Area terms and entanglement entropy in the $c=1$ string theory

We study entanglement entropy in the low-energy effective field theory of two-dimensional string theory as well as in the singlet sector of the dual $c=1$ matrix quantum mechanics. From the target space perspective, we argue that a generic bulk subregion is expected to have an associated generalized entanglement entropy combining a dilaton-dependent gravitational term and a matter contribution coming from the tachyon. Given that the gravitational area-like term is absent in previous analyses of entanglement entropy in the $c=1$ model, we examine several possible mechanisms for its emergence. We show that the nonlocal transformation induced by the leg-pole factor that relates the target space tachyon and the matrix model collective excitations cannot account for the area-like term, and we comment on its possible origin in the non-singlet sectors of the theory.

💡 Research Summary

This paper investigates entanglement entropy in the low‑energy effective field theory (EFT) of two‑dimensional (2D) string theory with central charge c = 1, as well as in the singlet sector of its dual matrix quantum mechanics (MQM). From the target‑space viewpoint, a generic bulk subregion R is expected to possess a generalized entropy consisting of a dilaton‑dependent “area‑like” term (the value of the dilaton Φ evaluated at the boundary ∂R) plus the usual matter contribution from the tachyon field T: \