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| Main Authors: | , , , , , , |
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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2512.00158 |
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| _version_ | 1866908680968994816 |
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| author | Anand, Harsh Benjamin, Nathan Kumar, Vipul Minwalla, Shiraz Mukherjee, Jyotirmoy Pal, Sridip Rahaman, Asikur |
| author_facet | Anand, Harsh Benjamin, Nathan Kumar, Vipul Minwalla, Shiraz Mukherjee, Jyotirmoy Pal, Sridip Rahaman, Asikur |
| contents | The thermal partition function, $Z$, of a $CFT_d$ on $S^{d-1}$ is parameterized by the inverse temperature $β$ along with $\lfloor d/2\rfloor$ angular velocities $ω_i$. In this paper, we investigate the behaviour of this partition function when $n$ of the $ω_i$ are scaled to unity (the largest allowed value) at fixed values of the other $(\lfloor d/2\rfloor-n)$ angular velocities. We argue that $\ln Z$ develops a simple pole in $(1-ω_i)$ for each $ω_i$ that is scaled to unity. The residue of this product of poles is a theory dependent (so non-universal) function of $β$ and the fixed angular velocities. The inverse Laplace transformation of this partition function constrains the functional form of the field theory entropy as a function of charges in a limit in which angular momenta and the twist are scaled as follows. While $n$ special angular momenta $J_1\ldots J_n$ are scaled to infinity, the twist and the other angular momenta - collectively denoted $x_i$ - are also taken to infinity but at the slower rate that ensures that the scaled charges $x_i/(J_1 J_2 \ldots J_n)^{\frac{1}{n+1}}$ are held fixed. In this limit, we demonstrate that the scaled entropy $S/(J_1 J_2 \ldots J_n)^{\frac{1}{n+1}}$ depends only on the $\lfloor d/2\rfloor-n+1$ scaled charges defined above (the precise form of this dependence is non-universal). We verify our predictions (and compute all non-universal functions) in the case of free scalar theories (which show surprisingly rich behaviour) as well as large $N$, strongly coupled ${\cal N}=4$ Yang Mills theory. The last theory is analyzed in the bulk via the AdS/CFT correspondence. In the scaling limit described above, its phase diagram displays sharp phase transitions between black hole, grey galaxy, and thermal gas phases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_00158 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Semi-universality of CFT$_d$ entropy at large spin Anand, Harsh Benjamin, Nathan Kumar, Vipul Minwalla, Shiraz Mukherjee, Jyotirmoy Pal, Sridip Rahaman, Asikur High Energy Physics - Theory The thermal partition function, $Z$, of a $CFT_d$ on $S^{d-1}$ is parameterized by the inverse temperature $β$ along with $\lfloor d/2\rfloor$ angular velocities $ω_i$. In this paper, we investigate the behaviour of this partition function when $n$ of the $ω_i$ are scaled to unity (the largest allowed value) at fixed values of the other $(\lfloor d/2\rfloor-n)$ angular velocities. We argue that $\ln Z$ develops a simple pole in $(1-ω_i)$ for each $ω_i$ that is scaled to unity. The residue of this product of poles is a theory dependent (so non-universal) function of $β$ and the fixed angular velocities. The inverse Laplace transformation of this partition function constrains the functional form of the field theory entropy as a function of charges in a limit in which angular momenta and the twist are scaled as follows. While $n$ special angular momenta $J_1\ldots J_n$ are scaled to infinity, the twist and the other angular momenta - collectively denoted $x_i$ - are also taken to infinity but at the slower rate that ensures that the scaled charges $x_i/(J_1 J_2 \ldots J_n)^{\frac{1}{n+1}}$ are held fixed. In this limit, we demonstrate that the scaled entropy $S/(J_1 J_2 \ldots J_n)^{\frac{1}{n+1}}$ depends only on the $\lfloor d/2\rfloor-n+1$ scaled charges defined above (the precise form of this dependence is non-universal). We verify our predictions (and compute all non-universal functions) in the case of free scalar theories (which show surprisingly rich behaviour) as well as large $N$, strongly coupled ${\cal N}=4$ Yang Mills theory. The last theory is analyzed in the bulk via the AdS/CFT correspondence. In the scaling limit described above, its phase diagram displays sharp phase transitions between black hole, grey galaxy, and thermal gas phases. |
| title | Semi-universality of CFT$_d$ entropy at large spin |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2512.00158 |