Naslov
Categorified symmetries

Autori
Schreiber, Urs ; Škoda, Zoran

Vrsta, podvrsta i kategorija rada
Radovi u zbornicima skupova, cjeloviti rad (in extenso), znanstveni

Izvornik
5th Summer School and Conference on Modern Mathematical Physics / Dragović, Branko ; Rakić, Zoran - Beograd : Institut za fiziku, Zemun, 2009, 397-424

Skup
Summer School and Conference on Modern Mathematical Physics, Institute of Physics, Belgrade, Serbia, July 6-17, 2008

Mjesto i datum
Beograd, Srbija, 06.07.2008. - 17.07.2008

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
categorification ; cocycle ; categorical group ; nonabelian cohomology ; quantum field theory ; Drinfeld double ; sigma model ; bibrane ; noncommutative geometry

Sažetak
Quantum field theory allows more general symmetries than groups and Lie algebras. For instance quantum groups, that is Hopf algebras, have been familiar to theoretical physicists for a while now. Nowdays many examples of symmetries of categorical flavor -- categorical groups, groupoids, Lie algebroids and their higher analogues -- appear in physically motivated constructions and faciliate constructions of geometrically sound models and quantization of field theories. Here we consider two flavours of categorified symmetries: one coming from noncommutative algebraic geometry where varieties themselves are replaced by suitable categories of sheaves ; another in which the gauge groups are categorified to higher groupoids. Together with their gauge groups, also the fiber bundles themselves become categorified, and their gluing (or descent data) is given by nonabelian cocycles, generalizing group cohomology, where $\infty$-groupoids appear in the role both of the domain and the coefficient object. Such cocycles in particular represent higher principal bundles, gerbes, -- possibly equivariant, possibly with connection -- as well as the corresponding associated higher vector bundles. We show how the Hopf algebra known as the Drinfeld double arises in this context.

Izvorni jezik
Engleski

Znanstvena područja
Matematika, Fizika

Napomena
Publicirana verzija je 28 stranica. Verzija arxiv/1004.2472v1 je verzija extended post publication i prosirena novim materijalom na 55 stranica. AMS MSC2010 Classification: 81T, 14A22, 18, 55N30

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