Analyzing the squeezed state generated by a twist deformation

The D1D5 conformal field theory has provided a useful microscopic model for studying black holes. The coupling in this theory is a twist deformation whose action on the vacuum generates a squeezed state. We give a new derivation of the expression for this squeezed state using the conformal Ward identity; this derivation provides an insight into several features of the state. We also examine the squeezed state in a continuum limit where we describe it in terms of position space correlations created by the twist.

Figure 1

The twist operator joins two copies of the CFT on two singly wound circles (a) into one copy of the CFT on a doubly wound circle (b).

Figure 2

The map from the complex plane (a) to its covering surface (b) is given by $z=z_0+t^2$, where $z$ is the coordinate on the complex plane and $t$ is the coordinate on the covering space. The two NS vacua at $z=0$ are mapped to two NS vacua at $t=\pm ia$ (these correspond the original two Ramond vacua at $\tau \to -\infty$ on the cylinder). The location of the twist insertion at $z=z_0$ is mapped to $t=0$ on the cover.

Figure 3

The circles becomes infinite lines in the continuum limit (a), but the twist operator still works locally as it did in the compact case (b).