Free fermion cyclic/symmetric orbifold CFTs and entanglement entropy
Aug 31, 2022
54 pages
Published in:
- JHEP 12 (2022) 004
- Published: Dec 1, 2022
e-Print:
- 2209.00206 [hep-th]
Report number:
- YITP-22-91,
- IPMU22-0042
View in:
Citations per year
Abstract: (Springer)
In this paper we study the properties of two-dimensional CFTs defined by cyclic and symmetric orbifolds of free Dirac fermions, especially by focusing on the partition function and entanglement entropy. Via the bosonization, we construct the twist operators which glue two complex planes to calculate the partition function of ℤ orbifold CFT on a torus. We also find an expression of ℤ cyclic orbifold in terms of Hecke operators, which provides an explicit relation between the partition functions of cyclic orbifolds and those of symmetric ones. We compute the entanglement entropy and Renyi entropy in cyclic orbifolds on a circle both for finite temperature states and for time-dependent states under quantum quenches. We find that the replica method calculation is highly non-trivial and new because of the contributions from replicas with different boundary conditions. We find the full expression for the ℤ orbifold and show that the periodicity gets doubled. Finally, we discuss extensions of our results on entanglement entropy to symmetric orbifold CFTs and make a heuristic argument towards holographic CFTs.Note:
- 54 pages, 8 figures
- AdS-CFT Correspondence
- Long Strings
- field theory: conformal
- entropy: entanglement
- fermion: Dirac
- operator: twist
- dimension: 2
- operator: Hecke
- orbifold
- cyclic
References(64)
Figures(8)
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