219
$endgroup$
1
$begingroup$
Thank you Jules! Especially the "lecture notes on conformal field theory" look very good, and from what I can see they include a description of the conformal net that I was alluding to in the question. I will leave the question open for a bit longer, but if nothing else comes up I will accept your answer.
$endgroup$
– Peter
Oct 13 '17 at 13:38
$begingroup$
@Peter You're welcome! I hope you're enjoying Germany :)
$endgroup$
– Jules Lamers
Oct 14 '17 at 12:43
$begingroup$
@Peter PS. A next time I would recommend MathOverflow for these kind of questions
$endgroup$
– Jules Lamers
Oct 31 '17 at 19:56
add a comment |
$begingroup$
André Henriques has written lecture notes on the topic: "Three-tier CFTs from Frobenius algebras" (arXiv:1304.7328) as well as more extensive lecture notes on conformal field theory for a course taught at Berkeley in 2014. Although they do not cover your entire wish-list, they are nicely written and self contained. You could also take a look at the PhD thesis of his student, Shan Shah, "Bicoloured torus loop groups" (arXiv:1704.02600).
answered Oct 13 '17 at 13:24
Jules LamersJules Lamers
18219
$endgroup$
1
$begingroup$
Thank you Jules! Especially the "lecture notes on conformal field theory" look very good, and from what I can see they include a description of the conformal net that I was alluding to in the question. I will leave the question open for a bit longer, but if nothing else comes up I will accept your answer.
$endgroup$
– Peter
Oct 13 '17 at 13:38
$begingroup$
@Peter You're welcome! I hope you're enjoying Germany :)
$endgroup$
– Jules Lamers
Oct 14 '17 at 12:43
$begingroup$
@Peter PS. A next time I would recommend MathOverflow for these kind of questions
$endgroup$
– Jules Lamers
Oct 31 '17 at 19:56
add a comment |
$begingroup$
André Henriques has written lecture notes on the topic: "Three-tier CFTs from Frobenius algebras" (arXiv:1304.7328) as well as more extensive lecture notes on conformal field theory for a course taught at Berkeley in 2014. Although they do not cover your entire wish-list, they are nicely written and self contained. You could also take a look at the PhD thesis of his student, Shan Shah, "Bicoloured torus loop groups" (arXiv:1704.02600).
answered Oct 13 '17 at 13:24
Jules LamersJules Lamers
18219
$endgroup$
André Henriques has written lecture notes on the topic: "Three-tier CFTs from Frobenius algebras" (arXiv:1304.7328) as well as more extensive lecture notes on conformal field theory for a course taught at Berkeley in 2014. Although they do not cover your entire wish-list, they are nicely written and self contained. You could also take a look at the PhD thesis of his student, Shan Shah, "Bicoloured torus loop groups" (arXiv:1704.02600).
answered Oct 13 '17 at 13:24
Jules LamersJules Lamers
18219
answered Oct 13 '17 at 13:24
Jules LamersJules Lamers
18219
answered Oct 13 '17 at 13:24
Jules LamersJules Lamers
18219
answered Oct 13 '17 at 13:24
Jules LamersJules Lamers
18219
18219
1
$begingroup$
Thank you Jules! Especially the "lecture notes on conformal field theory" look very good, and from what I can see they include a description of the conformal net that I was alluding to in the question. I will leave the question open for a bit longer, but if nothing else comes up I will accept your answer.
$endgroup$
– Peter
Oct 13 '17 at 13:38
$begingroup$
@Peter You're welcome! I hope you're enjoying Germany :)
$endgroup$
– Jules Lamers
Oct 14 '17 at 12:43
$begingroup$
@Peter PS. A next time I would recommend MathOverflow for these kind of questions
$endgroup$
– Jules Lamers
Oct 31 '17 at 19:56
add a comment |
1
$begingroup$
Thank you Jules! Especially the "lecture notes on conformal field theory" look very good, and from what I can see they include a description of the conformal net that I was alluding to in the question. I will leave the question open for a bit longer, but if nothing else comes up I will accept your answer.
$endgroup$
– Peter
Oct 13 '17 at 13:38
$begingroup$
@Peter You're welcome! I hope you're enjoying Germany :)
$endgroup$
– Jules Lamers
Oct 14 '17 at 12:43
$begingroup$
@Peter PS. A next time I would recommend MathOverflow for these kind of questions
$endgroup$
– Jules Lamers
Oct 31 '17 at 19:56
1
1
$begingroup$
Thank you Jules! Especially the "lecture notes on conformal field theory" look very good, and from what I can see they include a description of the conformal net that I was alluding to in the question. I will leave the question open for a bit longer, but if nothing else comes up I will accept your answer.
$endgroup$
– Peter
Oct 13 '17 at 13:38
$begingroup$
Thank you Jules! Especially the "lecture notes on conformal field theory" look very good, and from what I can see they include a description of the conformal net that I was alluding to in the question. I will leave the question open for a bit longer, but if nothing else comes up I will accept your answer.
$endgroup$
– Peter
Oct 13 '17 at 13:38
$begingroup$
@Peter You're welcome! I hope you're enjoying Germany :)
$endgroup$
– Jules Lamers
Oct 14 '17 at 12:43
$begingroup$
@Peter You're welcome! I hope you're enjoying Germany :)
$endgroup$
– Jules Lamers
Oct 14 '17 at 12:43
$begingroup$
@Peter PS. A next time I would recommend MathOverflow for these kind of questions
$endgroup$
– Jules Lamers
Oct 31 '17 at 19:56
$begingroup$
@Peter PS. A next time I would recommend MathOverflow for these kind of questions
$endgroup$
– Jules Lamers
Oct 31 '17 at 19:56
add a comment |
$begingroup$
In Antony Wassermann's paper Operator algebras and conformal nets the free Fermion super conformal net was constructed using Clifford algebras. The conformal net for $LSU(N)$ was constructed as a sub-theory of free fermions.
answered Dec 15 '18 at 4:41
Bin GuiBin Gui
111
$endgroup$
add a comment |
$begingroup$
In Antony Wassermann's paper Operator algebras and conformal nets the free Fermion super conformal net was constructed using Clifford algebras. The conformal net for $LSU(N)$ was constructed as a sub-theory of free fermions.
answered Dec 15 '18 at 4:41
Bin GuiBin Gui
111
$endgroup$
add a comment |
$begingroup$
In Antony Wassermann's paper Operator algebras and conformal nets the free Fermion super conformal net was constructed using Clifford algebras. The conformal net for $LSU(N)$ was constructed as a sub-theory of free fermions.
answered Dec 15 '18 at 4:41
Bin GuiBin Gui
111
$endgroup$
In Antony Wassermann's paper Operator algebras and conformal nets the free Fermion super conformal net was constructed using Clifford algebras. The conformal net for $LSU(N)$ was constructed as a sub-theory of free fermions.
answered Dec 15 '18 at 4:41
Bin GuiBin Gui
111
answered Dec 15 '18 at 4:41
Bin GuiBin Gui
111
answered Dec 15 '18 at 4:41
Bin GuiBin Gui
111
answered Dec 15 '18 at 4:41
Bin GuiBin Gui
111
111
add a comment |
add a comment |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2470388%2flecture-notes-book-on-conformal-nets%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
