Abstract
We present a new area law which is associated with the correlator of OPE blocks in higher dimensional conformal field theories (CFTs). The area law shows similar behaviour as black hole entropy or geometric entanglement entropy. It includes a leading term which is proportional to the area of the entanglement surface, and a logarithmic subleading term with degree q. We extract the UV cutoff independent coefficients and discuss various properties of the coefficients.
Highlights
OPE block may obey area law from the analytic continuation of (m − 1, 1)-type CCF
We present a new area law which is associated with the correlator of OPE blocks in higher dimensional conformal field theories (CFTs)
We summarize the area law and logarithmic behaviour schematically in the following formula
Summary
In CFTs, operators are classified into (quasi-)primary operators O and their descendants. The constants Cijk are called OPE coefficients which is related to the three point function of the primary operators. They are the only dynamical parameters in the theory. The objects Qikj(x1, x2) are called OPE blocks [12,13,14] They are non-local operators in the CFT and depend on the position of external operators x1 and x2. When the two external operators are the same, we have f (x1, x2) = 1 and the OPE block will be invariant under global conformal transformations. Any type-O OPE block corresponds to the point pair (2.6) or the unit ball ΣA (2.7) is [16]. We will introduce the definition of the CCF in the following subsection
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