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| 2. |
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Algebra, Geometry, and Mathematical Physics 2010
- 2012
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Ingår i: Journal of Physics: Conference Series. - : IOP Publishing. - 1742-6596 .- 1742-6588.
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Samlingsverk (redaktörskap) (övrigt vetenskapligt/konstnärligt)abstract
- This proceedings volume presents results obtained by the participants of the 6th Baltic–Nordic workshop 'Algebra, Geometry, and Mathematical Physics (AGMP-6)' held at the Sven Lovén Centre for Marine Sciences in Tjärnö, Sweden on October 25–30, 2010. The Baltic–Nordic Network AGMP 'Algebra, Geometry, and Mathematical Physics' http://www.agmp.eu was created in 2005 on the initiative of two Estonian universities and two Swedish universities: Tallinn University of Technology represented by Eugen Paal (coordinator of the network), Tartu University represented by Viktor Abramov, Lund University represented by Sergei Silvestrov, and Chalmers University of Technology and the University of Gothenburg represented by Alexander Stolin. The goal was to promote international and interdisciplinary cooperation between scientists and research groups in the countries of the Baltic–Nordic region in mathematics and mathematical physics, with special emphasis on the important role played by algebra and geometry in modern physics, engineering and technologies. The main activities of the AGMP network consist of a series of regular annual international workshops, conferences and research schools. The AGMP network also constitutes an important educational forum for scientific exchange and dissimilation of research results for PhD students and Postdocs. The network has expanded since its creation, and nowadays its activities extend beyond countries in the Baltic–Nordic region to universities in other European countries and participants from elsewhere in the world. As one of the important research-dissimilation outcomes of its activities, the network has a tradition of producing high-quality research proceedings volumes after network events, publishing them with various international publishers.
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| 3. |
- Felder, Giovanni, et al.
(författare)
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Correlation functions and boundary conditions in RCFT and three-dimensional topology
- 2002
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Ingår i: Compositio mathematica. - : Cambridge University Press. - 0010-437X. ; 131:02, s. 189-238
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Tidskriftsartikel (refereegranskat)abstract
- We give a general construction of correlation functions in rational conformal field theory on a possibly non-orientable surface with boundary in terms of 3-dimensional topological quantum field theory. The construction applies to any modular category. It is proved that these correlation functions obey modular and factorization rules. Structure constants are calculated and expressed in terms of the data of the modular category
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| 4. |
- Fjelstad, Jens, 1971-, et al.
(författare)
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Mapping class group representations from Drinfeld doubles of finite groups
- 2020
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Ingår i: Journal of knot theory and its ramifications. - : World Scientific Publishing Co. Pte Ltd. - 0218-2165. ; 29:5
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Tidskriftsartikel (refereegranskat)abstract
- We investigate representations of mapping class groups of surfaces that arise from the untwisted Drinfeld double of a finite group G, focusing on surfaces without marked points or with one marked point. We obtain concrete descriptions of such representations in terms of finite group data. This allows us to establish various properties of these representations. In particular we show that they have finite images, and that for surfaces of genus at least 3 their restriction to the Torelli group is non-trivial iff G is non-abelian.
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| 5. |
- Fjelstad, Jens, et al.
(författare)
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RCFT with defects : Factorization and fundamental world sheets
- 2012
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Ingår i: Nuclear Physics B. - : Elsevier BV. - 0550-3213 .- 1873-1562. ; 863, s. 213-259
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Tidskriftsartikel (refereegranskat)abstract
- It is known that for any full rational conformal field theory, the correlation functions that are obtained bythe TFT construction satisfy all locality, modular invariance and factorization conditions, and that there isa small set of fundamental correlators to which all others are related via factorization – provided that theworld sheets considered do not contain any non-trivial defect lines. In this paper we generalize both resultsto oriented world sheets with an arbitrary network of topological defect lines.
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| 6. |
- Fröhlich, Jürg, et al.
(författare)
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Algebras in tensor categories and coset conformal field theories
- 2004
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Ingår i: Fortschritte der Physik. - : Wiley. - 0015-8208 .- 1521-3978. ; 52:6-7, s. 672-677
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Tidskriftsartikel (refereegranskat)abstract
- The coset construction is the most important tool to construct rational conformal field theories with known chiral data. For some cosets at small level, so-called maverick cosets, the familiar analysis using selection and identification rules breaks down. Intriguingly, this phenomenon is linked to the existence of exceptional modular invariants. Recent progress in CFT, based on studying algebras in tensor categories, allows for a universal construction of the chiral data of coset theories which in particular also applies to maverick cosets
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| 7. |
- Fuchs, Jürgen, 1957-, et al.
(författare)
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A Modular Functor From State Sums For Finite Tensor Categories And Their Bimodules
- 2022
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Ingår i: Theory and Applications of Categories. - : MOUNT ALLISON UNIV. - 1201-561X. ; 38, s. 436-594
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Tidskriftsartikel (refereegranskat)abstract
- We construct a modular functor which takes its values in the monoidal bicategory of finite categories, left exact functors and natural transformations. The modular functor is defined on bordisms that are 2-framed. Accordingly we do not need to require that the finite categories appearing in our construction are semisimple, nor that the finite tensor categories that are assigned to two-dimensional strata are endowed with a pivotal structure. Our prescription can be understood as a state-sum construction. The state-sum variables are assigned to one-dimensional strata and take values in bimodule categories over finite tensor categories, whereby we also account for the presence of boundaries and defects. Our construction allows us to explicitly compute functors associated to surfaces and representations of mapping class groups acting on them.
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| 8. |
- Fuchs, Jürgen, 1957-, et al.
(författare)
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A trace for bimodule categories
- 2017
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Ingår i: Applied Categorical Structures. - : Springer Science and Business Media LLC. - 0927-2852 .- 1572-9095. ; 25:2, s. 227-268
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Tidskriftsartikel (refereegranskat)abstract
- We study a 2-functor that assigns to a bimodule category over a finite k-linear tensor category a k-linear abelian category. This 2-functor can be regarded as a category-valued tracefor 1-morphisms in the tricategory of finite tensor categories. It is defined by a universalproperty that is a categorification of Hochschild homology of bimodules over an algebra.We present several equivalent realizations of this 2-functor and show that it has a coherent cyclic invariance.Our results have applications to categories associated to circles in three-dimensional topological field theories with defects. This is made explicit for the subclass of Dijkgraaf-Wittentopological field theories.
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| 9. |
- Fuchs, Jürgen, 1957-, et al.
(författare)
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Bicategories for boundary conditions and for surface defects in 3-d TFT
- 2013
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Ingår i: Communications in Mathematical Physics. - Berlin : Springer. - 0010-3616 .- 1432-0916. ; 321:2, s. 543-575
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Tidskriftsartikel (refereegranskat)abstract
- We analyze topological boundary conditions and topological surface defects in three-dimensional topological field theories of Reshetikhin-Turaev type based on arbitrary modular tensor categories. Boundary conditions are described by central functors that lift to trivializations in the Witt group of modular tensor categories. The bicategory of boundary conditions can be described through the bicategory of module categories over any such trivialization. A similar description is obtained for topological surface defects. Using string diagrams for bicategories we also establish a precise relation between special symmetric Frobenius algebras and Wilson lines involving special defects. We compare our results with previous work of Kapustin-Saulina and of Kitaev-Kong on boundary conditions and surface defects in abelian Chern-Simons theories and in Turaev-Viro type TFTs, respectively
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| 10. |
- Fuchs, Jürgen, 1957-, et al.
(författare)
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Bulk from boundary in finite CFT by means of pivotal module categories
- 2021
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Ingår i: Nuclear Physics B. - : Elsevier. - 0550-3213 .- 1873-1562. ; 967
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Tidskriftsartikel (refereegranskat)abstract
- We present explicit mathematical structures that allow for the reconstruction of the field content of a full local conformal field theory from its boundary fields. Our framework is the one of modular tensor categories, without requiring semisimplicity, and thus covers in particular finite rigid logarithmic conformal field theories. We assume that the boundary data are described by a pivotal module category over the modular tensor category, which ensures that the algebras of boundary fields are Frobenius algebras. Bulk fields and, more generally, defect fields inserted on defect lines, are given by internal natural transformations between the functors that label the types of defect lines. We use the theory of internal natural transformations to identify candidates for operator products of defect fields (of which there are two types, either along a single defect line, or accompanied by the fusion of two defect lines), and for bulk-boundary OPEs. We show that the so obtained OPEs pass various consistency conditions, including in particular all genus-zero constraints in Lewellen's list.
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