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.
   • CommentAuthorDavid_Corfield
   • CommentTimeDec 4th 2021
   • (edited Dec 4th 2021)
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexAdded * [[Liang Kong]], Tian Lan, [[Xiao-Gang Wen]], Zhi-Hao Zhang, Hao Zheng, _Algebraic higher symmetry and categorical symmetry -- a holographic and entanglement view of symmetry_ ([arXiv:2005.14178](https://arxiv.org/abs/2005.14178)) Sounds interesting > We would like to mention that a structure similar to categorical symmetry was found previously in AdS/CFT correspondence, [63–65] where a global symmetry $G$ at the high-energy boundary is related to a gauge theory of group $G$ in the low-energy bulk. In this paper, we stress that the categorical symmetry encoded by the bulk $G$-gauge theory not only contains the $G$ symmetry at the boundary, it also contains a dual algebraic higher symmetry $\tilde{G}^{(n-1)}$ at the boundary. <a href="https://ncatlab.org/nlab/revision/diff/Xiao-Gang+Wen/8">diff</a>, <a href="https://ncatlab.org/nlab/revision/Xiao-Gang+Wen/8">v8</a>, <a href="https://ncatlab.org/nlab/show/Xiao-Gang+Wen">current</a>

   Added

   • Liang Kong, Tian Lan, Xiao-Gang Wen, Zhi-Hao Zhang, Hao Zheng, Algebraic higher symmetry and categorical symmetry – a holographic and entanglement view of symmetry (arXiv:2005.14178)

   Sounds interesting

   We would like to mention that a structure similar to categorical symmetry was found previously in AdS/CFT correspondence, [63–65] where a global symmetry $G$ at the high-energy boundary is related to a gauge theory of group $G$ in the low-energy bulk. In this paper, we stress that the categorical symmetry encoded by the bulk $G$-gauge theory not only contains the $G$ symmetry at the boundary, it also contains a dual algebraic higher symmetry $\tilde{G}^{(n-1)}$ at the boundary.

   diff, v8, current

2. • CommentRowNumber2.
   • CommentAuthorDavid_Corfield
   • CommentTimeDec 4th 2021
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexDid anything further come out of the ideas at [[holographic principle of higher category theory]]?

   Did anything further come out of the ideas at holographic principle of higher category theory?