It is shown that it is possible to define quantum field theory of a massless scalar free field on the event horizon of a 2D-Rindler spacetime. Free quantum field theory on the horizon enjoys diffeomorfism invariance and turns out to be unitarily and algebraically equivalent to the analogous theory of a scalar field prapogating inside Rindler spacetime, nomatter the value of the mass of the field in the bulk. More precisely, there exist a unique transformation that realizes the bulk-boundary correspondence upon an appropriate choice for Fock representation spaces. Secondly, the found correspondence is a subcase of an analogous algebraic correspondence described by the injective homomorphisms of the abstract algebras of observables generated by abstract quantum free-field operators. These field operators are smeared with suitable test functions in the bulk and exact 1-forms on the horizon. In this sense the correspondence is independent from the chosen vacua. It is proven that, under that correspondence the 'hidden' SL(2,R) quantum symmetry found in a previous work gets a clear geometric meaning, it being associated with a group of diffeomorphisms of the horizon itself. Finally it is found that there is a possible enlargement of the quantum symmetry on the horizon to a quantum Virasoro symmetry associated with vector fields on the event horizon.

Holography, SL(2,R) symmetry, Virasoro algebra and all that in Rindler spacetime / Pinamonti, Nicola; Moretti, Valter. - ELETTRONICO. - (2003), pp. 1-35.

Holography, SL(2,R) symmetry, Virasoro algebra and all that in Rindler spacetime

Moretti, Valter
2003-01-01

Abstract

It is shown that it is possible to define quantum field theory of a massless scalar free field on the event horizon of a 2D-Rindler spacetime. Free quantum field theory on the horizon enjoys diffeomorfism invariance and turns out to be unitarily and algebraically equivalent to the analogous theory of a scalar field prapogating inside Rindler spacetime, nomatter the value of the mass of the field in the bulk. More precisely, there exist a unique transformation that realizes the bulk-boundary correspondence upon an appropriate choice for Fock representation spaces. Secondly, the found correspondence is a subcase of an analogous algebraic correspondence described by the injective homomorphisms of the abstract algebras of observables generated by abstract quantum free-field operators. These field operators are smeared with suitable test functions in the bulk and exact 1-forms on the horizon. In this sense the correspondence is independent from the chosen vacua. It is proven that, under that correspondence the 'hidden' SL(2,R) quantum symmetry found in a previous work gets a clear geometric meaning, it being associated with a group of diffeomorphisms of the horizon itself. Finally it is found that there is a possible enlargement of the quantum symmetry on the horizon to a quantum Virasoro symmetry associated with vector fields on the event horizon.
2003
Trento, Italia
Università degli Studi di Trento. Dipartimento di Matematica
Holography, SL(2,R) symmetry, Virasoro algebra and all that in Rindler spacetime / Pinamonti, Nicola; Moretti, Valter. - ELETTRONICO. - (2003), pp. 1-35.
Pinamonti, Nicola; Moretti, Valter
File in questo prodotto:
File Dimensione Formato  
UTM640.pdf

accesso aperto

Tipologia: Versione editoriale (Publisher’s layout)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 518.47 kB
Formato Adobe PDF
518.47 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/358798
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? ND
  • OpenAlex ND
social impact