Abstract
The description of the general methodology for computing entanglement entropy in Chap. 2 gives a clean, albeit abstract prescription. As with any functional integral, it helps to develop some intuition as to where the computation can be carried out explicitly. For a general QFT in d > 2 the computation appears intractable in all but the simplest of cases of free field theories [42]. However, it turns out to be possible to leverage the power of conformal symmetry in d = 2, to explicitly compute entanglement entropy in some situations [18]. In fact, the revival of interest in entanglement entropy can be traced to the work of Cardy and Calabrese [57] who re-derived the results of [58] and went on to then explore its utility as a diagnostic of interesting physical phenomena in interacting systems. We will give a brief overview of this discussion, adapting it both to the general ideas outlined above and simultaneously preparing the group for our holographic considerations in the sequel.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsNotes
- 1.
For a review of analysis of entanglement entropy in free field theories, refer to [59].
- 2.
Higher-dimensional CFTs are similarly described by their operator spectrum and OPE coefficients.
- 3.
- 4.
While a general genus-g Riemann surface has 3g − 3 moduli, the branched cover Rényi geometries are a special subclass with the moduli being determined by the 2m − 3 cross-ratios.
References
P. Calabrese, J. Cardy, Entanglement entropy and conformal field theory. J. Phys. A A42, 504005 (2009). arXiv:0905.4013 [cond-mat.stat-mech]
M. Srednicki, Entropy and area. Phys. Rev. Lett. 71, 666–669 (1993). arXiv:hep-th/9303048 [hep-th]
H. Casini, M. Huerta, A Finite entanglement entropy and the c-theorem. Phys. Lett. B600, 142–150 (2004). arXiv:hep-th/0405111 [hep-th]
P. Calabrese, J.L. Cardy, Entanglement entropy and quantum field theory. J. Stat. Mech. 0406, P06002 (2004). arXiv:hep-th/0405152 [hep-th]
C. Holzhey, F. Larsen, F. Wilczek, Geometric and renormalized entropy in conformal field theory. Nucl. Phys. B424, 443–467 (1994). hep-th/9403108. http://arxiv.org/abs/hep-th/9403108
H. Casini, M. Huerta, Entanglement entropy in free quantum field theory. J. Phys. A42, 504007 (2009). arXiv:0905.2562 [hep-th]
P.H. Ginsparg, Applied conformal field theory, in Les Houches Summer School in Theoretical Physics: Fields, Strings, Critical Phenomena Les Houches, France, June 28-August 5, 1988 (1988). arXiv:hep-th/9108028 [hep-th]
P. Di Francesco, P. Mathieu, D. Senechal, Conformal Field Theory. Graduate Texts in Contemporary Physics (Springer, New York, 1997)
M. Headrick, Entanglement Renyi entropies in holographic theories. Phys. Rev. D82, 126010 (2010). arXiv:1006.0047 [hep-th]
F.M. Haehl, M. Rangamani, Permutation orbifolds and holography. J. High Energy Phys. 03, 163 (2015). arXiv:1412.2759 [hep-th]
L.J. Dixon, J.A. Harvey, C. Vafa, E. Witten, Strings on orbifolds. 2. Nucl. Phys. B274, 285–314 (1986)
L.J. Dixon, D. Friedan, E.J. Martinec, S.H. Shenker, The conformal field theory of orbifolds. Nucl. Phys. B282, 13–73 (1987)
P. Calabrese, J. Cardy, E. Tonni, Entanglement entropy of two disjoint intervals in conformal field theory. J. Stat. Mech. 0911, P11001 (2009). arXiv:0905.2069 [hep-th]
H. Casini, M. Huerta, Remarks on the entanglement entropy for disconnected regions. J. High Energy Phys. 0903, 048 (2009). arXiv:0812.1773 [hep-th]
M. Headrick, A. Lawrence, M. Roberts, Bose-Fermi duality and entanglement entropies. J. Stat. Mech. 1302, P02022 (2013). arXiv:1209.2428 [hep-th]
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this chapter
Cite this chapter
Rangamani, M., Takayanagi, T. (2017). Entanglement Entropy in CFT2 . In: Holographic Entanglement Entropy. Lecture Notes in Physics, vol 931. Springer, Cham. https://doi.org/10.1007/978-3-319-52573-0_3
Download citation
DOI: https://doi.org/10.1007/978-3-319-52573-0_3
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-52571-6
Online ISBN: 978-3-319-52573-0
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)