Structure and Classification of Superconformal Nets

Carpi, Sebastiano; Kawahigashi, Yasuyuki; Longo, Roberto

doi:10.1007/s00023-008-0381-9

Cited by 41 publications

(88 citation statements)

References 58 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We will denote this category by Rep net t (A K ). (3) Carpi, Longo and Kawahigashi have considered representations of net over the covering spaces of S 1 [14]. We think that unitary net representations are of the same nature of those considered by them.…”

Section: The Category Of Net Representationsmentioning

confidence: 97%

Quantum Charges and Spacetime Topology: The Emergence of New Superselection Sectors

Brunetti

Ruzzi

2008

Commun. Math. Phys.

127

View full text Add to dashboard Cite

In which is developed a new form of superselection sectors of topological origin. By that it is meant a new investigation that includes several extensions of the traditional framework of Doplicher, Haag and Roberts in local quantum theories. At first we generalize the notion of representations of nets of C * -algebras, then we provide a brand new view on selection criteria by adopting one with a strong topological flavour. We prove that it is coherent with the older point of view, hence a clue to a genuine extension. In this light, we extend Roberts' cohomological analysis to the case where 1-cocycles bear non trivial unitary representations of the fundamental group of the spacetime, equivalently of its Cauchy surface in case of global hyperbolicity. A crucial tool is a notion of group von Neumann algebras generated by the 1-cocycles evaluated on loops over fixed regions. One proves that these group von Neumann algebras are localized at the bounded region where loops start and end and to be factorial of finite type I. All that amounts to a new invariant, in a topological sense, which can be defined as the dimension of the factor. We prove that any 1-cocycle can be factorized into a part that contains only the charge content and another where only the topological information is stored. This second part resembles much what in literature are known as geometric phases. Indeed, by the very geometrical origin of the 1-cocycles that we discuss in the paper, they are essential tools in the theory of net bundles, and the topological part is related to their holonomy content. At the end we prove the existence of net representations.

show abstract

Section: The Category Of Net Representationsmentioning

confidence: 97%

Quantum Charges and Spacetime Topology: The Emergence of New Superselection Sectors

Brunetti

Ruzzi

2008

Commun. Math. Phys.

127

View full text Add to dashboard Cite

show abstract

“…[Böc96,CKL08] for further information. Following our above convention, we write F for the quasi-local C*-algebra of the net F.…”

Section: General Aspects Of Super-kms Functionalsmentioning

confidence: 99%

“…Combining supersymmetry with the above KMS property means in some sense to combine (thermo-) dynamics and supersymmetry into supersymmetric (thermo-) dynamics and corresponding supersymmetric phase transitions. Supersymmetric versions of conformal nets have been introduced mainly in [CKL08], while a few relations to supersymmetric (or sometimes called "graded") KMS functionals were studied in [BL00,Lon01]. Apart from supersymmetric dynamics and general structural interest in those functionals, one of the main motivations and applications is the construction of certain entire cyclic cocycles [JLW89,Kas89] and thus noncommutative geometric invariants [Con94].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Super-KMS Functionals for Graded-Local Conformal Nets

Hillier

2014

Ann. Henri Poincaré

View full text Add to dashboard Cite

Abstract. Motivated by a few preceding papers and a question of R. Longo, we introduce super-KMS functionals for graded translation-covariant nets over R with superderivations, roughly speaking as a certain supersymmetric modification of classical KMS states on translation-covariant nets over R, fundamental objects in chiral algebraic quantum field theory. Although we are able to make a few statements concerning their general structure, most properties will be studied in the setting of specific graded-local (super-) conformal models. In particular, we provide a constructive existence and partial uniqueness proof of super-KMS functionals for the supersymmetric free field, for certain subnets, and for the super-Virasoro net with central charge c ≥ 3/2. Moreover, as a separate result, we classify bounded super-KMS functionals for graded-local conformal nets over S 1 with respect to rotations.

show abstract

“…However, in view of the striking success of KK-theory on the one hand (e.g. [CMR07] for an overview) and the noncommutative geometrization program for (super-) conformal nets and their representations [Lon01,CKL08,CHKL10] on the other hand, we feel that there are good reasons to give a closer look at this subject, as it could possibly reveal a lot of potential for further investigations.…”

Section: Introductionmentioning

confidence: 99%