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Bridging Worldsheet CFTs and Wormholes

Yoav Zigdon

Abstract

I provide multiple examples of conformal field theories (CFTs) on the worldsheet that describe string propagation in target space wormholes connecting two disjoint asymptotic manifolds. The worldsheet approach goes beyond the framework of supergravity by incorporating wormholes for which the size of the throat is comparable to the string scale. Typically, strongly coupled CFTs describe these stringy wormholes, which include Euclidean wormholes, double cones, and Einstein-Rosen bridges. Finally, I interpret a conformal manifold that contains $\text{SU}(2)_k$ and $\big(\text{SU}(2)_k \times \text{U}(1)_{k'}\big)/\text{U}(1)$ CFTs as mediating a transition between a closed Universe and a wormhole.

Bridging Worldsheet CFTs and Wormholes

Abstract

I provide multiple examples of conformal field theories (CFTs) on the worldsheet that describe string propagation in target space wormholes connecting two disjoint asymptotic manifolds. The worldsheet approach goes beyond the framework of supergravity by incorporating wormholes for which the size of the throat is comparable to the string scale. Typically, strongly coupled CFTs describe these stringy wormholes, which include Euclidean wormholes, double cones, and Einstein-Rosen bridges. Finally, I interpret a conformal manifold that contains and CFTs as mediating a transition between a closed Universe and a wormhole.
Paper Structure (8 sections, 35 equations, 2 figures)

This paper contains 8 sections, 35 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Examples
  3. CFTs for Euclidean Wormholes
  4. CFT for a EAdS$_2$ Wormhole
  5. Double-Cone Wormholes from the Worldsheet
  6. Worldsheet Perspective on Einstein-Rosen Bridges
  7. Closed Universe/Wormhole Transition
  8. Summary and Future Directions

Figures (2)

  • Figure 1: The transmission coefficient of a massless, spin-less probe sent from the left mouth of the wormhole to the right mouth as a function of $\sqrt{k} \omega$.
  • Figure 2: A closed Universe phase exists in the bulk of the conformal manifold; its boundaries admit a wormhole interpretation. (Jokingly, the conformal manifold itself is a wormhole!)