Higher-point conformal blocks and entanglement entropy in heavy states

Abstract

We consider conformal blocks of two heavy operators and an arbitrary number of light operators in a (1+1)-d CFT with large central charge. Using the monodromy method, these higher-point conformal blocks are shown to factorize into products of 4-point conformal blocks in the heavy-light limit for a class of OPE channels. This result is reproduced by considering suitable worldline configurations in the bulk conical defect geometry. We apply the CFT results to calculate the entanglement entropy of an arbitrary number of disjoint intervals for heavy states. The corresponding holographic entanglement entropy calculated via the minimal area prescription precisely matches these results from CFT. Along the way, we briefly illustrate the relation of these conformal blocks to Riemann surfaces and their associated moduli space.

Figures (10)

• Figure 1: The OPE channel which we shall consider here for the conformal block of an even number light operators and two heavy operators. The conformal dimensions are scaled as $\epsilon_i =6h_i/c$. Note the pairwise fusion of the light operators into operators of conformal dimension $\tilde{h}_p$ which are same in the intermediate channels shown in the figure -- this provides a major simplification for the monodromy analysis.
• Figure 2: OPE channel and monodromy contours for $\mathbf{\Omega}_1$ for the 5-point block.
• Figure 3: OPE channel and monodromy contours for $\mathbf{\Omega}_3$ for the 5-point block.
• Figure 4: The OPE channel and contour configuration of $\mathbf{\Omega}_1$ for the case of the 6-point block.
• Figure 5: OPE channel and monodromy contours for $\mathbf{\Omega}_1$ for the 8-point block.