The Abelian Chern-Simons theory is considered on a cylindrical spacetime RxD, in a not necessarily flat Lorentzian background. As in the flat bulk case with planar boundary, we find that also on the radial boundary of a curved background a Kaç-Moody algebra exists, with the same central charge as in the flat case, which henceforth depends neither on the bulk metric nor on the geometry of the boundary. The holographically induced theory on the 2D boundary is topologically protected, in the sense that it describes a Luttinger liquid, no matter which the bulk metric is. The main result of this paper is that a remnant of the 3D bulk theory resides in the chiral velocity of the edge modes, which is not a constant like in the flat bulk case, but it is local, depending on the determinant of the induced metric on the boundary. This result may provide a theoretical framework for the recently observed accelerated chiral bosons on the edge of some Hall systems.

Notes from the bulk: Metric dependence of the edge states of Chern-Simons theory

Bertolini, Erica;Maggiore, Nicola
2021

Abstract

The Abelian Chern-Simons theory is considered on a cylindrical spacetime RxD, in a not necessarily flat Lorentzian background. As in the flat bulk case with planar boundary, we find that also on the radial boundary of a curved background a Kaç-Moody algebra exists, with the same central charge as in the flat case, which henceforth depends neither on the bulk metric nor on the geometry of the boundary. The holographically induced theory on the 2D boundary is topologically protected, in the sense that it describes a Luttinger liquid, no matter which the bulk metric is. The main result of this paper is that a remnant of the 3D bulk theory resides in the chiral velocity of the edge modes, which is not a constant like in the flat bulk case, but it is local, depending on the determinant of the induced metric on the boundary. This result may provide a theoretical framework for the recently observed accelerated chiral bosons on the edge of some Hall systems.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

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: http://hdl.handle.net/11567/1061943
 Attenzione

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

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 1
  • ???jsp.display-item.citation.isi??? 1
social impact