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Cosmology from confinement?

Mark Van Raamsdonk

TL;DR

This work develops a holographic framework in which 4D big-bang/big-crunch cosmologies arise from a Euclidean sandwich of two 3D CFTs coupled to a lighter 4D CFT on an interval, with confinement in the IR driving a Euclidean AdS wormhole. The Lorentzian cosmology is obtained by analytic continuation, and in flat spatial sections an eternally traversable 4D wormhole may emerge under suitable conditions, tied to negative energy supplied by an interface/ETW-brane sector. The authors sketch explicit microscopic realizations using ${\cal N}=4$ SYM in 4D and 3D SCFTs of opposite orientation, interpreted as a brane-antibrane system whose joining signals confinement and gravity localization on the ETW branes. They also develop bottom-up EFT and holographic-interface descriptions to estimate the needed negative energy and discuss observable implications, including potential connections to islands in cosmology. Overall, the paper provides a concrete, definable setting to study cosmological spacetimes within holography and to compute cosmological observables from boundary CFT data.

Abstract

We describe a class of holographic models that may describe the physics of certain four-dimensional big-bang / big-crunch cosmologies. The construction involves a pair of 3D Euclidean holographic CFTs each on a homogeneous and isotropic space $M$ coupled at either end of an interval ${\cal I}$ to a Euclidean 4D CFT on $M \times {\cal I}$ with many fewer local degrees of freedom. We argue that in some cases, when the size of $M$ is much greater than the length of ${\cal I}$, the theory flows to a gapped / confining three-dimensional field theory on $M$ in the infrared, and this is reflected in the dual description by the asymptotically AdS spacetimes dual to the two 3D CFTs joining up in the IR to give a Euclidean wormhole. The Euclidean construction can be reinterpreted as generating a state of Lorentzian 4D CFT on $M \times {\rm time}$ whose dual includes the physics of a big-bang / big-crunch cosmology. When $M$ is $\mathbb{R}^3$, we can alternatively analytically continue one of the $\mathbb{R}^3$ directions to get an eternally traversable four-dimensional planar wormhole. We suggest explicit microscopic examples where the 4D CFT is ${\cal N}=4$ SYM theory and the 3D CFTs are superconformal field theories with opposite orientation. In this case, the two geometries dual to the pair of 3D SCFTs can be understood as a geometrical version of a brane-antibrane pair, and the tendency of the geometries to connect up is related to the standard instability of brane-antibrane systems.

Cosmology from confinement?

TL;DR

This work develops a holographic framework in which 4D big-bang/big-crunch cosmologies arise from a Euclidean sandwich of two 3D CFTs coupled to a lighter 4D CFT on an interval, with confinement in the IR driving a Euclidean AdS wormhole. The Lorentzian cosmology is obtained by analytic continuation, and in flat spatial sections an eternally traversable 4D wormhole may emerge under suitable conditions, tied to negative energy supplied by an interface/ETW-brane sector. The authors sketch explicit microscopic realizations using SYM in 4D and 3D SCFTs of opposite orientation, interpreted as a brane-antibrane system whose joining signals confinement and gravity localization on the ETW branes. They also develop bottom-up EFT and holographic-interface descriptions to estimate the needed negative energy and discuss observable implications, including potential connections to islands in cosmology. Overall, the paper provides a concrete, definable setting to study cosmological spacetimes within holography and to compute cosmological observables from boundary CFT data.

Abstract

We describe a class of holographic models that may describe the physics of certain four-dimensional big-bang / big-crunch cosmologies. The construction involves a pair of 3D Euclidean holographic CFTs each on a homogeneous and isotropic space coupled at either end of an interval to a Euclidean 4D CFT on with many fewer local degrees of freedom. We argue that in some cases, when the size of is much greater than the length of , the theory flows to a gapped / confining three-dimensional field theory on in the infrared, and this is reflected in the dual description by the asymptotically AdS spacetimes dual to the two 3D CFTs joining up in the IR to give a Euclidean wormhole. The Euclidean construction can be reinterpreted as generating a state of Lorentzian 4D CFT on whose dual includes the physics of a big-bang / big-crunch cosmology. When is , we can alternatively analytically continue one of the directions to get an eternally traversable four-dimensional planar wormhole. We suggest explicit microscopic examples where the 4D CFT is SYM theory and the 3D CFTs are superconformal field theories with opposite orientation. In this case, the two geometries dual to the pair of 3D SCFTs can be understood as a geometrical version of a brane-antibrane pair, and the tendency of the geometries to connect up is related to the standard instability of brane-antibrane systems.

Paper Structure

This paper contains 22 sections, 73 equations, 16 figures.

Table of Contents

  1. Introduction
  2. General construction
  3. Euclidean wormholes, eternal traversable wormholes, and cosmology
  4. Coupling auxiliary degrees of freedom
  5. Confinement and symmetry breaking
  6. From two-sided black hole to eternally traversable wormhole
  7. Microsopic construction
  8. Dual geometries for the single-boundary case
  9. The two-boundary case
  10. Probe example
  11. Non-perturbative version
  12. Asymptotic behavior of the dual geometry
  13. Bottom-up and effective field theory descriptions
  14. Effective field theory setup
  15. Holographic analysis of interface CFTs
  16. ...and 7 more sections

Figures (16)

  • Figure 1: Basic field theory construction (the CFT sandwich): a pair of 3D holographic CFTs related by a reflection are coupled at either end of an interval $I$ to a 4D CFT.
  • Figure 2: Dual geometries for various field theory setups, showing end-of-the-world branes (red) with asymptotically AdS${}^4$ regions. (a) Dual of a single 3D CFT (b) Dual of a 3D CFT coupled to the boundary of a 4D CFT. Gravity remains well-localized to the ETW brane when $c_{4D} \ll c_{3D}$. (c) Possible dual of a pair of 3D CFTs coupled to a 4D CFT, where the IR physics is a conformal 3D CFT (d) Possible dual of a pair of 3D CFTs coupled to a 4D CFT, where the IR physics is a confining 3D theory.
  • Figure 3: Connection to cosmology. (a) State of the 4D CFT on $\mathbb{R}^3$ produced by the Euclidean path integral terminated by a 3D CFT $b$ in the Euclidean past at $\tau = - \tau_0$. (b) $\tau < 0$ half of the Euclidean solution dual to the doubled bra-ket path-integral. (c) The $\tau = 0$ slice of the Euclidean solution serves as the initial data for Lorentzian evolution. (d) Full Lorentzian solution dual to $|\Psi\rangle_{b, \tau_0}$.
  • Figure 4: CFTs on $R^{2,1}$ times $S^1$, with each CFT covering an interval on the $S^1$. A holographic model suggests that the negative Casimir energy of the CFT with larger central charge can become much larger than that for this CFT on $R^{2,1} \times S^1$ for special choices of the interface corresponding to a bulk interface tension close to a lower critical value in the holographic model.
  • Figure 5: (a) Probe brane solution dual to ${\cal N}=4$ SYM with parallel D5-brane defects. (b)Probe brane configuration for parallel defects with opposite orientation (D5-$\bar{D5}$). (c) Dual gravity solution for SUSY-preserving BCFT, with ETW branes that stay separated. (d) Suggested dual gravity solution with boundary SCFTs of opposite orientation, breaking SUSY.
  • ...and 11 more figures