On the Representation Theory of Virasoro Nets

Carpi, Sebastiano

doi:10.1007/s00220-003-0988-0

Cited by 56 publications

(88 citation statements)

References 50 publications

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“…We follow the strategy adopted in [8] for the case of Virasoro nets, cf. also [12,40]. An alternative construction in the case of the discrete series (c < 3/2) is outlined in Sect.…”

Section: Super-virasoro Netsmentioning

confidence: 99%

Structure and Classification of Superconformal Nets

Carpi

Kawahigashi

Longo

2008

Ann. Henri Poincaré

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We study the general structure of Fermi conformal nets of von Neumann algebras on S 1 , consider a class of topological representations, the general representations, that we characterize as Neveu-Schwarz or Ramond representations, in particular a Jones index can be associated with each of them. We then consider a supersymmetric general representation associated with a Fermi modular net and give a formula involving the Fredholm index of the supercharge operator and the Jones index. We then consider the net associated with the super-Virasoro algebra and discuss its structure. If the central charge c belongs to the discrete series, this net is modular by the work of F. Xu and we get an example where our setting is verified by considering the Ramond irreducible representation with lowest weight c/24. We classify all the irreducible Fermi extensions of any super-Virasoro net in the discrete series, thus providing a classification of all superconformal nets with central charge less than 3/2.

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“…We follow the strategy adopted in [8] for the case of Virasoro nets, cf. also [12,40]. An alternative construction in the case of the discrete series (c < 3/2) is outlined in Sect.…”

Section: Super-virasoro Netsmentioning

confidence: 99%

Structure and Classification of Superconformal Nets

Carpi

Kawahigashi

Longo

2008

Ann. Henri Poincaré

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“…In Sect. 4 we show that the maps corresponding to projective unitary representations of Diff + (S 1 ) continuously extend to a certain family of nonsmooth diffeomorphisms in an appropriate topology. The result is proved at the Lie algebra level.…”

Section: Introductionmentioning

confidence: 92%

“…With what was said before we have described all irreducible positive energy representations of the diffeomorphism group: recall ([4, Theorem A.1]) that an irreducible positive energy representation of Diff + (S 1 ) is equivalent to V (c,h) for some value of c and h. The proof in [4] is based on results in [21].…”

Section: Diffeomorphism Covariance and The Virasoro Netsmentioning

confidence: 99%

On the Uniqueness of Diffeomorphism Symmetry in Conformal Field Theory

Carpi

Weiner

2005

Commun. Math. Phys.

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A Möbius covariant net of von Neumann algebras on S 1 is diffeomorphism covariant if its Möbius symmetry extends to diffeomorphism symmetry. We prove that in case the net is either a Virasoro net or any at least 4-regular net such an extension is unique: the local algebras together with the Möbius symmetry (equivalently: the local algebras together with the vacuum vector) completely determine it. We draw the two following conclusions for such theories. (1) The value of the central charge c is an invariant and hence the Virasoro nets for different values of c are not isomorphic as Möbius covariant nets. (2) A vacuum preserving internal symmetry always commutes with the diffeomorphism symmetries. We further use our result to give a large class of new examples of nets (even strongly additive ones), which are not diffeomorphism covariant; i.e. which do not admit an extension of the symmetry to Diff + (S 1 ).

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“…For a more detailed introduction on the stress-energy tensor see for example [6,5]. The proof of the statements made in defining T relies on the so-called Virasoro operators, which can always be introduced (see the remarks in the beginning of [6,Sect.…”

Section: Diffeomorphism Covariancementioning

confidence: 99%

Conformal Covariance and Positivity of Energy in Charged Sectors

Weiner

2006

Commun. Math. Phys.

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It has been recently noted that the diffeomorphism covariance of a Chiral Conformal QFT in the vacuum sector automatically ensures Möbius covariance in all charged sectors. In this article it is shown that the diffeomorphism covariance and the positivity of the energy in the vacuum sector even ensure the positivity of the energy in the charged sectors.The main observation of this paper is that the positivity of the energy -at least in case of a Chiral Conformal QFT -is a local concept: it is related to the fact that the energy density, when smeared with some local nonnegative test functions, remains bounded from below (with the bound depending on the test function).The presented proof relies in an essential way on recently developed methods concerning the smearing of the stress-energy tensor on nonsmooth functions.

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On the Representation Theory of Virasoro Nets

Cited by 56 publications

References 50 publications

Structure and Classification of Superconformal Nets

Structure and Classification of Superconformal Nets

On the Uniqueness of Diffeomorphism Symmetry in Conformal Field Theory

Conformal Covariance and Positivity of Energy in Charged Sectors

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