Deep learning-based holography for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>T</mml:mi> </mml:math> -linear resistivity

We employ deep learning within holographic duality to investigate <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>T</a:mi> </a:math> -linear resistivity, a hallmark of strange metals. Utilizing physics-informed neural networks, we incorporate boundary data for <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mi>T</c:mi> </c:math> -linear resistivity and bulk differential equations into a loss function. This approach allows us to derive dilaton potentials in Einstein-Maxwell-dilaton-axion theories, capturing essential features of strange metals, such as <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mi>T</e:mi> </e:math> -linear resistivity and linear specific heat scaling. We also explore the impact of the resistivity slope on dilaton potentials. Regardless of slope, dilaton potentials exhibit exponential growth at low temperatures, driving <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mi>T</g:mi> </g:math> -linear resistivity and matching infrared geometric analyses. At a specific slope, our method rediscovers the Gubser-Rocha model, a well-known holographic model of strange metals. Additionally, the robustness of <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mi>T</i:mi> </i:math> -linear resistivity at higher temperatures correlates with the asymptotic Anti-de Sitter behavior of the dilaton coupling to the Maxwell term. Our findings suggest that deep learning could help uncover mechanisms in holographic condensed matter systems and advance our understanding of strange metals.