Not signed in

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

• Username
• Password
• Remember me

• Sign in using OpenID
• Remember me

• Forgot your password?
• Apply for membership

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory internal-categories k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeJan 14th 2020
   • PermaLink
   Author: Urs
   Format: MarkdownItexstarting something -- not done yet, but need to save <a href="https://ncatlab.org/nlab/revision/holography+as+Koszul+duality/1">v1</a>, <a href="https://ncatlab.org/nlab/show/holography+as+Koszul+duality">current</a>

   starting something – not done yet, but need to save

   v1, current

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeFeb 19th 2020
   • (edited Feb 19th 2020)
   • PermaLink
   Author: Urs
   Format: MarkdownItexPrompted by a new article on the arXiv today, I added pointers to "holographic duality", though these may eventually need to go to their own entry: * Kevin Costello, Davide Gaiotto, _Twisted Holography_ ([arXiv:1812.09257](https://arxiv.org/abs/1812.09257)) * Jihwan Oh, Yehao Zhou, _Feynman diagrams and $\Omega$-deformed M-theory_ ([arXiv:2002.07343](https://arxiv.org/abs/2002.07343)) Is Koszul duality still considered a thing here? It's not being mentioned anymore... <a href="https://ncatlab.org/nlab/revision/diff/holography+as+Koszul+duality/3">diff</a>, <a href="https://ncatlab.org/nlab/revision/holography+as+Koszul+duality/3">v3</a>, <a href="https://ncatlab.org/nlab/show/holography+as+Koszul+duality">current</a>

   Prompted by a new article on the arXiv today, I added pointers to “holographic duality”, though these may eventually need to go to their own entry:

   • Kevin Costello, Davide Gaiotto, Twisted Holography (arXiv:1812.09257)

   • Jihwan Oh, Yehao Zhou, Feynman diagrams and $\Omega$-deformed M-theory (arXiv:2002.07343)

   Is Koszul duality still considered a thing here? It’s not being mentioned anymore…

   diff, v3, current

3. • CommentRowNumber3.
   • CommentAuthorDavid_Corfield
   • CommentTimeFeb 19th 2020
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexNot being mentioned where? It appears in the second article you just added.

   Not being mentioned where? It appears in the second article you just added.

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeFeb 19th 2020
   • PermaLink
   Author: Urs
   Format: MarkdownItexAh, right, thanks. I was being stupid.

   Ah, right, thanks. I was being stupid.

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeOct 22nd 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to today's * [[Natalie Paquette]], Brian R. Williams, *Koszul duality in quantum field theory* ([arXiv:2110.10257](https://arxiv.org/abs/2110.10257)) <a href="https://ncatlab.org/nlab/revision/diff/holography+as+Koszul+duality/4">diff</a>, <a href="https://ncatlab.org/nlab/revision/holography+as+Koszul+duality/4">v4</a>, <a href="https://ncatlab.org/nlab/show/holography+as+Koszul+duality">current</a>

   added pointer to today’s

   • Natalie Paquette, Brian R. Williams, Koszul duality in quantum field theory (arXiv:2110.10257)

   diff, v4, current

6. • CommentRowNumber6.
   • CommentAuthorDavid_Corfield
   • CommentTimeOct 22nd 2021
   • (edited Oct 22nd 2021)
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexLooking at this entry there should be an indication explaining the 'holography' of the title. It's doing this indirectly via the link to [[AdS/CFT duality]]. But then even there at [[AdS/CFT duality]] we don't reach the term 'holography' until a way down the page, and even then there's not a link to [[holographic principle]]. I'd add something myself, but I don't know quite the extent of these terms.

   Looking at this entry there should be an indication explaining the ’holography’ of the title. It’s doing this indirectly via the link to AdS/CFT duality.

   But then even there at AdS/CFT duality we don’t reach the term ’holography’ until a way down the page, and even then there’s not a link to holographic principle.

   I’d add something myself, but I don’t know quite the extent of these terms.

7. • CommentRowNumber7.
   • CommentAuthorUrs
   • CommentTimeOct 22nd 2021
   • (edited Oct 22nd 2021)
   • PermaLink
   Author: Urs
   Format: MarkdownItexOkay, I have added a paragraph mentioning the "holographic principle" to the beginning of the Idea-section at *[[AdS/CFT correspondence]]* (as just announced in its discussion thread [here](https://nforum.ncatlab.org/discussion/9277/adscft/?Focus=96178#Comment_96178)). Regarding the present entry here on Koszul duality and holography, I should admit that, for the time being, I am using it just to record references so that I know where to find them once I want to go and read them, which by and large I have not yet. So I am not going to defend anything here for the time being, starting with the title of the entry. Scanning over the lastest article [arXiv:2110.10257](https://arxiv.org/abs/2110.10257) I find it curious that the identification of MC-elements with dgca-morphisms out of the Koszul dual is highlighted, a basic point which I had once tried to highlight [here](https://ncatlab.org/nlab/show/Maurer-Cartan+equation#AsHomomorphisms) and which underlies most articles related to $L_\infty$-algebras which I ever co-authored. Maybe that signals a point of contact. Or... scanning further through the article... maybe not :-)

   Okay, I have added a paragraph mentioning the “holographic principle” to the beginning of the Idea-section at AdS/CFT correspondence (as just announced in its discussion thread here).

   Regarding the present entry here on Koszul duality and holography, I should admit that, for the time being, I am using it just to record references so that I know where to find them once I want to go and read them, which by and large I have not yet. So I am not going to defend anything here for the time being, starting with the title of the entry.

   Scanning over the lastest article arXiv:2110.10257 I find it curious that the identification of MC-elements with dgca-morphisms out of the Koszul dual is highlighted, a basic point which I had once tried to highlight here and which underlies most articles related to $L_\infty$-algebras which I ever co-authored. Maybe that signals a point of contact. Or… scanning further through the article… maybe not :-)