Abstract
We construct solutions within Jackiw-Teitelboim (JT) gravity in the presence of nontrivial couplings between the dilaton and the Abelian $1$-form where we analyse the asymptotic structure as well as the phase stability corresponding to charged black hole solutions in $1+1$ D. We consider the Almheiri-Polchinski (AP) model as a specific example within $1+1$ D JT gravity which plays a pivotal role in the study of Sachdev-Ye-Kitaev (SYK)/anti-de Sitter (AdS) duality. The corresponding vacuum solutions exhibit a rather different asymptotic structure than their uncharged counterpart. We find interpolating vacuum solutions with AdS$_2$ in the IR and Lifshitz$_2$ in the UV with dynamical exponent $z_{\text{dyn}}=3/2$. Interestingly, the presence of charge also modifies the black hole geometry from asymptotically AdS to asymptotically Lifshitz with same value of the dynamical exponent. We consider specific examples, where we compute the corresponding free-energy and explore the thermodynamic phase stability associated with charged black hole solutions in $1+1$ D. Our analysis reveals the existence of a universal thermodynamic feature that is expected to reveal its immediate consequences on the dual SYK physics at finite density and strong coupling.
Highlights
AND MOTIVATIONSFor the last couple of decades, there had been considerable efforts toward a profound understanding of the underlying nonperturbative dynamics in large N gauge theories using the celebrated anti–de Sitter (AdS)=CFT framework [1,2,3]
We find interpolating vacuum solutions with AdS2 in the IR and Lifshitz2 in the UV with dynamical exponent zdyn 1⁄4 3=2
Our analysis reveals the existence of a universal thermodynamic feature that is expected to reveal its immediate consequences on the dual SYK physics at finite density and strong coupling
Summary
For the last couple of decades, there had been considerable efforts toward a profound understanding of the underlying nonperturbative dynamics in large N gauge theories using the celebrated AdS=CFT framework [1,2,3]. The original SYK/AdS duality deals with Majorana fermions for which neutral dual gravity models are enough to consider. This has been the line of analyses for most of the models so far. Very recently charged SYK models have been constructed in [50,51] whose dual gravitational counterpart has been proposed to be given by the 2D effective gravity action of the following form1 [50]:. VII where we mention the possible implications of our findings on the corresponding SYK counterpart
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