arXiv subjects

Seok Kim

Publications and source records attributed to Seok Kim.

At least 19 recordsLinked to original sources

arXiv2026

Quantum black hole cohomologies

Microstates of BPS AdS black holes have been studied from the classical cohomologies of the maximal super-Yang-Mills theories, but their quantum natures have been conjectural. It was recently found that a classical black hole (fortuitous) cohomology in the $SO(7)$ theory is lifted by 1-loop corrections. We show that such lifts also happen in the $SU(2)$ theory, presenting both lifted/unlifted examples. In particular, the lightest fortuitous cohomology and its `hairy' versions are unlifted, while many heavier `core' fortuitous ones are lifted. We argue that the entropy of classical cohomologies in the Cardy limit is larger than the indicial entropy of strictly protected states by at least $\approx 1.2 \%$.

hep-th↗

arXiv2025

BPS phases and fortuity in higher spin holography

We study the BPS states of $U(N)_k\times U(1)_{-k}$ vector Chern-Simons theory on a sphere at weak coupling $\lambda=\frac{N}{k}\ll 1$, dual to an AdS$_4$ higher spin gravity. Higher spin currents are well known to be anomalous at $\lambda\neq 0$. We show that these non-BPS higher spin particles form multi-particle `BPS bounds' at low energy, and interpret them as a primordial form of small black hole states. We also construct a new heavy BPS operator at $N=2$. We study the BPS phases of this system from the large $N$ index at Planckian `temperatures'. The deconfined saddles at high temperature exist only above a threshold, similar to the BTZ black holes. The low temperature saddles are given by novel 2-cut eigenvalue distributions. Their phase transition involves subtle issues like the holomorphic anomaly and the background independence, whose studies we initiate. In particular, we obtain a lower bound on the critical temperature by studying the eigenvalue instantons.

hep-th↗

arXiv2025

Supersymmetric Grey Galaxies, Dual Dressed Black Holes and the Superconformal Index

Motivated by the recent construction of grey galaxy and Dual Dressed Black Hole solutions in $AdS_5\times S^5$, we present two conjectures relating to the large $N$ entropy of supersymmetric states in ${\cal N}=4$ Yang-Mills theory. Our first conjecture asserts the existence of a large number of supersymmetric states which can be thought of as a non interacting mix of supersymmetric black holes and supersymmetric `gravitons'. It predicts a microcanonical phase diagram of supersymmetric states with eleven distinct phases, and makes a sharp prediction for the supersymmetric entropy (as a function of 5 charges) in each of these phases. The microcanonical version of the superconformal index involves a sum over states - with alternating signs - over a line in 5 parameter charge space. Our second (and more tentative) conjecture asserts that this sum is dominated by the point on the line that has the largest supersymmetric entropy. This conjecture predicts a large $N$ formula for the superconformal index as a function of indicial charges, and predicts a microcanonical indicial phase diagram with nine distinct phases. It predicts agreement between the superconformal index and black hole entropy in one phase (so over one range of charges), but disagreement in other phases (and so at other values of charges). We compare our predictions against numerically evaluated superconformal index at $N\leq10$, and find qualitative agreement.

hep-th↗

arXiv2024

Brane-fused black hole operators

We construct infinitely many new $\frac{1}{16}$-BPS cohomologies of the 4d maximal super-Yang-Mills theory and interpret them as a black hole wrapped by dual giant graviton hairs. Since the black hole inside a dual giant feels the RR 5-form flux reduced by one unit, its microstate should essentially be an $SU(N-1)$ cohomology. However, due to the fortuitous nature of the black hole microstates, promoting an $SU(N-1)$ black hole state to $SU(N)$ generally fails to yield a cohomology. We show at $N=3$ that suitable fusion products with the dual giants yield cohomologies. The core black hole size is probed by the minimal size of the dual giant which can wrap it. We also discuss two types of large black hole hairs: large conformal descendants of gravitons and large dual giants. We prove that any $SU(N)$ black hole cohomology admits infinitely many hairs of the first type.

hep-th↗

arXiv2024

Dual Dressed Black Holes as the end point of the Charged Superradiant instability in ${\cal N} = 4$ Yang Mills

Charged Black holes in $AdS_5 \times S^5$ suffer from superradiant instabilities over a range of energies. Hairy black hole solutions (constructed within gauged supergravity) have previously been proposed as endpoints to this instability. We demonstrate that these hairy black holes are themselves unstable to the emission of large dual giant gravitons. We propose that the endpoint to this instability is given by Dual Dressed Black Holes (DDBH)s; configurations consisting of one, two, or three very large dual giant gravitons surrounding a core $AdS$ black hole with one, two, or three $SO(6)$ chemical potentials equal to unity. The dual giants each live at $AdS$ radial coordinates of order $\sqrt{N}$ and each carry charge of order $N^2$. The large separation makes DDBHs a very weakly interacting mix of their components and allows for a simple computation of their thermodynamics. We conjecture that DDBHs dominate the phase diagram of ${\cal N}=4$ Yang-Mills over a range of energies around the BPS plane, and provide an explicit construction of this phase diagram, briefly discussing the interplay with supersymmetry. We develop the quantum description of dual giants around black hole backgrounds and explicitly verify that DDBHs are stable to potential tunneling instabilities, precisely when the chemical potentials of the core black holes equal unity. We also construct the 10-dimensional DDBH bulk solutions.

hep-th↗

arXiv2023

Finite $N$ black hole cohomologies

We study new cohomologies for the BPS operators of the $\mathcal{N}=4$ Yang-Mills theory with $SU(3)$ and $SU(4)$ gauge groups, to better understand the black hole microstates. We first study the index of these black hole operators and identify their apparent threshold levels. For $SU(3)$, we find many towers of states and partial no-hair behaviors. We explicitly construct the threshold cohomology in the $SU(3)$ theory. We study throughout this paper a subsector of the field theory corresponding to the BMN matrix theory. We also argue that the BMN sector exhibits a black hole like entropy growth at large $N$.

hep-th↗

arXiv2023

'Grey Galaxies' as an endpoint of the Kerr-AdS superradiant instability

Kerr-AdS$_{d+1}$ black holes for $d\geq 3$ suffer from classical superradiant instabilities over a range of masses above extremality. We conjecture that these instabilities settle down into Grey Galaxies (GGs) - a new class of coarse-grained solutions to Einstein's equations which we construct in $d=3$. Grey Galaxies are made up of a black hole with critical angular velocity $\omega=1$ in the `centre' of $AdS$, surrounded by a large flat disk of thermal bulk gas that revolves around the centre of $AdS$ at the speed of light. The gas carries a finite fraction of the total energy, as its parametrically low energy density and large radius are inversely related. GGs exist at masses that extend all the way down to the unitarity bound. Their thermodynamics is that of a weakly interacting mix of Kerr-AdS black holes and the bulk gas. Their boundary stress tensor is the sum of a smooth `black hole' contribution and a peaked gas contribution that is delta function localized around the equator of the boundary sphere in the large $N$ limit. We also construct another class of solutions with the same charges; `Revolving Black Holes (RBHs)'. RBHs are macroscopically charged $SO(d,2)$ descendants of AdS-Kerr solutions, and consist of $\omega=1$ black holes revolving around the centre of $AdS$ at a fixed radial location but in a quantum wave function in the angular directions. RBH solutions are marginally entropically subdominant to GG solutions and do not constitute the endpoint of the superradiant instability. Nonetheless, we argue that supersymmetric versions of these solutions have interesting implications for the spectrum of supersymmetric states in, e.g. ${\cal N}=4$ Yang-Mills theory.

hep-th↗

arXiv2023

Towards quantum black hole microstates

We study the cohomology of local BPS operators in $\mathcal{N}=4$ Yang-Mills theory. The finite $N$ cohomologies consist of the graviton part (subject to the stringy exclusion principle) and the rest which may describe black hole microstates in quantum AdS/CFT. We construct an infinite tower of non-graviton cohomologies in the $SU(2)$ theory and study to what extent they simulate quantum black holes. We find signals for partial no-hair behaviors by showing that certain gravitons are forbidden to dress these cohomologies. This is in qualitative agreement with the perturbative hairs allowed around black holes, which also leads us to a natural setup to construct hairy BPS black holes. The cohomologies are simpler to study in the BMN matrix model truncation of the classical field theory.

hep-th↗

arXiv2022

The shape of non-graviton operators for $SU(2)$

The BPS spectrum of AdS/CFT exhibits multi-gravitons at low energies, while having black hole states at higher energies. This can be studied concretely in AdS$_5$/CFT$_4$ in terms of classical cohomologies, even in the quantum regimes at finite $1/N$. Recently, Chang and Lin found a threshold for non-graviton states in the $SU(2)$ maximal super-Yang-Mills theory. We explicitly construct and present this threshold cohomology.

hep-th↗

arXiv2022

From giant gravitons to black holes

We study AdS$_5$ black holes from a recently suggested giant graviton expansion formula for the index of $U(N)$ maximal super-Yang-Mills theory. We compute the large $N$ entropy at fixed charges and giant graviton numbers $n_I$ by a saddle point analysis, and further maximize it in $n_I$. This agrees with the dual black hole entropy in the small black hole limit. To get black holes at general sizes, one should note that various giant graviton indices cancel because gauge theory does not suffer from a Hagedorn-like pathology by an infinite baryonic tower. With one assumption on the mechanism of this cancellation, we account for the dual black hole entropy at general sizes. We interpret our results as analytic continuations of the large $N$ free energies of SCFTs, and based on it compute the entropies of AdS$_{4,7}$ black holes from M5, M2 giant gravitons.

hep-th↗

arXiv2022

Supersymmetric Spectral Form Factor and Euclidean Black Holes

The late-time behavior of spectral form factor (SFF) encodes the inherent discreteness of a quantum system, which should be generically non-vanishing. We study an index analog of the microcanonical spectrum form factor in four-dimensional $\mathcal{N}=4$ super Yang-Mills theory. In the large $N$ limit and at large enough energy, the most dominant saddle corresponds to the black hole in the AdS bulk. This gives rise to the slope that decreases exponentially for a small imaginary chemical potential, which is a natural analog of an early time. We find that the `late-time' behavior is governed by the multi-cut saddles that arise in the index matrix model, which are non-perturbatively sub-dominant at early times. These saddles become dominant at late times, preventing the SFF from decaying. These multi-cut saddles correspond to the orbifolded Euclidean black holes in the AdS bulk, therefore giving the geometrical interpretation of the `ramp.' Our analysis is done in the standard AdS/CFT setting without ensemble average or wormholes.

hep-th↗

arXiv2021

Exact QFT duals of AdS black holes

We construct large $N$ saddle points of the matrix model for the $\mathcal{N}=4$ Yang-Mills index dual to the BPS black holes in $AdS_5\times S^5$, in two different setups. When the two complex chemical potentials for the angular momenta are collinear, we find linear eigenvalue distributions which solve the large $N$ saddle point equation. When the chemical potentials are not collinear, we find novel solutions given by areal eigenvalue distributions after slightly reformulating the saddle point problem. We also construct a class of multi-cut saddle points, showing that they sometimes admit nontrivial filling fractions. As a byproduct, we find that the Bethe ansatz equation emerges from our saddle point equation.

hep-th↗

arXiv2021

The Yang-Mills duals of small AdS black holes

We study the large $N$ matrix model for the index of 4d $\mathcal{N}=4$ Yang-Mills theory and its truncations to understand the dual AdS$_5$ black holes. Numerical studies of the truncated models provide insights on the black hole physics, some of which we investigate analytically with the full Yang-Mills matrix model. In particular, we find many branches of saddle points which describe the known black hole solutions. We analytically construct the saddle points dual to the small black holes whose sizes are much smaller than the AdS radius. They include the asymptotically flat BMPV black holes embedded in large AdS with novel thermodynamic instabilities.

hep-th↗

arXiv2021

Twin Mechanical Metamaterials

By mimicking the geometrical relation of nano-twin crystals, we propose novel architected twin mechanical metamaterials (TMMs), which can impede local shearing band formation under external loading, thus avoiding global catastrophic failure. The effects of twin-space and twin angle on the mechanical performance of TMMs were also explored, such as: energy absorption, strength, and crack propagation resistance. The results showed that the twin topology design can not only significantly improve the energy-absorption efficiency but also remarkably improve the crack-propagation resistances of stretching-dominant mechanical metamaterials. We also studied the effect of twin-space and twin angle on the tensile strength of TMMs. This study is the first to report on the inverse Hall-Petch effect of TMMs. Our findings open an avenue for the design and fabrication of advanced materials with exceptionally tuneable mechanical properties.

cond-mat.mtrl-sci↗

arXiv2020

AdS black holes and finite N indices

We study the index of 4d $\mathcal{N}=4$ Yang-Mills theory with $U(N)$ gauge group, focussing on the physics of the dual BPS black holes in $AdS_5\times S^5$. Certain aspects of these black holes can be studied from finite $N$ indices with reasonably large $N^2$. We make numerical studies of the index for $N\leq 6$, by expanding it up to reasonably high orders in the fugacity. The entropy of the index agrees very well with the Bekenstein-Hawking entropy of the dual black holes, say at $N^2=25$ or $36$. Our data clarifies and supports the recent ideas which allowed analytic studies of these black holes from the index, such as the complex saddle points of the Legendre transformation and the oscillating signs in the index. In particular, the complex saddle points naturally explain the $\frac{1}{N}$-subleading oscillating patterns of the index. We also illustrate the universality of our ideas by studying a model given by the inverse of the MacMahon function.

hep-th↗

arXiv2020

Entropy functions of BPS black holes in AdS$_4$ and AdS$_6$

We find the entropy functions of supersymmetric black holes in AdS$_4$ and AdS$_6$ with electric charges and angular momenta. Extremizing these functions, one obtains the entropies and the chemical potentials of known analytic black hole solutions.

hep-th↗

arXiv2019

Scalable additive manufacturing via integral image formation

Additive manufacturing techniques enable the fabrication of functional microstructures with mechanical and chemical properties tailored to their intended use. One common technique is stereolithography, which has recently been augmented in response to modern demands to support smaller features, larger build areas, and/or faster speeds. However, a limitation is that such systems typically utilize a single-aperture imaging configuration, which restricts their ability to produce microstructures at large volumes due to the tradeoff between the image resolution and image field area. In this paper, we demonstrate three versatile imaging functions based on the coupling a planar lens array, namely, parallel image transfer, kaleidoscopic superposition, and integral reconstruction, the combination of which is termed integral lithography. In this approach, the individual microlenses in the planar lens array maintain a high numerical aperture and are employed in the creation of digital light patterns that can expand the printable area by the number of microlenses (103-104). The proposed lens array-based integral imaging system provides the concurrent ability to scale-up and scale-down incoming image fields, thereby enabling the scalable stereolithographic fabrication of three-dimensional features that surpass the resolution-to-area scaling limit. The proposed system opens up new possibilities for producing periodic microarchitectures spanning four orders of magnitude from micrometers to centimeters that can be applied to biological scaffolds, metastructures, chemical reactors, and functional surfaces.

physics.app-ph↗

arXiv2019

Quantum vortices, M2-branes and black holes

We study the partition functions of BPS vortices and magnetic monopole operators, in gauge theories describing $N$ M2-branes. In particular, we explore two closely related methods to study the Cardy limit of the index on $S^2\times\mathbb{R}$. The first method uses the factorization of this index to vortex partition functions, while the second one uses a continuum approximation for the monopole charge sums. Monopole condensation confines most of the $N^2$ degrees of freedom except $N^{\frac{3}{2}}$ of them, even in the high temperature deconfined phase. The resulting large $N$ free energy statistically accounts for the Bekenstein-Hawking entropy of large BPS black holes in $AdS_4\times S^7$. Our Cardy free energy also suggests a finite $N$ version of the $N^{\frac{3}{2}}$ degrees of freedom.

hep-th↗