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

TL;DR

This paper explores how torsional topological defects in five-dimensional Einstein-Gauss-Bonnet anti-de Sitter gravity relate to dislocation defects in holographically dual four-dimensional materials, revealing novel ring-shaped defects and potential anomalies.

Contribution

It demonstrates that torsional defects in Einstein-Gauss-Bonnet AdS gravity correspond to dislocation defects in dual holographic materials, including ring-shaped defects and possible holographic anomalies.

Findings

Existence of axially symmetric solutions describing dislocation defects.

Identification of ring-shaped defects from background Riemann-Cartan geometry.

Discussion of potential odd-parity holographic anomaly related to Nieh-Yan invariant.

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.