581 research outputs found
Integrable perturbations of conformal field theories and Yetter-Drinfeld modules
No full textIn this paper we relate a problem in representation theory - the study of Yetter-Drinfeld modules over certain braided Hopf algebras - to a problem in two-dimensional quantum field theory, namely, the identification of integrable perturbations of a conformal field theory. A prescription that parallels Lusztig's construction allows one to read off the quantum group governing the integrable symmetry. As an example, we illustrate how the quantum group for the loop algebra of sl(2) appears in the integrable structure of the perturbed uncompactified and compactified free boson. (C) 2014 AIP Publishing LLC.German Research Foundation (DFG) [SFB 676
Modifizierte Spuren und monadische Kointegrale für quasi-Hopfalgebren
No full textWe introduce the notion of γ-symmetrized cointegrals for a finite-dimensional pivotal quasi-Hopf algebra H over a field k, where γ is the modulus of J In case H is unimodular and k is algebraically closed, we give explicit bijections relating them to non-degenerate left and right modified traces on the tensor ideal of projective H-modules in the (finite tensor) category of finite-dimensional left H-modules, generalizing previous Hopf-algebraic results from Beliakova-Blanchet-Gainutdinov.
Then we introduce monadic cointegrals in (pivotal) finite tensor categories. For a pivotal finite tensor category C, four versions (A₁, ..., A₄) of the so-called central Hopf monad exist. A monadic cointegral for A_i is a morphism of A_i-modules 1 -> A_i(D), where D is the distinguished invertible object of C; we relate them to Shimizu's categorical cointegral, and in the braided case to the integral of Lyubashenko's Hopf algebra ∫^(X in C) X* x X. If C is the category of modules over a pivotal Hopf algebra H, then one easily sees that the four monadic cointegrals are given by four notions of cointegrals for H, including γ-symmetrized cointegrals. We show that this relation, up to non-trivial isomorphisms, remains true if H is a quasi-Hopf algebra, i.e. we relate the cointegrals of Hausser and Nill and the γ-symmetrized cointegrals above to monadic cointegrals for the category of H-modules.
Finally, for a modular tensor category C, we concern ourselves with the projective SL(2,Z)-actions (on certain Hom-spaces in C) constructed by Lyubashenko. In the case that C is the category of modules over a factorizable ribbon quasi-Hopf algebra H, we derive a simple expression for the action of the S- and T-generators on the center of H using the monadic cointegral. Let now H be the quasi-Hopf algebra modification of the restricted quantum group of SL(2,Z) at a primitive 2p-th root of unity as constructed by Creutzig-Gainutdinov-Runkel, for an integer p ≥ 2. We show that Lyubashenko's action on the center of H agrees projectively with the SL(2,Z)-action on the center of the (original) restricted quantum group, as constructed by Feigin-Gainutdinov-Semikhatov-Tipunin
Logarithmic bulk and boundary conformal field theory and the full centre construction
No full textWe review the definition of bulk and boundary conformal field theory in a way suited for logarithmic conformal field theory. The notion of a maximal bulk theory which can be non-degenerately joined to a boundary theory is defined. The purpose of this construction is to obtain the more complicated bulk theories from simpler boundary theories. We then describe the algebraic counterpart of the maximal bulk theory, namely the so-called full centre of an algebra in an abelian braided monoidal category. Finally, we illustrate the previous discussion in the example of the W 2,3-model with central charge 0
Sabotaging Potential Rivals
No full textThis paper studies sabotage in a contest with non-identical players. Unlike previous papers, we consider sabotage in an elimination contest and allow contestants to sabotage a potential or future rival. It turns out that for a certain partition of players there is a pure-strategy equilibrium in which only the most able contestant engages in sabotage while less able contestants do not. The most able contestant may therefore prefer a situation where sabotage is allowed to one where sabotage is not allowed. For another partition of players, there is a unique equilibrium in which none of the players invests in sabotage.all-pay auction, elimination contests, potential rival, sabotage
Mapping class group actions and their applications to 3D gravity
No full textIn this thesis we study mapping class group actions of the three-dimensional Reshetikhin-Turaev topological quantum field theory motivated by questions in three-dimensional quantum gravity where mapping class group averages appear as candidates for gravity partition functions. One of the main results is a bulk-boundary correspondence between mapping class group averages and a rational conformal field theory whose chiral mapping class group representations are irreducible and obey a finiteness property. As primary examples we find that Ising-type modular fusion categories and their Reshetikhin-Turaev topological quantum field theories are characterised by these properties. Finally, for a given modular fusion category C we show that if the mapping class group representation on every surface without marked points is irreducible then there is a unique indecomposable C-module category with module trace, namely C itself. Such module categories describe surface defects in three-dimensional Reshetikhin-Turaev topological quantum field theories. This links irreducibility of mapping class group representations and absence of non-trivial surface defects
Ingo Plag, Word-Formation in English (2
No full text1. General observations Ingo Plag is Professor of English Linguistics at Heinrich-Heine-Universität Düsseldorf. He has published articles in specialized journals like Linguistics, Language or English Language and Linguistics and in works like the Yearbook of Morphology [2001], Word-Formation: An International Handbook of the Languages of Europe [2016] or Word Knowledge and Word Usage: A Cross-Disciplinary Guide to the Mental Lexicon [2017]. He is the author of Morphological Productivity: Stru..
Defects and orbifolds in 3-dimensional TQFTs
No full textIn this work we discuss defects and generalised orbifolds in 3-dimensional topological quantum field theories (TQFTs) of Reshetikhin-Turaev (RT) type. Generalised orbifolds provide one with a way to construct new TQFTs via a state-sum construction, internal to a fixed defect TQFT, i.e. having decorated stratified bordisms as the source category. The input needed for this procedure is called an orbifold datum. The main results of this work consist of constructing modular fusion categories out of orbifold data in the defect TQFTs of RT type and proving that the resulting generalised orbifolds are themselves TQFTs of RT type. We also explore several examples of modular fusion categories obtained this way, relating our approach to other constructions on modular fusion categories and demonstrating how it can be used to address some classification problems concerning them. Finally, we apply the above results to study surface defects separating two different theories of RT type
Topologische Gitterquantenfeldtheorien in zwei Dimensionen
No full textIn this thesis I constructed a combinatorial model for r-spin, in particular spin, and framed surfaces. It is based on triangulations plus extra combinatorial data and describes closed surfaces as well as surfaces with parametrised boundary. Using this model I constructed a two-dimensional lattice topological quantum field theory (tqft) on r-spin and on framed surfaces. The algebraic input data to this tqft then consists of a Δ-separable Frobenius algebra. For r-spin tqfts its Nakayama automorphism N must satisfy N^r = 1, for framed surfaces there is no condition on N.
The lattice construction is also compared to results from the cobordism hypothesis, a comparison made more interesting in this case as framed surfaces on the lattice side can be considered.
The lattice construction used in this thesis is closely related to defect networks, applicable to general 2d-qfts. It is expected that translating the method to defect networks allows constructing (r-)spin-qfts from ordinary qfts and this thesis is indeed the foundation for that program.
A completion of the above mentioned defect-networks program should shed more light on this connection.Die Arbeit besteht aus zwei wesentlichen Teilen. Im ersten Teil wird ein kombinatorisches Modell für Flächen mit r-Spinstruktur und Flächen mit Rahmung konstruiert. Das verwendete Modell besteht aus Triangulierungen mit Zusatzdaten und schließt auch Flächen mit parametrisiertem Rand mit ein. Im zweiten Teil wird das kombinatorische Modell zur Konstruktion einer topologischen Gitterquantenfeldtheorie auf diesen Flächen verwendet. Die notwendigen algebraischen Eingangsdaten sind dann eine Δ-separable Frobeniusalgebra. Im r-spin Fall muss deren Nakayamaautomorphismus zur r-ten Potenz die Identitätsabbildung sein während es im Fall von gerahmten Flächen keine Bedingung für N gibt.
Die konstruierte Gitterfeldtheorie kann mit Resultaten aus der Kobordismushypothese verglichen werden. Dies ist vor allem deshalb interessant weil in der Gitterkonstruktion Flächen mit Rahmung betrachtet werden können.
Die Gitterkonstruktion ist auch nah verwandt mit Defektnetzwerken, welche in zweidimensionalen Quantenfeldtheorien verwendet werden können. Diese Arbeit legt die Grundlagen um solche Defektnetzwerke zur Konstruktion von (r-)Spin-Quantenfeldtheorien aus anderen Quantenfeldtheorien zu verwenden.
Eine weitergehende Untersuchung der genannten Defektnetzwerke sollte diese Verbindung noch besser klären
Reshetikhin–Turaev TQFTs Close Under Generalised Orbifolds
No full textWe specialise the construction of orbifold graph TQFTs introduced in Carqueville et al. (Orbifold graph TQFTs) to Reshetikhin–Turaev defect TQFTs. We explain that the modular fusion category CA constructed in Mulevičius and Runkel (Quant Topol 13(3):459–523, 2023. https://doi.org/10.4171/QT/170 ) from an orbifold datum A in a given modular fusion category C is a special case of the Wilson line ribbon categories introduced as part of the general theory of orbifold graph TQFTs. Using this, we prove that the Reshetikhin–Turaev TQFT obtained from CA is equivalent to the orbifold of the TQFT for C with respect to the orbifold datum A
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