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

Abstract We study torsional topological defects in Einstein–Gauss–Bonnet gravity in ( $$4+1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>4</mml:mn> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> )-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 ( $$3+1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>3</mml:mn> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> )-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.