Abstract
The relation between two-dimensional conformal quantum field theories with and without a timelike boundary is explored.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Böckenhauer J., Evans D.E. and Kawahigashi Y. (1999). On α-induction, chiral generators and modular invariants for subfactors. Commun. Math. Phys. 208: 429–487
Buchholz D., Mack G. and Todorov I.T. (1988). The current algebra on the circle as a germ of local field theories. Nucl. Phys. B (Proc. Suppl.) 5B: 20–56
Cardy J. (1984). Conformal invariance and surface critical behavior. Nucl. Phys. B 240: 514–532
Carey A.L., Ruijsenaars S.N.M. and Wright J.D. (1985). The massless Thirring model: Positivity of Klaiber’s N-point functions. Commun. Math. Phys. 99: 347–364
D’Antoni, C., Doplicher, S., Fredenhagen, K., Longo, R.: Convergence of local charges and continuity properties of W* inclusions. Commun. Math. Phys. 110, 325–348 (1987); [Erratum ibid. 116, 175–176, (1988)]
Doplicher S. and Longo R. (1984). Standard and split inclusions of von Neumann algebras. Invent. Math. 75: 493–536
Doplicher, S., Haag, R., Roberts, J.E.: Local observables and particle statistics, 1+2. Commun. Math. Phys. 23, 199–230 (1971); Commun. Math. Phys. 35, 49–85, (1974)
Fredenhagen K. and Jörß M. (1996). Conformal Haag-Kastler nets, pointlike localized fields and the existence of operator product expansions. Commun. Math. Phys. 176: 541–554
Fredenhagen K., Rehren K.-H. and Schroer B. (1989). Superselection sectors with braid group statistics, I. Commun. Math. Phys. 125: 201–226
Fredenhagen, K., Rehren, K.-H., Schroer, B.: Superselection sectors with braid group statistics, II. Rev. Math. Phys. SI1, Special issue, 113–157 (1992)
Frenkel I.B. and Kac V. (1980). Basic representation of affine Lie algebras and dual resonance models. Invent. Math. 62: 23–66
Guido D., Longo R. and Wiesbrock H.-W. (1998). Extensions of conformal nets and superselection structures. Commun. Math. Phys. 192: 217–244
Kawahigashi Y. and Longo R. (2004). Classification of local conformal nets. Case c < 1. Ann. Math. 160: 493–522
Kawahigashi Y., Longo R. and Müger M. (2001). Multi-interval subfactors and modularity of representations in conformal field theory. Commun. Math. Phys. 219: 631–669
Kawahigashi Y., Longo R., Pennig U. and Rehren K.-H. (2007). The classification of non-local chiral CFT with c < 1. Commun. Math. Phys. 271: 375–385
Longo R. (2003). Conformal subnets and intermediate subfactors. Commun. Math. Phys. 237: 7–30
Longo R. and Rehren K.-H. (1995). Nets of subfactors. Rev. Math. Phys. 7: 567–597
Longo R. and Rehren K.-H. (2004). Local fields in boundary conformal QFT. Rev. Math. Phys. 16: 909–960
Longo R. and Xu F. (2004). Topological sectors and a dichotomy in conformal field theory. Commun. Math. Phys. 251: 321–364
Rehren K.-H. (2000). Canonical tensor product subfactors. Commun. Math. Phys. 211: 395–406
Schroer B., Swieca J.A. and Völkel A.H. (1975). Global operator expansions in conformally invariant relativistic quantum field theory. Phys. Rev. D11: 1509–1520
Verlinde E. (1988). Fusion rules and modular transformations in 2D conformal field theories. Nucl. Phys. B300: 360–376
Acknowledgments
KHR thanks the Dipartimento di Matematica of the Universitá di Roma “Tor Vergata” for hospitality and financial support, and M. Weiner and I. Runkel for discussions related to the subject.
Open Access
This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by Y. Kawahigashi
Dedicated to Klaus Fredenhagen on the occasion of his 60th birthday
Rights and permissions
Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Longo, R., Rehren, KH. How to Remove the Boundary in CFT – An Operator Algebraic Procedure. Commun. Math. Phys. 285, 1165–1182 (2009). https://doi.org/10.1007/s00220-008-0459-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00220-008-0459-8