arXiv subjects

Ji Hoon Lee

Publications and source records attributed to Ji Hoon Lee.

9 recordsLinked to original sources

arXiv2026

Bubbling wormholes and matrix models

The thermofield double state entangles two copies of a CFT via a sum over energy eigenstates and is dual to the two-sided eternal black hole. We explore an analogous construction using sums over gauge group representations of half-BPS Wilson loops in multiple copies of $U(N)$ $\mathcal{N}=4$ super Yang-Mills. These sums act as delta function-like operators that correlate the eigenvalues of the corresponding half-BPS matrix models. We suggest that the holographic duals are ''bubbling wormhole'' geometries: multi-covers of AdS$_5$ $\times S^5$ whose conformal boundary consists of multiple four-spheres intersecting on a common circle. We analyze the matrix model free energy, discuss its bulk interpretation, and study probe loops in these backgrounds.

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arXiv2025

AdS$_3$ Quantum Gravity and Finite $N$ Chiral Primaries

String theory on AdS$_3$ $\times$ S$^3$ $\times$ $\mathcal{M}_4$ provides a well-studied realization of AdS$_3$/CFT$_2$ holography, but its non-perturbative structure at finite $N \sim 1/G_N^{(3)}$ is largely unknown. A long-standing puzzle concerns the stringy exclusion principle: what bulk mechanism can reproduce the boundary expectation that the chiral primary Hilbert space of the symmetric orbifold contains only a finite number of states at finite $N$? In this work, we present a bulk prescription for computing the finite $N$ spectrum of chiral primary states in symmetric orbifolds of $\mathbb{T}^4$ or K3. We show that the integer spectrum at any $N$ is reproduced exactly by summing over one-loop supersymmetric partition functions of the IIB theory on (AdS$_3$ $\times$ S$^3$)/$\mathbb{Z}_k$ $\times$ $\mathcal{M}_4$ orbifolds and their spectral flows. Using the worldsheet in the tensionless limit, we verify that the terms appearing in our proposal coincide with the partition functions of these orbifold geometries and their asymmetric generalizations. These partition functions contribute with alternating signs due to BPS modes with negative conformal dimensions and charges in twisted sectors. The resulting alternating sum collapses via large cancellations to the finite $N$ polynomials observed in symmetric orbifold CFTs, providing a bulk explanation of the stringy exclusion principle. We identify different Stokes sectors where different infinite subsets of these geometries contribute to the path integral, and propose a classification as functions of the chemical potentials.

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arXiv2024

Bulk thimbles dual to trace relations

The maximal giant graviton is a D-brane wrapping a maximal $S^3\subset S^5$ within $\text{AdS}_5\times S^5$. It represents an upper bound on the $R$ charge that can be carried by certain bulk states. We study the maximal giant and its half-BPS fluctuations, motivated by a recent proposal \cite{Lee:2023iil} connecting these fluctuations to trace relations in the boundary theory. In a computation of the partition function of half-BPS states, we find that the maximal giant is an unstable saddle point and that its Lefschetz thimble corresponds to the quantization of an imaginary phase space. The states resulting from the quantization of this phase space contribute negatively to the partition function and can be regarded as bulk duals of trace relations. Finally, we study a model for a path integral that would connect together components of the bulk half-BPS field space with different numbers of giants.

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arXiv2023

Trace relations and open string vacua

We study to what extent, and in what form, the notion of gauge-string duality may persist at finite $N$. It is shown, in the half-BPS sector, that the states of D3 giant graviton branes in $\mathrm{AdS}_5 \times S^5$ are holographically dual to certain auxiliary ghosts that compensate for finite $N$ trace relations in $U(N)$ $\mathcal{N}=4$ super Yang-Mills. The complex formed from spaces of states of bulk D3 giants is observed to furnish a BRST-like resolution of the half-BPS Hilbert space of $U(N)$ $\mathcal{N}=4$ SYM at finite $N$. We argue that the identification between the states of certain bulk D-branes and the auxiliary ghosts in the boundary holds rather generally at vanishing 't Hooft coupling $λ= 0$. We propose that a complex, which furnishes a BRST-like resolution of the finite $N$ Hilbert space of a boundary $U(N)$ gauge theory at $λ= 0$, should be identified as the space of states of the dual string theory in the $α' \to \infty$ limit. The Lefschetz trace formula provides the holographic map in this regime, where bulk observables are computed by taking the alternating sum of the expectation values in an ensemble of states built on each open string vacuum. The giant graviton expansion is recovered and generalized in a limit of the resolution.

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arXiv2022

Exact Stringy Microstates from Gauge Theories

We study how the microstates of BPS sectors in string theory are organized in the dual $U(N)$ gauge theory. The microstates take the form of a coherent sum of stacks of branes and their open/closed string excitations. We propose a prescription to holographically construct the indices of string/brane configurations by analyzing the modifications of determinant operators in gauge theory. The string/brane configurations should be interpreted in the tensionless limit, but their indices are well-defined at finite $N$. In various examples, we provide evidence that a sum, of the giant graviton-type recently proposed in the literature, over all such configurations gives the finite $N$ gauge theory index. Finally, we discuss how these microstates assemble in the BPS Hilbert space and in what circumstances the branes can form bound states to produce black hole degeneracies.

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arXiv2022

Bounds on gravitational brane couplings and tomography in AdS3 black hole microstates

We study information theoretic properties of planar black hole microstates in 2 + 1 dimensional asymptotically anti-de Sitter spacetime, modeled by black holes with an end-of-the-world brane behind the horizon. The von Neumann entropy of sufficiently large subregions in the dual CFT exhibits a time-dependent phase, which from a doubly-holographic perspective corresponds to the appearance of quantum extremal islands in the brane description. Considering the case where dilaton gravity is added to the brane, we show that tuning the associated couplings affects the propagation of information in the dual CFT state. By requiring that information theoretic bounds on the growth of entanglement entropy are satisfied in the dual CFT, we can place bounds on the allowed values of the couplings on the brane. Furthermore, we initiate the study of brane tomography, by showing how subleading corrections to the entanglement velocity can be used to learn about the properties of the brane as well as any gravitational dynamics localized on it.

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arXiv2021

Kondo line defects and affine Gaudin models

We describe the relation between integrable Kondo problems in products of chiral $SU(2)$ WZW models and affine $SU(2)$ Gaudin models. We propose a full ODE/IM solution of the spectral problem for these models.

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arXiv2021

The Giant Graviton Expansion

We propose and test a novel conjectural relation satisfied by the superconformal index of maximally supersymmetric $U(N)$ gauge theory in four dimensions. Analogous relations appear to be also valid for the superconformal indices of a large collection of other gauge theories, as well as for a broad class of index-like generating functions. The relation expresses the finite $N$ index as a systematic series of corrections to a large $N$ answer. Individual corrections have an holographic interpretation as the analytic continuation of contributions from "giant graviton" branes fixed by a specific symmetry generator.

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arXiv2021

Integrable Kondo problems

We discuss the integrability and wall-crossing properties of Kondo problems, where an 1d impurity is coupled to a 2d chiral CFT and triggers a defect RG flow. We review several new and old examples inspired by constructions in four-dimensional Chern-Simons theory and by affine Gaudin models.

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