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The resolution of field identification fixed points in diagonal coset theories
High Energy Physics - Theory · Submitted 20 Sep 1995
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim The fixed point resolution problem is solved for diagonal coset theories.
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The abstract, sentence by sentence
The fixed point resolution problem is solved for diagonal coset theories. The primary fields into which the fixed points are resolved are described by submodules of the branching spaces, obtained as eigenspaces of the automorphisms that implement field identification. To compute the characters and the modular S-matrix we use `orbit Lie algebras' and `twining characters', which were introduced in a previous paper (hep-th/9506135). The characters of the primary fields are expressed in terms of branching functions of twining characters. This allows us to express the modular S-matrix through the S-matrices of the orbit Lie algebras associated to the identification group. Our results can be extended to the larger class of `generalized diagonal cosets'.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The fixed point resolution problem is solved for diagonal coset theories. | contribution 0.53 | 0.91 | 0.88 | asserted 1.00 |
| s1 | The primary fields into which the fixed points are resolved are described by submodules of the branching spaces, obtained as eigenspaces of the automorphisms that implement field identification. | result 0.71 | 0.86 | 0.23 | asserted 1.00 |
| s2 | To compute the characters and the modular S-matrix we use `orbit Lie algebras' and `twining characters', which were introduced in a previous paper (hep-th/9506135). | method 0.99 | 0.56 | 0.06 | asserted 1.00 |
| s3 | The characters of the primary fields are expressed in terms of branching functions of twining characters. | result 0.88 | 0.90 | 0.10 | asserted 1.00 |
| s4 | This allows us to express the modular S-matrix through the S-matrices of the orbit Lie algebras associated to the identification group. | result 0.95 | 0.91 | 0.19 | asserted 0.98 |
| s5 | Our results can be extended to the larger class of `generalized diagonal cosets'. | future work 0.37 | 0.72 | 0.12 | asserted 0.56 |
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Original abstract
The fixed point resolution problem is solved for diagonal coset theories. The primary fields into which the fixed points are resolved are described by submodules of the branching spaces, obtained as eigenspaces of the automorphisms that implement field identification. To compute the characters and the modular S-matrix we use `orbit Lie algebras' and `twining characters', which were introduced in a previous paper (hep-th/9506135). The characters of the primary fields are expressed in terms of branching functions of twining characters. This allows us to express the modular S-matrix through the S-matrices of the orbit Lie algebras associated to the identification group. Our results can be extended to the larger class of `generalized diagonal cosets'.
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References
How the literature uses it
5 arXiv papers cite this in 10 sentences
Papers citing it · 4 sentences without a confident label
Uses its method or tool 1 paper
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The other subtlety is a consequence of the fact that, unlike the bosonic case, some $N=1$ superconformal cosets actually have a fixed-point, which needs to be resolved carefully, e.g. following the general prescription given in [ref] .
Defects in N=1 minimal models and RG flows · Introduction · 0.98
Uses its data or values 1 paper
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The list of Maverick cosets known to date [ref] and their central charges is: [equation] It is straightforward to check that for the Maverick cosets $G_k / H_k̃$ above there is indeed a non-abelian boson in the spectrum of the associated $G_k ×H_-k̃$ TQFT.
Non-Invertible Anyon Condensation and Level-Rank Dualities · Maverick Cosets and Dualities · 0.93
Cites it as background 4 papers
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A systematic treatment exists only for a limited class of theories, notably (generalized) diagonal coset models [ref] and Kac–Moody algebras [ref] .
Rational points in the 6d supergravity landscape and simple current extensions · Comments on fixed point resolutions · 0.96
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This is called fixed point resolution, see [ref] for some progress in this direction.
A Comment On Topological Degeneracy In Gauged WZW Models · Review Of The GKO Coset Construction · 0.85
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For the subtleties involving identification currents, we refer the reader to the original works [ref] .
Symmetries, Universes and Phases of QCD$_2$ with an Adjoint Dirac Fermion · GKO Construction, Field Identification and Fixed Points · 0.93
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