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Yoon-Seok Choun

Publications and source records attributed to Yoon-Seok Choun.

17 recordsLinked to original sources
arXiv2026

Fuchsian Resonance and a Horizon-to-Boundary Dictionary for Pole-Skipping

Pole-skipping occurs at special complex frequencies and momenta where the retarded Green function of a black-hole or black-brane background is not uniquely defined. The local near-horizon mechanism is well known: at resonance, a Frobenius recurrence matrix loses rank and the space of smooth horizon solutions enlarges. We address the global question of how two boundary-normalized solutions enter this resonant horizon solution space. For a general second-order scalar radial equation on a nonextremal background analytic near the horizon, the Frobenius recurrence at the resonant order yields a solvability condition. We prove that its vanishing is equivalent to singularity of the horizon recurrence matrix, absence of the logarithmic Frobenius term, and existence of two independent smooth horizon solutions. Away from resonance, the source zero is equivalent to horizon smoothness of the response-normalized solution, while the response zero is equivalent to horizon smoothness of the source-normalized solution. We then analyze the parameter-dependent simple pole of the nonresonant ingoing solution as resonance is approached. After removing this singularity, its resonant limit is proportional to the larger-root Frobenius solution, with proportionality factor given by the same solvability function. Continuing to the boundary shows that the same condition is equivalent to simultaneous vanishing of the two regularized boundary connection coefficients. This establishes a horizon-to-boundary dictionary between local Fuchsian resonance and the boundary source-response 0/0 structure of pole-skipping. Finally, different directions of approach can select different resonant solutions, with the selection governed by the first parameter variation of the same solvability function.

hep-th↗
arXiv2026

A Horizon-to-Boundary Dictionary Linking Smooth Horizon Continuation, Pole-Skipping, and \(SL(2,\mathbb R)\) Lowest-Weight Structure

We study pole-skipping for a scalar field in the JT/AdS$_2$ black-hole background. Previous work established the local mechanism: at a pole-skipping point, a near-horizon recurrence relation becomes degenerate and an additional regular expansion coefficient is left undetermined. We take this local degeneracy as the starting point and track two independent solutions normalized at the AdS boundary, denoted by $R_1$ and $R_2$ for the source and response branches, respectively. Let $\widehat A$ and $\widehat B$ denote the source and response coefficients after their common singular factor is removed, and let $χ_μ$ denote the universal ingoing horizon factor. We find \[ \widehat A=0 \Longleftrightarrow \frac{R_2}{χ_μ}\in C^\infty, \qquad \widehat B=0 \Longleftrightarrow \frac{R_1}{χ_μ}\in C^\infty . \] Thus the source and response zeros correspond separately to horizon smoothness of the two boundary-normalized solutions after the ingoing factor is removed. At integer resonance the local regular solution contains an additional coefficient $a_N$. In the JT/AdS$_2$ model, continuation of the nonresonant ingoing solution fixes $a_N=0$ and thereby selects a unique retarded value at resonance, although unrestricted approaches in parameter space remain path dependent. At the endpoint of the pole-skipping lattice, the response branch is a lowest-weight state of the background $SL(2,\mathbb R)$ symmetry. A static holographic-superconductor example further shows that simultaneous horizon smoothness is insufficient if the two boundary branches are linearly dependent. A two-branch pole-zero intersection therefore requires \[ W[R_1,R_2]\neq0. \] These results distinguish the known local horizon degeneracy from the global relation between boundary branches and the resonant horizon solution space.

hep-th↗
arXiv2025

On the Incompatibility of Rearrangement with Convergence: An Axiomatic Approach to Holomorphic Recurrence Relations

In classical analysis, the convergence behavior of power series solutions to differential or recurrence equations is generally assumed to be invariant under internal rearrangement. This paper challenges that belief by proving that, for holomorphic solutions to higher-order recurrence relations (order 3 or more), rearrangement of internal terms systematically reduces the radius of convergence. This contradicts assumptions underlying both Fuchs' theorem and the Poincare-Perron theorem. To address this, the paper proposes the Principle of Indivisible Integrity, an axiom that restricts arbitrary reordering within analytic computations. Both analytic arguments and numerical examples (see Theorem 3.3 and Table 3) show that violation of this principle can lead to structural divergence, even when classical conditions suggest convergence. This framework suggests the need to reexamine analytic structures in recurrence-based methods across mathematical physics, including quantum mechanics, general relativity, and spectral theory. It also raises foundational questions about computation and mathematical rigor in an age of automated symbolic processing. Rather than offering just a technical correction, this paper advocates a philosophical principle: that the integrity of mathematical order must be preserved by structure, not merely by computational convenience.

math.CA↗
arXiv2024

Holographic dual effective field theory in the Luttinger-Ward functional approach: Application to an SYK model

We construct an emergent holographic dual description in the Luttinger-Ward functional approach, where the renormalization group (RG) flows of collective bi-local fields appear manifestly in the bulk effective action with an emergent extra dimension. This holographic dual effective field theory reproduces $1/N$ quantum corrections in a self-consistent manner when we take the UV limit in the bulk effective action. Going into the IR regime in the extra dimension, we observe that a partial class of the field theoretic $1/N$, $1/N^{2}$, ... quantum corrections are resummed in the all-loop order and reorganized to form a holographic dual effective field theory in a large $N$ fashion living on the one-higher dimensional spacetime. In this study, we apply this theoretical framework into an Sachdev-Ye-Kitaev (SYK) model. Taking the large $N$ limit in the holographic dual effective field theory, we obtain nonlinearly coupled second-order bulk differential equations of motion for the three bi-local order-parameter fields of fermion self-energy, Green's function, and polarization function. Here, both UV and IR boundary conditions are derived self-consistently from the boundary effective action. We solve these highly intertwined nonlinear differential equations based on the so called matching method. Our ansatz for the bi-local order-parameter fields coincide with the conformally invariant solution of the field theoretic large $N$ limit in the UV limit, but their overall coefficients $RG-flow$ along the extra dimensional space, respectively, reflecting effects of higher-order quantum corrections. As a result, we find an insulating behavior, where the self-energy diverges at IR. ...

hep-th↗
arXiv2024

Quantum Scaling Dimension from the Equivalence principle

We propose a method to constrain the scaling dimension of the operators of the strongly interacting systems (SIS) using the holographic setup. %where the (d+1)-dimensional black hole is used to describe the d-dimensional SIS. We demonstrate our method using the holographic superconductor theory. The idea is to consider the inside as well as the outside of the AdS black hole in which the gap equations has higher order singularities. Then the equivalence principle requests the solution be smoothly connected at the horizon, which request the vanishing of log divergent term as well as an indefinite conditionally convergent terms that can lead to any real number according to Riemann. As a result, one gets quantized values of the scaling dimension of the condensing operator. This is a pleasant surprise because so far one gets the constraints on the scaling dimension only by a hard analysis with bootstrap ansatz.

hep-th↗
arXiv2023

Scaling dimension of Cooper pair operator from the black hole interior

We have shown that in holographic superconductivity theory for 3+1 dimensional system, the scaling dimension of Cooper pair operator can be obtained as a quantized value if we request that the the scalar function describing the order parameter is finite inside the black hole as well as outside. This should be contrasted to the usual situation where we set the mass squared of the scalar by hand. Our method can be applied to any order parameters.

hep-th↗
arXiv2023

The violation of a uniqueness theorem and an invariant in the application of Poincaré--Perron theorem to Heun's equation

The domain of convergence of a Heun function obtained through the Poincaré--Perron (P--P) theorem is not absolute convergence but conditional one [2]. We show that a uniqueness theorem is not available if we apply the P--P theorem into the Heun's equation. We verify that the uniqueness theorem is only applicable when a local Heun function is absolutely convergent.

math.CA↗
arXiv2023

The convergence test to the application in a multi-term recurrence relation of a linear ODE

The recursive relation starts to appear by putting a function $y(x)=\sum_{n=0}^{\infty }d_n x^n$ into a linear ordinary differential equation (ODE). There can be $d$-term of sequences in the recurrence relation of a power series where $d\geq 2$. We discuss the absolute convergence test to the $d$-term recurrence relation with non-constant coefficients of a linear ODE.

math.CA↗
arXiv2023

Momentum dependent gap in holographic superconductors revisited

We reconsider the angular dependence in gap structure of holographic superconductors, which has not been treated carefully so far. For the vector field model, we show that the normalizable ground state is in the p-wave state because s-wave state is not normalizable. On the other hand, in the scalar order model, the ground state is in the $s$-wave. The angle dependent gap function is explicitly constructed in these models. We also suggest the modified ansatz of the vector order which enables to discuss the order $p_{x}\pm ip_{y}$ gap, which has not been possible so far. We have also analytically investigated the critical temperature and the behavior of the gap near there. Interestingly, for the fixed conformal dimension of the Cooper pair operator, the critical temperature in vector model is higher than that of the scalar model.

hep-th↗
arXiv2022

Heun's equation and analytic structure of the Gap in Holographic superconductivity

We present the new method to calculate the critical temperature as a function of $Δ$, conformal dimension of the cooper operator. We find that, in the regime $1/2\leq Δ<1$ where the AC conductivity does not show a gap, the critical temperature is not well defined. We also got expression of AC conductivity for $Δ=2$, which agrees with numerical result in the probe approximation.

hep-th↗
arXiv2020

Inexistence of quark mass in chiral symmetry and its relation to confinement dynamics

In 1985, Gürsey showed that the spectrum of the semi-relativistic Hamiltonian for the bag model, introduced by Lichtenberg et al. for mesons, follows the Regge trajectory if the current quark mass is negligible. The model leads to the biconfluent Heun equation, which is a second-order linear ordinary differential equation (ODE) with a regular singularity at the origin and an irregular singularity at infinity. Based on rigorous mathematical computation, it is concluded that the energy spectrum is consistent with the Regge trajectory only when the quark mass vanishes. From this result, we suggest that the chiral symmetry is a consequence of confinement dynamics.

quant-ph↗
arXiv2020

Quantization of the charge in Coulomb plus harmonic potential

We consider two models where the wave equation can be reduced to the effective Schrödinger equation whose potential contains both harmonic and the Coulomb terms, $ω^{2}r^{2}-a/r$. The equation reduces to the biconfluent Heun's equation, and we find that the charge as well as the energy must be quantized and state dependent. We also find that two quantum numbers are necessary to count radial degrees of freedom and suggest that this is a general feature of differential equation with higher singularity like the Heun's equation.

hep-ph↗
arXiv2020

Bridging the Chiral symmetry and Confinement with Singularity

We consider a holographic quark model where the confinement is a consequence of the quark condensate. Surprisingly, the equation of motion of our holographic model can be mapped to the old spin-less bag model. Both models correctly reproduce the linear Regge trajectory of hadrons for zero quark mass. For the case of non-zero quark mass, the model lead us to Heun's equation. The mass term is precisely the origin of the higher singularity, which changes the system behavior drastically. Our result can shed some light on why the chiral transition is so close to the confinement transition. In the massive case, the Schroedinger equation is exactly solvable, but only if a surprising new quantization condition, additional to the energy quantization, is applied.

hep-th↗
arXiv2020

Chiral symmetry and Heun's equation

We show that the current quark mass should vanish to be consistent with the QCD color confinement: a bag model leads us to Heun's equation, which requests that not only the energy but also the string tension should be quantized. This is due to the presence of higher order singularity which requests higher regularity condition demanding that parameters of the theory should be related to one another. As a result, the Hadron spectrum is consistent with the Regge trajectory only when quark mass vanishes. Therefore, in this model, the chiral symmetry is a consequence of the confinement.

hep-ph↗
arXiv2020

Impossibility of convergence of a confluent Heun function on the boundary of the disc of convergence

The confluent Heun equation is one of 4 confluent forms of Heun's differential equation in which is the Fuchsian equation of second order with four regular singularities. A confluent Heun function is applicable to diverse areas such as theory of rotating/non-rotating black hole, the gauge theories on thick brane words, Schr$\ddot{\mbox{o}}$dinger equation for hydrogen molecule ion in Stark effect and etc. The confluent Heun function consists of the three term recurrence relation in its power series, and we show that the function is divergent on the boundary of the disc of convergence.

math.CA↗
arXiv2020

Impossibility of convergence of a Heun function on the boundary of the disc of convergence

The Heun's equation is the Fuchsian equation of second order with four regular singularities. Heun functions generalize well-known special functions such as Spheroidal Wave, Lamé, Mathieu, hypergeometric-type functions, etc. The recursive relation of coefficients starts to appear by putting a power series into the Heun equation. A local Heun function consists of the three term recurrence relation in its power series, and we prove that the function is not convergent on the boundary of the disc of convergence.

math.CA↗