Thermal behavior of charged dilatonic black branes in AdS and UV completions of Lifshitz-like geometries
Bibliographic record
Abstract
Several classes of gravitational backgrounds in $3+1$ dimensions have been proposed as holographic duals to Lifshitz-like theories describing critical phenomena in $2+1$ dimensions with critical exponent $z\ensuremath{\ge}1$. We numerically explore one such model, characterized by a temperature $T$ and chemical potential $\ensuremath{\mu}$, and find how to embed these solutions into anti--de Sitter (AdS) for a range of values of $z$. We find no phase transition going from the $T\ensuremath{\ll}\ensuremath{\mu}$ to the $T\ensuremath{\gg}\ensuremath{\mu}$ regimes, and find that the solutions smoothly interpolate between the Lifshitz-like behavior and the relativistic AdS-like behavior. Finally, we exploit some conserved quantities to find a relationship between the energy density $\mathcal{E}$, entropy density $s$, and number density $n$, $\mathcal{E}=\frac{2}{3}(Ts+\ensuremath{\mu}n)$. We show that this result is expected from general scaling arguments, and generalizes to $\mathcal{E}=\frac{d}{d+1}(Ts+\ensuremath{\mu}n)$ for a theory dual to ${\mathrm{AdS}}_{d+2}$ (Poincar\'e patch) asymptotics with a local $U(1)$ gauge invariance.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".