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Publications (10 of 71) Show all publications
Fuchs, J., Gannon, T., Schaumann, G. & Schweigert, C. (2018). The logarithmic Cardy case: Boundary states and annuli. Nuclear Physics B, 930, 287-327
Open this publication in new window or tab >>The logarithmic Cardy case: Boundary states and annuli
2018 (English)In: Nuclear Physics B, ISSN 0550-3213, E-ISSN 1873-1562, Vol. 930, p. 287-327Article in journal (Refereed) Published
Abstract [en]

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.

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)
Available from: 2018-04-06 Created: 2018-04-06 Last updated: 2018-09-05Bibliographically approved
Fuchs, J. & Schweigert, C. (2017). Low-dimensional topology, low-dimensional field theory and representation theory. In: Krause, H Littelmann, P Malle, G Neeb, KH Schweigert, C (Ed.), Representation theory: Current trends and perspectives. Paper presented at Research Priority Programme SPP 1388 "Representation theory", Hamburg Universität (pp. 255-267). European Mathematical Society Publishing House
Open this publication in new window or tab >>Low-dimensional topology, low-dimensional field theory and representation theory
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]

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".

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
Available from: 2017-12-29 Created: 2017-12-29 Last updated: 2018-06-26Bibliographically approved
Fuchs, J., Priel, J., Schweigert, C. & Valentino, A. (2015). On the Brauer Groups of Symmetries of Abelian Dijkgraaf-Witten Theories. Communications in Mathematical Physics, 339(2), 385-405
Open this publication in new window or tab >>On the Brauer Groups of Symmetries of Abelian Dijkgraaf-Witten Theories
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]

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.

National Category
Physical Sciences
Research subject
Physics
Identifiers
urn:nbn:se:kau:diva-41597 (URN)10.1007/s00220-015-2420-y (DOI)000358130400003 ()
Available from: 2016-04-11 Created: 2016-04-11 Last updated: 2017-11-30Bibliographically approved
Buchberger, I. & Fuchs, J. (2015). On the Killing form of Lie Algebras in Symmetric Ribbon Categories. SIGMA. Symmetry, Integrability and Geometry, 11, Article ID 017.
Open this publication in new window or tab >>On the Killing form of Lie Algebras in Symmetric Ribbon Categories
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]

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.

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 ()
Available from: 2016-04-11 Created: 2016-04-11 Last updated: 2017-11-30Bibliographically approved
Fuchs, J. & Schweigert, C. (2015). Surface defects and symmetries. In: XXXTH International Colloquium on Group Theoretical Methods in Physics (ICGTMP) (GROUP30): . Paper presented at 30th International Colloquium on Group Theoretical Methods in Physics (ICGTMP), Jul 14-18, 2014, Ghent, Belgium. Institute of Physics (IOP), Article ID 012002.
Open this publication in new window or tab >>Surface defects and symmetries
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]

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.

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
Available from: 2016-04-11 Created: 2016-04-11 Last updated: 2016-05-31Bibliographically approved
Fuchs, J., Schweigert, C. & Valentino, A. (2014). A geometric approach to boundaries and surface defects in Dijkgraaf-Witten theories. Communications in Mathematical Physics, 332, 981-1015
Open this publication in new window or tab >>A geometric approach to boundaries and surface defects in Dijkgraaf-Witten theories
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]

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.

National Category
Subatomic Physics
Research subject
Physics
Identifiers
urn:nbn:se:kau:diva-34289 (URN)10.1007/s00220-014-2067-0 (DOI)000342421400004 ()
Funder
Swedish Research Council, 621-2009-3993
Available from: 2014-10-12 Created: 2014-10-12 Last updated: 2017-12-05Bibliographically approved
Fuchs, J. & Schweigert, C. (2014). A note on permutation twist defects in topological bilayer phases. Letters in Mathematical Physics, 104(1), 1385-1405
Open this publication in new window or tab >>A note on permutation twist defects in topological bilayer phases
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]

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.

National Category
Subatomic Physics
Research subject
Physics
Identifiers
urn:nbn:se:kau:diva-34290 (URN)10.1007/s11005-014-0719-9 (DOI)000343727400003 ()
Funder
Swedish Research Council, 621-2009-3993
Available from: 2014-10-12 Created: 2014-10-12 Last updated: 2017-12-05Bibliographically approved
Bai, C., Fuchs, J., Huang, Y.-Z., Kong, L., Runkel, I. & Schweigert, C. (Eds.). (2014). Conformal Field Theories and Tensor Categories: Proceedings of a Workshop Held at Beijing International Center for Mathematical Research. Paper presented at Workshop on Conformal Field Theories and Tensor Categories, Beijing International Center for Mathematical Research, 13.17 june 2011. Heidelberg: Springer Berlin/Heidelberg
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
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2014 (English)Conference proceedings (editor) (Refereed)
Abstract [en]

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.

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
Funder
Swedish Research Council, 621-2009- 3993
Available from: 2014-10-12 Created: 2014-10-12 Last updated: 2015-09-09Bibliographically approved
Fuchs, J., Schweigert, C. & Stigner, C. (2014). Higher genus mapping class group invariants from factorizable Hopf algebras. Advances in Mathematics, 250, 285-319
Open this publication in new window or tab >>Higher genus mapping class group invariants from factorizable Hopf algebras
2014 (English)In: Advances in Mathematics, ISSN 0001-8708, E-ISSN 1090-2082, Vol. 250, p. 285-319Article in journal (Refereed) Published
Abstract [en]

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.

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 ()
Available from: 2013-11-26 Created: 2013-11-26 Last updated: 2017-12-06Bibliographically approved
Fuchs, J., Schweigert, C. & Valentino, A. (2013). Bicategories for boundary conditions and for surface defects in 3-d TFT. Communications in Mathematical Physics, 321(2), 543-575
Open this publication in new window or tab >>Bicategories for boundary conditions and for surface defects in 3-d TFT
2013 (English)In: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 321, no 2, p. 543-575Article in journal (Refereed) Published
Abstract [en]

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

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 ()
Available from: 2013-04-13 Created: 2013-04-13 Last updated: 2017-12-06Bibliographically approved
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Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0003-4081-6234

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