<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>T</mml:mi><mml:mover accent="true"><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mo stretchy="false">¯</mml:mo></mml:mrow></mml:mover></mml:mrow></mml

We investigate <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>T</a:mi><a:mover accent="true"><a:mi>T</a:mi><a:mo stretchy="false">¯</a:mo></a:mover></a:math> deformation on non-Hermitian coupled Sachdev-Ye-Kitaev (SYK) model and the holographic picture. The relationship between ground state and thermofield double state is preserved under the <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>T</e:mi><e:mover accent="true"><e:mi>T</e:mi><e:mo stretchy="false">¯</e:mo></e:mover></e:math> deformation. We prove that <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>T</i:mi><i:mover accent="true"><i:mi>T</i:mi><i:mo stretchy="false">¯</i:mo></i:mover></i:math> deformed theory provides a reparametrization in large <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mi>N</m:mi></m:math> limit. We numerically calculate the deformation effects on the correlation function in imaginary time and the free energy. The thermodynamic phase structures show the equivalence of the wormhole-black hole picture between non-Hermitian model and Hermitian model still holds under <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mi>T</o:mi><o:mover accent="true"><o:mi>T</o:mi><o:mo stretchy="false">¯</o:mo></o:mover></o:math> deformation. The correlation function in Lorentz time, revival dynamic, and the deformed holography are also evaluated. Published by the American Physical Society 2024