arXiv subjects

Sangheon Yun

Publications and source records attributed to Sangheon Yun.

13 recordsLinked to original sources

arXiv2026

Perturbative Double-Scalar Hair on Planar Black Holes in AdS$_{4}$ Einstein-Scalar Gravity

We construct a two-scalar hairy planar black hole in four-dimensional Einstein gravity coupled to two scalars whose potential descends from the ABJM consistent truncation of eleven-dimensional supergravity. Starting from the known single-scalar hairy black brane, we switch on the second scalar $\phim$ perturbatively in its amplitude $\eps$ and solve the coupled Einstein-scalar system to order $\eps^{2}$. The linearized $\phim$ profile is an exact hypergeometric function, independent of the $\pp$ hair, whose horizon-regular branch always carries a source, so there is no spontaneous $\phim$ hair. Because the dual operator $\mathcal{O}_{-}$ is irrelevant ($Δ=4$), the second-order response develops a logarithmically running condensate with a closed-form, scheme-independent slope $\tfrac{\sqrt{21}}{70}C_{s}^{2}$. The renormalized free energy is scheme dependent, but the geometric temperature shift $δT/T_{0}\approx-0.345\,\eps^{2}$ at fixed entropy is not. The full metric and $\pp$ back-reaction is obtained in closed form, diagonalizing into two Pöschl-Teller problems with $δ\pp=\tfrac{6}{\sqrt7}\,δH$. Three transport coefficients of the dual fluid remain exactly conformal to this order, while the sound speed, like the free energy, is scheme dependent.

hep-th↗

arXiv2026

Perturbative Hairy Black Branes in the $G_{2}$-Invariant Sector of Dyonic ISO(7) Gauged Supergravity

We construct perturbative black-brane solutions carrying neutral scalar hair in the $G_{2}$-invariant truncation of four-dimensional dyonic $\mathcal{N}=8$ ISO(7) gauged supergravity, an exact consistent truncation of massive type~IIA supergravity on $S^{6}$. Expanding around the $G_{2}$-symmetric AdS$_{4}$-Schwarzschild black brane in powers of a dimensionless scalar-charge parameter $\eps$, we show that the perturbation hierarchy reduces, order by order, to a nested sequence of inhomogeneous Legendre equations (demonstrated through second order). The first-order scalar satisfies a Pöschl--Teller equation with exact parameter $ν(ν+1)=2/3$, giving $ν=-\frac{1}{2}+\frac{\sqrt{33}}{6}$, and the first-order metric is fixed algebraically by the same function, $A^{(1)}=-\tfrac{\sqrt{7}}{2}ϕ^{(1)}$, so the entire $\mathcal{O}(\eps)$ sector is one Legendre function. An identity $ν+1=Δ_{+}/3$, with $Δ_{+}=(3+\sqrt{33})/2\approx 4.372$ the conformal dimension of the dual scalar operator, relates the Pöschl-Teller parameter to the AdS/CFT dictionary via the nonlinear Fefferman-Graham map $z \propto z_{\mathrm{FG}}^{3}$. The $\mathcal{O}(\eps^{2})$ back-reaction yields explicit corrections to the renormalized free energy and Bekenstein-Hawking entropy density at fixed temperature, consistent with the first law; equivalently, at fixed entropy or energy density it \emph{lowers} the Hawking temperature by $δT/T=\mathcal{O}(\eps^{2})$. For the leading transport coefficients the shear viscosity saturates $η/s=1/(4π)$, while the Eling-Oz horizon formula gives a nonzero bulk viscosity $ζ/η=\bigl(\tfrac{Δ_{+}-3}{2}\bigr)^{2}\eps^{2}=\tfrac{3(7-\sqrt{33})}{8}\eps^{2}\approx0.471\,\eps^{2}$. With $c_{s}^{2}=\tfrac12-\mathcal O(\eps^{2})<\tfrac12$, this indicates a softening of the equation of state.

hep-th↗

arXiv2026

Exact Planar Black Hole in AdS-Einstein-Scalar Gravity with IR-Emergent Nearly Conformal Fluid

We study an exact analytic solution describing a static plane-symmetric hairy black hole in four-dimensional Einstein gravity minimally coupled to a neutral scalar, arising as a consistent truncation of type IIA supergravity on AdS$_4\times\mathbb{CP}^3$, the compactification dual to the strongly coupled thermal dynamics of the ABJM theory. The solution is characterized by two independent parameters. We perform the thermodynamic description by treating the scalar hair parameter as an independent variable, deriving the generalized first law and verifying the Euler relation. The UV boundary theory is a three-dimensional QFT at finite temperature deformed by an effectively marginally relevant scalar operator with logarithmic RG flow. The boundary theory exhibits explicit scale-symmetry breaking at high energies but recovers the behavior of a conformal fluid in the infrared thermal limit.

hep-th↗

arXiv2025

Scaling Bidirectional Spans and Span Violations in Attention Mechanism

The canonical $O(N^2)$ Transformer remains the empirical performance frontier in sequence modeling, and its training can be further optimized by addressing geometric inefficiency. We propose an optimization framework that leverages an asymmetric projection to decompose the backward-pass gradients into parallel spans and orthogonal violations, while keeping the canonical forward-pass $QKV$ structure intact. Through consistent experimental validation across various decomposition and projection setups, we provide strong theoretical evidence: the standard attention gradient is suboptimal. We demonstrated that selectively scaling these components, focusing primarily on $0^{th}$ order bidirectional parallel spans, yields the most effective learning signal. On the limited WikiText-2 dataset, and using a crude configuration, this method achieved a $0.56\%$ reduction in validation loss, confirming the framework's fundamental validity and suggesting significant potential gains on larger datasets and deeper training regimes

cs.LG↗

arXiv2020

Toroidal AdS Charged Branes and Toda Equations

In this note, we consider the equations of motion for charged branes in AdS space and show that they can be cast into one-dimensional coupled Toda type. Then we solve the equations of motion to construct static charged AdS brane solutions which are invariant under translation along $p$ directions and have toroidal symmetry. The solutions are described by mass, charges and a dilaton coupling constant.

gr-qc↗

arXiv2017

Calabi-Yau Manifolds, Hermitian Yang-Mills Instantons and Mirror Symmetry

We address the issue why Calabi-Yau manifolds exist with a mirror pair. We observe that the irreducible spinor representation of the Lorentz group Spin(6) requires us to consider the vector spaces of two-forms and four-forms on an equal footing. The doubling of the two-form vector space due to the Hodge duality doubles the variety of six-dimensional spin manifolds. We explore how the doubling is related to the mirror symmetry of Calabi-Yau manifolds. Via the gauge theory formulation of six-dimensional Riemannian manifolds, we show that the curvature tensor of a Calabi-Yau manifold satisfies the Hermitian Yang-Mills equations on the Calabi-Yau manifold. Therefore the mirror symmetry of Calabi-Yau manifolds can be recast as the mirror pair of Hermitian Yang-Mills instantons. We discuss the mirror symmetry from the gauge theory perspective.

hep-th↗

arXiv2011

Symmetry Breaking Phase Transitions in ABJM Theory with a Finite U(1) Chemical Potential

We consider the U(1) charged sector of ABJM theory at finite temperature, which corresponds to the Reissner-Nordstrom AdS black hole in the dual type IIA supergravity description. Including back-reaction to the bulk geometry, we show that phase transitions occur to a broken phase where SU(4) R-symmetry of the field theory is broken spontaneously by the condensation of dimension one or two operators. We show both numerically and analytically that the relevant critical exponents for the dimension one operator agree precisely with those of mean field theory in the strongly coupled regime of the large N planar limit.

hep-th↗

arXiv2011

Domain Walls in AdS-Einstein-scalar Gravity

In this note, we will show that the supergravity theory which is dual to ABJM field theory can be consistently reduced to scalar-coupled AdS-Einstein gravity and then consider the reflection symmetric domain wall and its small fluctuation. This domain wall solution is none other than dimensional reduction of M2-brane configuration.

gr-qc↗

arXiv2010

Thermal Aspects of ABJM theory: Currents and Condensations

To study thermal aspects of the ABJM theory in the strongly coupled regime, we carry out the CP3 invariant dimensional reduction of the type IIA supergravity down to four dimensions. We then investigate zero and finite temperature responses of the operators which are dual to the AdS scalar and vector fields. Two scalar operators are shown to have finite-temperature condensations by coupling of constant source term. The currents dual to the massless and massive gauge fields are not induced by coupling of constant boundary vector potential, which implies that the phase described by black brane background is not superconducting. We also discuss a generalization to charged (dyonic) black holes.

hep-th↗

arXiv2009

Brane Solutions with Tension

In this note, we apply a special metric ansatz to simplify the equations of motion for gravitational systems. Then we construct charged brane solutions in $D=n+p+2$ dimensions which have spherical symmetry of $S^n$ and translational symmetry along $p$ directions. They are characterized by mass density, uniform tension and electric/magnetic charges, and nonsingular only for specific tension. In particular, we find the limits and the coordinate transformations which reduce the charged brane solutions to $M2$- and $M5$-branes. We also obtain the regularity condition for an electrically charged two-brane solution which has two tensions.

gr-qc↗

arXiv2007

Higher derivative correction to Kaluza-Klein black hole solution

We investigate the attractor mechanism in Kaluza-Klein black hole solution in the presence of higher derivative terms. In particular, we discuss the attractor behavior of static black holes by using the effective potential approach as well as entropy function formalism. We consider different higher derivative terms with a general coupling to moduli field. For the $R^2$ theory, we use effective potential approach, looking for solutions which are analytic near the horizon and show that they exist and enjoy the attractor behavior. The attractor point is determined by extremization of the modified effective potential at the horizon. We study the effect of the general higher derivative corrections of $R^n$ terms. Using the entropy function we define the modified effective potential and we find the conditions to have the attractor solution. In particular for a single charged Kaluza-Klein black hole solution we show that higher derivative correction dresses the naked singularity for an appropriate coupling, and we can find the attractor solution.

hep-th↗

arXiv2007

Moduli flow and non-supersymmetric AdS attractors

We investigate the attractor mechanism in gauged supergravity in the presence of higher derivatives terms. In particular, we discuss the attractor behaviour of static black hole horizons in anti-de Sitter spacetime by using the effective potential approach as well as Sen's entropy function formalism. We use the holographic techniques to interpret the moduli flow as an RG flow towards the IR attractor horizon. We find that the holographic c-function obeys the expected properties and point out some subtleties in understanding attractors in AdS.

hep-th↗

arXiv2007

Non-Supersymmetric Unattractors in Born-Infeld Black Holes

We investigate unattractor behavior in non-extremal black holes in Einstein-Born-Infeld-Dilaton theory of gravity in four-dimensional asymptotically flat spacetime. We obtain solutions which are non-singular near the horizon and dependent on the value of the dilaton field at the infinity, using perturbation method. It is shown that the value of the scalar field at the horizon is determined by its asymptotic value and the charges carried by the black hole. And we also find it is not true in general that the dilaton value at the horizon is a monotonically increasing function of the first coefficient of its series expansion in non-extremal Born-Infeld black holes.

hep-th↗