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Fuchs, Jürgenorcid.org/0000-0003-4081-6234

Open this publication in new window or tab >>The logarithmic Cardy case: Boundary states and annuli### Fuchs, Jürgen

### Gannon, Terry

### Schaumann, Gregor

### Schweigert, Christoph

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_0_j_idt188_some",{id:"formSmash:j_idt184:0:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_0_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_0_j_idt188_otherAuthors",{id:"formSmash:j_idt184:0:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_0_j_idt188_otherAuthors",multiple:true}); 2018 (English)In: Nuclear Physics B, ISSN 0550-3213, E-ISSN 1873-1562, Vol. 930, p. 287-327Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

Elsevier, 2018
##### National Category

Mathematics Physical Sciences
##### Research subject

Physics
##### Identifiers

urn:nbn:se:kau:diva-66940 (URN)10.1016/j.nuclphysb.2018.03.005 (DOI)000435647100012 ()2-s2.0-85044165224 (Scopus ID)
#####

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Available from: 2018-04-06 Created: 2018-04-06 Last updated: 2018-09-05Bibliographically approved

Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Engineering and Physics (from 2013).

University of Alberta, Edmonton, Canada.

Universität Wien, Austria.

Universität Hamburg, Germany.

We present a model-independent study of boundary states in the Cardy case that covers all conformal field theories for which the representation category of the chiral algebra is a – not necessarily semisimple – modular tensor category. This class, which we call finite CFTs, includes all rational theories, but goes much beyond these, and in particular comprises many logarithmic conformal field theories. We show that the following two postulates for a Cardy case are compatible beyond rational CFT and lead to a universal description of boundary states that realizes a standard mathematical setup: First, for bulk fields, the pairing of left and right movers is given by (a coend involving) charge conjugation; and second, the boundary conditions are given by the objects of the category of chiral data. For rational theories our proposal reproduces the familiar result for the boundary states of the Cardy case. Further, with the help of sewing we compute annulus amplitudes. Our results show in particular that these possess an interpretation as partition functions, a constraint that for generic finite CFTs is much more restrictive than for rational ones.

Open this publication in new window or tab >>Low-dimensional topology, low-dimensional field theory and representation theory### Fuchs, Jürgen

### Schweigert, Christoph

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_1_j_idt188_some",{id:"formSmash:j_idt184:1:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_1_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_1_j_idt188_otherAuthors",{id:"formSmash:j_idt184:1:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_1_j_idt188_otherAuthors",multiple:true}); 2017 (English)In: Representation theory: Current trends and perspectives / [ed] Krause, H Littelmann, P Malle, G Neeb, KH Schweigert, C, European Mathematical Society Publishing House, 2017, p. 255-267Conference paper, Published paper (Refereed)
##### Abstract [en]

##### Place, publisher, year, edition, pages

European Mathematical Society Publishing House, 2017
##### Series

Hamburger Beiträge zur Mathematik ; 571
##### Keywords

Topological field theory, tensor categories, categorification
##### National Category

Mathematics
##### Identifiers

urn:nbn:se:kau:diva-65475 (URN)000398985900010 ()
##### Conference

Research Priority Programme SPP 1388 "Representation theory", Hamburg Universität
#####

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Available from: 2017-12-29 Created: 2017-12-29 Last updated: 2018-06-26Bibliographically approved

Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Engineering and Physics (from 2013). Karlstads Univ, Teoret Fys, Univ Gatan 21, S-65188 Karlstad, Sweden..

Univ Hamburg, Fachbereich Math, Algebra & Zahlentheorie, Bundesstr 55, D-20148 Hamburg, Germany..

Structures in low-dimensional topology and low-dimensional geometry often combined with ideas from (quantum) field theory can explain and inspire concepts in algebra and in representation theory and their categorified versions. We present a personal view on some of these instances which have appeared within the Research Priority Programme SPP 1388 "Representation theory".

Open this publication in new window or tab >>On the Brauer Groups of Symmetries of Abelian Dijkgraaf-Witten Theories### Fuchs, Jürgen

### Priel, Jan

### Schweigert, Christoph

### Valentino, Alessandro

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_2_j_idt188_some",{id:"formSmash:j_idt184:2:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_2_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_2_j_idt188_otherAuthors",{id:"formSmash:j_idt184:2:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_2_j_idt188_otherAuthors",multiple:true}); 2015 (English)In: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 339, no 2, p. 385-405Article in journal (Refereed) Published
##### Abstract [en]

##### National Category

Physical Sciences
##### Research subject

Physics
##### Identifiers

urn:nbn:se:kau:diva-41597 (URN)10.1007/s00220-015-2420-y (DOI)000358130400003 ()
#####

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Available from: 2016-04-11 Created: 2016-04-11 Last updated: 2017-11-30Bibliographically approved

Karlstad University, Faculty of Technology and Science, Department of Physics and Electrical Engineering.

Univ Hamburg, Fachbereich Math, D-20146 Hamburg, Germany..

Univ Hamburg, Fachbereich Math, D-20146 Hamburg, Germany..

Univ Hamburg, Fachbereich Math, D-20146 Hamburg, Germany..

Symmetries of three-dimensional topological field theories are naturally defined in terms of invertible topological surface defects. Symmetry groups are thus Brauer-Picard groups. We present a gauge theoretic realization of all symmetries of abelian Dijkgraaf-Witten theories. The symmetry group for a Dijkgraaf-Witten theory with gauge group a finite abelian group A, and with vanishing 3-cocycle, is generated by group automorphisms of A, by automorphisms of the trivial Chern-Simons 2-gerbe on the stack of A-bundles, and by partial e-m dualities. We show that transmission functors naturally extracted from extended topological field theories with surface defects give a physical realization of the bijection between invertible bimodule categories of a fusion category and braided auto-equivalences of its Drinfeld center . The latter provides the labels for bulk Wilson lines; it follows that a symmetry is completely characterized by its action on bulk Wilson lines.

Open this publication in new window or tab >>On the Killing form of Lie Algebras in Symmetric Ribbon Categories### Buchberger, Igor

### Fuchs, Jürgen

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_3_j_idt188_some",{id:"formSmash:j_idt184:3:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_3_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_3_j_idt188_otherAuthors",{id:"formSmash:j_idt184:3:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_3_j_idt188_otherAuthors",multiple:true}); 2015 (English)In: SIGMA. Symmetry, Integrability and Geometry, ISSN 1815-0659, E-ISSN 1815-0659, Vol. 11, article id 017Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

NATL ACAD SCI UKRAINE, 2015
##### Keywords

Lie algebra, monoidal category, Killing form, Lie superalgebra
##### National Category

Physical Sciences
##### Research subject

Physics
##### Identifiers

urn:nbn:se:kau:diva-41659 (URN)10.3842/SIGMA.2015.017 (DOI)000350561700001 ()
#####

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Available from: 2016-04-11 Created: 2016-04-11 Last updated: 2017-11-30Bibliographically approved

Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Engineering and Physics. Karlstads Univ, Teoret Fys, S-65188 Karlstad, Sweden..

Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Engineering and Physics.

As a step towards the structure theory of Lie algebras in symmetric monoidal categories we establish results involving the Killing form. The proper categorical setting for discussing these issues are symmetric ribbon categories.

Open this publication in new window or tab >>Surface defects and symmetries### Fuchs, Jürgen

### Schweigert, Christoph

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_4_j_idt188_some",{id:"formSmash:j_idt184:4:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_4_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_4_j_idt188_otherAuthors",{id:"formSmash:j_idt184:4:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_4_j_idt188_otherAuthors",multiple:true}); 2015 (English)In: XXXTH International Colloquium on Group Theoretical Methods in Physics (ICGTMP) (GROUP30), Institute of Physics (IOP), 2015, article id 012002Conference paper, Published paper (Refereed)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Institute of Physics (IOP), 2015
##### Series

Journal of Physics Conference Series, ISSN 1742-6588 ; 597
##### National Category

Physical Sciences
##### Research subject

Physics
##### Identifiers

urn:nbn:se:kau:diva-41650 (URN)10.1088/1742-6596/597/1/012002 (DOI)000354929400002 ()
##### Conference

30th International Colloquium on Group Theoretical Methods in Physics (ICGTMP), Jul 14-18, 2014, Ghent, Belgium
#####

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Available from: 2016-04-11 Created: 2016-04-11 Last updated: 2016-05-31Bibliographically approved

Karlstad University, Faculty of Technology and Science, Department of Physics and Electrical Engineering.

Univ Hamburg, Fachbereich Math, Algebra & Zahlentheorie, D-20148 Hamburg, Germany..

In quantum field theory, defects of various codimensions are natural ingredients and carry a lot of interesting information. In this contribution we concentrate on topological quantum field theories in three dimensions, with a particular focus on Dijkgraaf-Witten theories with abelian gauge group. Surface defects in Dijkgraaf-Witten theories have applications in solid state physics, topological quantum computing and conformal field theory. We explain that symmetries in these topological field theories are naturally defined in terms of invertible topological surface defects and are thus Brauer-Picard groups.

Open this publication in new window or tab >>A geometric approach to boundaries and surface defects in Dijkgraaf-Witten theories### Fuchs, Jürgen

### Schweigert, Christoph

### Valentino, Alessandro

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_5_j_idt188_some",{id:"formSmash:j_idt184:5:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_5_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_5_j_idt188_otherAuthors",{id:"formSmash:j_idt184:5:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_5_j_idt188_otherAuthors",multiple:true}); 2014 (English)In: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 332, p. 981-1015Article in journal (Refereed) Published
##### Abstract [en]

##### National Category

Subatomic Physics
##### Research subject

Physics
##### Identifiers

urn:nbn:se:kau:diva-34289 (URN)10.1007/s00220-014-2067-0 (DOI)000342421400004 ()
#####

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##### Funder

Swedish Research Council, 621-2009-3993
Available from: 2014-10-12 Created: 2014-10-12 Last updated: 2017-12-05Bibliographically approved

Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Engineering and Physics.

Dijkgraaf-Witten theories are extended three-dimensional topological field theories of Turaev-Viro type. They can be constructed geometrically from categories of bundles via linearization. Boundaries and surface defects or interfaces in quantum field theories are of interest in various applications and provide structural insight. We perform a geometric study of boundary conditions and surface defects in Dijkgraaf-Witten theories. A crucial tool is the linearization of categories of relative bundles. We present the categories of generalized Wilson lines produced by such a linearization procedure. We establish that they agree with the Wilson line categories that are predicted by the general formalism for boundary conditions and surface defects in three-dimensional topological field theories that has been developed in arXive:1203.4568.

Open this publication in new window or tab >>A note on permutation twist defects in topological bilayer phases### Fuchs, Jürgen

### Schweigert, Christoph

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_6_j_idt188_some",{id:"formSmash:j_idt184:6:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_6_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_6_j_idt188_otherAuthors",{id:"formSmash:j_idt184:6:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_6_j_idt188_otherAuthors",multiple:true}); 2014 (English)In: Letters in Mathematical Physics, ISSN 0377-9017, E-ISSN 1573-0530, Vol. 104, no 1, p. 1385-1405Article in journal (Refereed) Published
##### Abstract [en]

##### National Category

Subatomic Physics
##### Research subject

Physics
##### Identifiers

urn:nbn:se:kau:diva-34290 (URN)10.1007/s11005-014-0719-9 (DOI)000343727400003 ()
#####

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##### Funder

Swedish Research Council, 621-2009-3993
Available from: 2014-10-12 Created: 2014-10-12 Last updated: 2017-12-05Bibliographically approved

Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Engineering and Physics.

We present a mathematical derivation of some of the most important physical quantities arising in topological bilayer systems with permutation twist defects as introduced by Barkeshli et al. in cond-mat/1208.4834. A crucial tool is the theory of permutation equivariant modular functors developed by Barmeier et al. in math.CT/0812.0986 and math.QA/1004.1825.

Open this publication in new window or tab >>Conformal Field Theories and Tensor Categories: Proceedings of a Workshop Held at Beijing International Center for Mathematical Research### Bai, Chengming

### Fuchs, Jürgen

Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Engineering and Physics.### Huang, Yi-Zhi

### Kong, Liang

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_7_j_idt188_some",{id:"formSmash:j_idt184:7:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_7_j_idt188_some",multiple:true}); ### Runkel, Ingo

### Schweigert, Christoph

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_7_j_idt188_otherAuthors",{id:"formSmash:j_idt184:7:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_7_j_idt188_otherAuthors",multiple:true}); Show others...PrimeFaces.cw("SelectBooleanButton","widget_formSmash_j_idt184_7_j_idt188_j_idt202",{id:"formSmash:j_idt184:7:j_idt188:j_idt202",widgetVar:"widget_formSmash_j_idt184_7_j_idt188_j_idt202",onLabel:"Hide others...",offLabel:"Show others..."}); 2014 (English)Conference proceedings (editor) (Refereed)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Heidelberg: Springer Berlin/Heidelberg, 2014. p. 279
##### Series

Mathematical Lectures from Peking University, ISSN 2197-4209
##### National Category

Mathematics
##### Research subject

Mathematics
##### Identifiers

urn:nbn:se:kau:diva-34292 (URN)10.1007/978-3-642-39383-9 (DOI)978-3-642-39382-2 (ISBN)
##### Conference

Workshop on Conformal Field Theories and Tensor Categories, Beijing International Center for Mathematical Research, 13.17 june 2011
#####

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##### Funder

Swedish Research Council, 621-2009- 3993
Available from: 2014-10-12 Created: 2014-10-12 Last updated: 2015-09-09Bibliographically approved

Republic of China.

USA.

Republic of China.

Germany.

Germany.

The present volume is a collection of seven papers that are either based on the talks presented at the workshop "Conformal field theories and tensor categories" held June 13 to June 17, 2011 at theBeijing International Center for Mathematical Research, Peking University, or are extensions of the material presented in the talks at the workshop. These papers present new developments beyond rational conformal field theories and modular tensor categories and new applications in mathematics and physics. The topics covered include tensor categories from representation categories of Hopf algebras, applications of conformal field theories and tensor categories to topological phases and gapped systems, logarithmic conformal field theories and the corresponding non-semisimple tensor categories, and new developments in the representation theory of vertex operator algebras. Some of the papers contain detailed introductory material that is helpful for graduate students and researchers looking for an introduction to these research directions. The papers also discuss exciting recent developments in the area of conformal field theories, tensor categories and their applications and will be extremely useful for researchers working in these areas.

Open this publication in new window or tab >>Higher genus mapping class group invariants from factorizable Hopf algebras### Fuchs, Jürgen

Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Engineering and Physics.### Schweigert, Christoph

### Stigner, Carl

Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Engineering and Physics.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_8_j_idt188_some",{id:"formSmash:j_idt184:8:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_8_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_8_j_idt188_otherAuthors",{id:"formSmash:j_idt184:8:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_8_j_idt188_otherAuthors",multiple:true}); 2014 (English)In: Advances in Mathematics, ISSN 0001-8708, E-ISSN 1090-2082, Vol. 250, p. 285-319Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

Elsevier, 2014
##### Keywords

Factorizable Hopf algebras; Mapping class groups; Modular invariant partition functions
##### National Category

Other Mathematics
##### Research subject

Physics; Mathematics
##### Identifiers

urn:nbn:se:kau:diva-30285 (URN)10.1016/j.aim.2013.09.019 (DOI)000327000400009 ()
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Available from: 2013-11-26 Created: 2013-11-26 Last updated: 2017-12-06Bibliographically approved

Hamburg University.

Lyubashenko's construction associates representations of mapping class groups Map_{g,n} of Riemann surfaces of any genus g with any number n of holes to a factorizable ribbon category. We consider this construction as applied to the category of bimodules over a finite-dimensional factorizable ribbon Hopf algebra H. For any such Hopf algebra we find an invariant of Map_{g,n} for all values of g and n. More generally, we obtain such invariants for any pair (H,omega), where omega is a ribbon automorphism of H. Our results are motivated by the quest to understand correlation functions of bulk fields in two-dimensional conformal field theories with chiral algebras that are not necessarily semisimple, so-called logarithmic conformal field theories.

Open this publication in new window or tab >>Bicategories for boundary conditions and for surface defects in 3-d TFT### Fuchs, Jürgen

### Schweigert, Christoph

### Valentino, Allessandro

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##### Abstract [en]

##### Place, publisher, year, edition, pages

Berlin: Springer, 2013
##### Keywords

topological boundary conditions, Reshetikhin-Turaev, Kitaev-Kong, High Energy Physics
##### National Category

Other Physics Topics
##### Research subject

Physics
##### Identifiers

urn:nbn:se:kau:diva-26925 (URN)10.1007/s00220-013-1723-0 (DOI)000320133900007 ()
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Available from: 2013-04-13 Created: 2013-04-13 Last updated: 2017-12-06Bibliographically approved

Karlstad University, Faculty of Technology and Science, Department of Physics and Electrical Engineering.

Hamburg University.

Hamburg University.

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