Holographic CFT phase transitions and criticality for charged AdS black holes
Bibliographic record
Abstract
A bstract We study the holographic dual of the extended thermodynamics of spherically symmetric, charged AdS black holes in the context of the AdS/CFT correspondence. The gravitational thermodynamics of AdS black holes can be extended by allowing for variations of the cosmological constant and Newton’s constant. In the dual CFT this corresponds to including the central charge C and its chemical potential μ as a new pair of conjugate thermodynamic variables, in addition to the standard pairs: temperature vs. entropy ( T, S ), electric potential vs. charge ( $$ \overset{\sim }{\Phi},\overset{\sim }{Q} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>Φ</mml:mi> <mml:mo>~</mml:mo> </mml:mover> <mml:mo>,</mml:mo> <mml:mover> <mml:mi>Q</mml:mi> <mml:mo>~</mml:mo> </mml:mover> </mml:math> ) and field theory pressure vs. volume ( p, $$ \mathcal{V} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>V</mml:mi> </mml:math> ). For the (grand) canonical ensembles at fixed ( $$ \overset{\sim }{Q},\mathcal{V},C $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>Q</mml:mi> <mml:mo>~</mml:mo> </mml:mover> <mml:mo>,</mml:mo> <mml:mi>V</mml:mi> <mml:mo>,</mml:mo> <mml:mi>C</mml:mi> </mml:math> ) , ( $$ \overset{\sim }{\Phi},\mathcal{V},C $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>Φ</mml:mi> <mml:mo>~</mml:mo> </mml:mover> <mml:mo>,</mml:mo> <mml:mi>V</mml:mi> <mml:mo>,</mml:mo> <mml:mi>C</mml:mi> </mml:math> ) and ( $$ \overset{\sim }{Q},\mathcal{V},\mu $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>Q</mml:mi> <mml:mo>~</mml:mo> </mml:mover> <mml:mo>,</mml:mo> <mml:mi>V</mml:mi> <mml:mo>,</mml:mo> <mml:mi>μ</mml:mi> </mml:math> ), based on the holographic dictionary, we argue the CFT description of charged AdS black holes contains either critical phenomena or interesting phase behaviour. In the fixed ( $$ \overset{\sim }{Q},\mathcal{V},\mu $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>Q</mml:mi> <mml:mo>~</mml:mo> </mml:mover> <mml:mo>,</mml:mo> <mml:mi>V</mml:mi> <mml:mo>,</mml:mo> <mml:mi>μ</mml:mi> </mml:math> ) we find a new zeroth-order phase transition between a high- and low-entropy phase at some μ -dependent temperature. Finally, we point out there is no critical behaviour in the fixed p ensembles, i.e. there is no p − $$ \mathcal{V} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>V</mml:mi> </mml:math> criticality, and hence the CFT state dual to a classical charged black hole cannot be a Van der Waals fluid. Whether or not this phase structure is supported by CFT computations remains an interesting open question.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".