Sixfold Way of Traversable Wormholes in the Sachdev-Ye-Kitaev Model

In the infrared limit, a nearly anti–de Sitter spacetime in two dimensions (<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:msub><a:mrow><a:mi>AdS</a:mi></a:mrow><a:mrow><a:mn>2</a:mn></a:mrow></a:msub></a:mrow></a:math>) perturbed by a weak double trace deformation and a two-site (<c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mrow><c:mi>q</c:mi><c:mo>></c:mo><c:mn>2</c:mn></c:mrow></c:math>)-body Sachdev-Ye-Kitaev (SYK) model with <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>N</e:mi></e:math> Majoranas and a weak <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mn>2</g:mn><g:mi>r</g:mi></g:math>-body intersite coupling share the same near-conformal dynamics described by a traversable wormhole. We exploit this relation to propose a symmetry classification of traversable wormholes depending on <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>N</i:mi></i:math>, <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>q</k:mi></k:math>, and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mi>r</m:mi></m:math>, with <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mi>q</o:mi><o:mo>></o:mo><o:mn>2</o:mn><o:mi>r</o:mi></o:math>, and confirm it by a level statistics analysis using exact diagonalization techniques. Intriguingly, a time-reversed state never results in a new state, so only six universality classes occur—A, AI, BDI, CI, C, and D—and different symmetry sectors of the model may belong to distinct universality classes.