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Holography of dislocations and ring defects in Einstein-Gauss-Bonnet AdS gravity

Vladimir Juričić, Olivera Miskovic, Francisca Ramírez Carrasco

Abstract

We study torsional topological defects in Einstein-Gauss-Bonnet gravity in ($4+1$)-dimensional anti-de Sitter spacetime. In the holographic interpretation, these correspond to crystalline dislocation defects associated with the discrete lattice translational symmetry. The Gauss-Bonnet coupling is fixed at the Chern-Simons point. By solving the equations of motion through an asymptotic expansion near the boundary, we show that the dual ($3+1$)-dimensional theory admits axially symmetric solutions. These solutions describe holographic materials with dislocation defects at finite temperature, encoded by a black hole in the bulk. At the same time, they feature ring-shaped defects arising from the background Riemann-Cartan geometry, characterized by nontrivial Burgers vectors. We also discuss the possible appearance of an odd-parity Abelian holographic anomaly, proportional to the Nieh-Yan invariant. Our results motivate further studies of holographic defects using bulk gravitational theories and support the view that torsion provides a holographic counterpart of crystalline dislocation defects.

Holography of dislocations and ring defects in Einstein-Gauss-Bonnet AdS gravity

Abstract

We study torsional topological defects in Einstein-Gauss-Bonnet gravity in ()-dimensional anti-de Sitter spacetime. In the holographic interpretation, these correspond to crystalline dislocation defects associated with the discrete lattice translational symmetry. The Gauss-Bonnet coupling is fixed at the Chern-Simons point. By solving the equations of motion through an asymptotic expansion near the boundary, we show that the dual ()-dimensional theory admits axially symmetric solutions. These solutions describe holographic materials with dislocation defects at finite temperature, encoded by a black hole in the bulk. At the same time, they feature ring-shaped defects arising from the background Riemann-Cartan geometry, characterized by nontrivial Burgers vectors. We also discuss the possible appearance of an odd-parity Abelian holographic anomaly, proportional to the Nieh-Yan invariant. Our results motivate further studies of holographic defects using bulk gravitational theories and support the view that torsion provides a holographic counterpart of crystalline dislocation defects.

Paper Structure

This paper contains 31 sections, 168 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Einstein-Gauss-Bonnet AdS5 gravity
  3. Chern-Simons AdS gravity.
  4. Holographic field theory
  5. Our setup
  6. Obtaining holographic equations
  7. Introducing temperature
  8. Introducing dislocation
  9. Holographic Ward identities
  10. Purely axial holographic dislocation
  11. Holographic dislocation with diagonal torsion
  12. 'No-go' for the dislocation c2=1
  13. Solution with a generic dislocation c2=1
  14. 'No-go' for the constant norm B2=const
  15. Irrotational solution
  16. ...and 16 more sections

Figures (3)

  • Figure 1: Periodic solution with the strength of the torsion field given by Eq. \ref{['eq:periodic-sol']}: (Left) Temperature, $T=\frac{|c|}{\pi}\sqrt{\frac{m}{2}}$, with the mass of the black hole in Eq. \ref{['eq:mass-periodic']}, as a function of the dislocation parameter, $c$. (Center) The radius of the ring, $\bar{\rho}$, as given by Eqs. \ref{['bR']} and \ref{['R']}, as a function of the dislocation parameter, $c$. (Right) Dependence of the radius from the temperature, obtained from integrating out the dislocation parameter numerically.
  • Figure 2: Temperature (left) and the ring radius (center) as functions of the dislocation parameter $c$, as well as the dependence $\bar{\rho}(T)$ (right), in case of the non-periodic solution, the positive branch. The solution exists in the narrow interval $c_{02} \leq |c| <c_\infty$, as shown in Table \ref{['tab:critical points']}.
  • Figure 3: Temperature (left) and the ring radius (center) as functions of the dislocation parameter in the case of the non-periodic solution, the negative branch. The direct dependence $\bar{\rho}(T)$ (right). The solution exists in the interval $c_{02} \leq |c| <1$, as shown in Table \ref{['tab:critical points']}.