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
   • CommentTimeSep 27th 2018
   • PermaLink
   Author: Urs
   Format: MarkdownItexPage created, but author did not leave any comments. <a href="https://ncatlab.org/nlab/revision/boundary+conformal+field+theory/1">v1</a>, <a href="https://ncatlab.org/nlab/show/boundary+conformal+field+theory">current</a>

   Page created, but author did not leave any comments.

   v1, current

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeSep 28th 2018
   • PermaLink
   Author: Urs
   Format: MarkdownItexhave now written an Idea-section here with some basics. Am still collecting references. I'd like to know to which extent the proposal has been checked concretely, that the D-brane charge classification by (equivariant, twisted) topological K-theory of the target spacetime is reproduced by equivalence classes of boundary states in the BCFT under renormalization group flow. I see some special cases have been checked, also some discrepancies seem to have been reported, but I am still looking for a non-preliminary statement. In particular I'd like to see this for fractional D-branes at $G$-orbifold singularities. How exactly does boundary state formalism here compare to the expected answer that the fractional D-branes are classified by $KU_G(\ast) \simeq R_{\mathbb{C}}(G)$? I see plenty of authors behave like this is true, but did anyone write anything close to a comprehensive proof and classification? <a href="https://ncatlab.org/nlab/revision/diff/boundary+conformal+field+theory/2">diff</a>, <a href="https://ncatlab.org/nlab/revision/boundary+conformal+field+theory/2">v2</a>, <a href="https://ncatlab.org/nlab/show/boundary+conformal+field+theory">current</a>

   have now written an Idea-section here with some basics. Am still collecting references.

   I’d like to know to which extent the proposal has been checked concretely, that the D-brane charge classification by (equivariant, twisted) topological K-theory of the target spacetime is reproduced by equivalence classes of boundary states in the BCFT under renormalization group flow. I see some special cases have been checked, also some discrepancies seem to have been reported, but I am still looking for a non-preliminary statement.

   In particular I’d like to see this for fractional D-branes at $G$-orbifold singularities. How exactly does boundary state formalism here compare to the expected answer that the fractional D-branes are classified by $KU_G(\ast) \simeq R_{\mathbb{C}}(G)$?

   I see plenty of authors behave like this is true, but did anyone write anything close to a comprehensive proof and classification?

   diff, v2, current

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeDec 17th 2022
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to: * [[Ralph Blumenhagen]], [[Erik Plauschinn]], Chapter 6 of: *Introduction to Conformal Field Theory -- With Applications to String Theory*, Lecture Notes in Physics **779**, Springer (2009) &lbrack;[doi:10.1007/978-3-642-00450-6](https://doi.org/10.1007/978-3-642-00450-6)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/boundary+conformal+field+theory/14">diff</a>, <a href="https://ncatlab.org/nlab/revision/boundary+conformal+field+theory/14">v14</a>, <a href="https://ncatlab.org/nlab/show/boundary+conformal+field+theory">current</a>

   added pointer to:

   • Ralph Blumenhagen, Erik Plauschinn, Chapter 6 of: Introduction to Conformal Field Theory – With Applications to String Theory, Lecture Notes in Physics 779, Springer (2009) [doi:10.1007/978-3-642-00450-6]

   diff, v14, current