arXiv subjects

Jae-Hyuk Oh

Publications and source records attributed to Jae-Hyuk Oh.

At least 19 recordsLinked to original sources

arXiv2025

Analytic approaches to anisotropic holographic superfluids in asymptotically hyperscaling violation geometry

We explore anisotropic holographic superfluidity and find analytic solutions near critical point where superfluid/normalfluid phase transition appears in a holographic dual fluid system. In arXiv:hep-th/1109.4592, the authors obtained such an analytic solution in 5-dimensional Einstein-SU(2)Yang-Mills system, and it is asymptotically AdS$_5$. What is more in this note is that we get analytic solutions near the critical point in 3- and 4- dimensional Einstein-Scalar-U(1)$\times$SU(2)Yang-Mills systems, which become asymptotically hyperscaling violation geometry. We also get leading order back reactions to the background geometry, which clearly show spatial anisotropy of the bulk geometry. To explore the properties of the spacetime, we compute holographic entanglement entropy and confirm that the superfluid/normalfluid phase transition must occur at the critical point.

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arXiv2024

A conformal scalar $n$-point function in momentum space

We suggest a certain type of conformal $n$-point function of scalar primaries where the scalar operators share the same scaling dimension. The conformal correlation functions are obtained in momentum space, and we show that they satisfy the conformal Ward identities.

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arXiv2024

Momentum-space Langevin dynamics of holographic Wilsonian RG flow: self-interacting massive scalar field theory

We explore mathematical relationship between holographic Wilsonian renormalization group(HWRG) and stochastic quantization(SQ) motivated by the similarity of the monotonicity in RG flow with Langevin dynamics of non-equilibrium thermodynamics. We look at scalar field theory in AdS space with its generic mass, self-interaction, and boundary deformation in the momentum space. Identifying the stochastic time $t$ with radial coordinate $r$ in AdS, we establish maps between the fictitious time evolution of stochastic multi point correlation function and the radial evolution of multi-trace deformation, which respectively, express the relaxation process of Langevin dynamics and holographic RG flow. We especially consider marginal multi-trace deformation on the AdS boundary which is successfully captured by a Langevin dynamics of SQ.

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arXiv2023

Stochastic quantization and holographic Wilsonian renormalization group of conformally coupled scalar in AdS$_{4}$

In this paper, we explore the relationship between holographic Wilsonian renormalization groups and stochastic quantization in conformally coupled scalar theory in AdS$_{4}$. The relationship between these two different frameworks is firstly proposed in arXiv:1209.2242 and tested in various free theories. However, research on the theory with interactions has recently begun. In this paper, we show that the stochastic four-point function obtained by the Langevin equation is completely captured by the holographic quadruple trace deformation when the Euclidean action $S_{E}$ is given by $S_{E}=-2I_{os}$ where $I_{os}$ is the holographic on-shell action in the conformally coupled scalar theory in AdS$_{4},$ together with a condition that the stochastic fictitious time $t$ is also identified with AdS radial variable $r$. We extensively explore a case that the boundary condition on the conformal boundary is Dirichlet boundary condition, and in that case, the stochastic three-point function trivially vanishes. This agrees with that the holographic triple trace deformation vanishes when Dirichlet boundary condition is applied on the conformal boundary.

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arXiv2023

Stochastic quantization and holographic Wilsonian renormalization group of scalar theory with generic mass, self-interaction and multiple trace deformation

We explore the mathematical relationship between holographic Wilsonian renormalization group(HWRG) and stochastic quantization(SQ) of scalar field theory with its generic mass, self-interaction and $n$-multiple-trace deformation on the $d$-dimensional conformal boundary defined in AdS$_{d+1}$ spacetime. We understand that once we define our Euclidean action, $S_E$ as $S_E\equiv -2S_B$, then the stochastic process will reconstruct the holographic Wilsonian renormalization group data via solving Langevin equation and computing stochastic correlation functions. The $S_B$ is given by $S_B=S_{\rm ct}+S_{\rm def}$, where $S_{\rm ct}$ is the boundary counter term and $S_{\rm def}$ is the boundary deformation which gives a boundary condition. In our study, we choose the boundary condition adding (marginal)$n$-multiple trace deformation to the holographic dual field theory. In this theory, we establish maps bewteen ficticious time, $t$ evolution of stochastic $n$-point, ($2n-2$)-point correlation functions and the (AdS)radial, $r$ evolution of $n$-multiple-trace and ($2n-2$)-multiple-trace deformations respectively once we take identifications of $r=t$ and between some of constants appearing in both sides.

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arXiv2023

Holographic entanglement entropy probe on spontaneous symmetry breaking with vector order

We study holographic entanglement entropy in 5-dimensional charged black brane geometry obtained from Einstein-SU(2)Yang-Mills theory defined in asymptotically AdS space. This gravity system undergoes second order phase transition near its critical point affected by a spatial component of the Yang-Mills fields, which is normalizable mode of the solution. This is known as phase transition between isotropic and anisotropic phases. We get analytic solutions of holographic entanglement entropies by utilizing the solution of bulk spacetime geometry given in arXiv:1109.4592, where we consider subsystems defined on AdS boundary of which shapes are wide and thin slabs and a cylinder. It turns out that the entanglement entropies near the critical point shows scaling behavior such that for both of the slabs and cylinder, $Δ_\varepsilon S\sim\left(1-\frac{T}{T_c}\right)^β$ and the critical exponent $β=1$, where $Δ_\varepsilon S\equiv S^{iso}-S^{aniso}$, and $S^{iso}$ denotes the entanglement entropy in isotropic phase whereas $S^{aniso}$ denotes that in anisotropic phase. We suggest a quantity $O_{12}\equiv S_1-S_2$ as a new order parameter near the critical point, where $S_1$ is entanglement entropy when the slab is perpendicular to the direction of the vector order whereas $S_2$ is that when the slab is parallel to the vector order. $O_{12}=0$ in isotropic phase but in anisotropic phase, the order parameter becomes non-zero showing the same scaling behavior. Finally, we show that even near the critical point, the first law of entanglement entropy is hold. Especially, we find that the entanglement temperature for the cylinder is $\mathcal T_{cy}=\frac{c_{ent}}{a}$, where $c_{ent}=0.163004\pm0.000001$ and $a$ is the radius of the cylinder.

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arXiv2021

On holographic Wilsonian renormalization group of massive scalar theory with its self-interactions in AdS

Holographic model of massive scalar field with its self-interaction $λϕ^n$ in AdS space is able to give a logarithmic scale dependence to marginal multi trace deformation couplings on its dual conformal field theory, where $λ$ is the self-interaction coupling of the scalar field, $ϕ$ and $n$ is an integral number. In arXiv:1501.06664, the authors realize this feature by looking at bulk scalar solutions near AdS boundary imposing a specific boundary condition between the coefficients of non-normalizable and normalizable modes of the scalar field excitations. We study the same holographic model to see scale dependence of marginal deformations on the dual conformal field theory by employing completely different method: {\it holographic Wilsonian renormalization group}. We solve Hamilton-Jacobi equation derived from the holographic model of massive scalar with $λϕ^n$ interaction and obtain the solution of marginal multi trace deformations up to the leading order in $λ$. It turns out that the solution of marginal multi trace deformation also presents logarithmic behavior in energy scale near UV region.

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arXiv2021

First order formalism of holographic Wilsonian renormalization group: Langevin equation

We study a mathematical relationship between holographic Wilsonian renormalization group and stochastic quantization framework. We extend the original proposal given in arXiv:1209.2242 to interacting theories. The original proposal suggests that fictitious time(or stochastic time) evolution of stochastic 2-point correlation function will be identical to the radial evolution of the double trace operator of certain classes of holographic models, which are free theories in AdS space. We study holographic gravity models with interactions in AdS space and establish a map between the holographic renormalization flow of multi-trace operators and stochastic $n$-point functions. To give precise examples, we extensively study conformally coupled scalar theory in AdS$_6$. What we have found is that the stochastic time $t$ dependent 3-point function obtained from Langevin equation with its Euclidean action being given by $S_E=2I_{os}$ is identical to holographic renormalization group evolution of holographic triple trace operator as its energy scale $r$ changes once an identification of $t=r$ is made. $I_{os}$ is the on-shell action of holographic model of conformally coupled scalar theory at the AdS boundary. We argue that this can be fully extended to mathematical relationship between multi point functions and multi trace operators in each framework.

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arXiv2021

Aspects of $(d+D)$-dimensional Anisotropic Conformal Gravity

We discuss various aspects of anisotropic gravity in $(d+D)$-dimensional spacetime where $D$ dimensions are treated as extra dimensions. It is based on the foliation preserving diffeomorphism invariance and anisotropic conformal invariance. The anisotropy is embodied by introducing a factor $z$ which discriminates the scaling degree of the extra $D$ dimensions against the $d$-dimensional base spacetime and Weyl scalar field which mediates the anisotropic scaling symmetry. There is no intrinsic scale but a physical scale $M_*$ emerges as a consequence of spontaneous conformal symmetry breaking. Some vacuum solutions are obtained and we discuss an issue of `size separation' between the base spacetime and the extra dimensions. The size separation means large hierarchy between the scales appearing in the base spacetime and the extra dimensions respectively. We also discuss interesting theories obtained from our model. In the case of (4,1), we propose a resolution of hierarchy problem and discuss comparison with the results of the brane-world model. In a $(d,D)=(2,2)$ case, we suggest a UV-complete unitary quantum gravity which might become Einstein gravity in IR. In a certain (2,1) case, we obtain CGHS-model.

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arXiv2021

Partially massless theory as a quantum gravity candidate

We study partially massless gravity theory(PM gravity theory) and suggest an alternative way to add higher order interaction vertices to the theory. Rather than introducing self interaction vertices of the gravitational fields to the partially massless gravity action, we consider interactions with matter fields, since it is well known that addition of the self interaction terms necessarily breaks the $U(1)$ gauge symmetry that PM gravity theory enjoys. For the coupling with matter fields, we consider two different types of interaction vertices. The first one is given by an interaction Lagrangian density, $\mathcal L_{int}\sim h_{μν}T^{μν}$, where $h_{μν}$ is the PM gravity field and $T^{μν}$ is the stress-energy tensor of the matter fields. To retain the $U(1)$ gauge symmetry, the matter fields also transform accordingly and it turns out that the transform must be non-local in this case. The second type interaction is obtained by employing a gauge covariant derivative with the PM gravity field, where the PM gravity fields play a role of a gauge connection canceling the phase shift of the matter fields. We also study the actions and the equations of motion of the partially massless gravity fields. As expected, it shows 4 unitary degrees of freedom. 2 of them are traceless tensor modes and they are light like fields. The other 2 are transverse vector modes and their dispersion relation changes as background space time (de Sitter) evolutes. In the very early time, they are light like but in the very late time, their velocity become a half of speed of light. The vector mode dispersion relation shows momentum dependent behavior. In fact, the higher(lower) frequency modes show the faster(slower) velocity. We suggest their quantization, compute Hamiltonians to present their exited quanta and construct their free propagators.

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arXiv2021

Electric-magnetic duality as a quantum operator and more symmetries of $U(1)$ gauge theory

We promote the Noether charge of the electric-magnetic duality symmetry of $U(1)$ gauge theory, "$G$" to a quantum operator. We construct ladder operators, $D_{(\pm)a}^\dagger(k)$ and $D_{(\pm)a}(k)$ which create and annihilate the simultaneous quantum eigen states of the quantum Hamiltonian(or number) and the electric-magnetic duality operators respectively. Therefore all the quantum states of the $U(1)$ gauge fields can be expressed by a form of $|E,g\rangle$, where $E$ is the energy of the state, the $g$ is the eigen value of the quantum operator $G$, where the $g$ is quantized in the unit of 1. We also show that 10 independent bilinears comprised of the creation and annihilation operators can form $SO(2,3)$ which is as demonstrated in the Dirac's paper published in 1962. The number operator and the electric-magnetic duality operator are the members of the $SO(2,3)$ generators. We note that there are two more generators which commute with the number operator(or Hamiltonian). We prove that these generators are indeed symmetries of the $U(1)$ gauge field theory action.

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arXiv2020

4-point function from conformally coupled scalar in AdS$_6$

We explore conformally coupled scalar theory in AdS$_{6}$ extensively and their classical solutions by employing power expansion order by order in its self-interaction coupling $λ$. We study holographic correlation functions of scalar operator deformations to a certain 5-dimensional conformal field theory where the operators share the same scaling dimension $Δ=3$, from the classical solutions. For our solutions, we choose a scheme where we remove co-linear divergences of momenta along the AdS boundary directions which frequently appear in the classical solutions. This shows clearly that the holographic correlation functions are free from the co-linear divergences. It turns out that this theory provides correct conformal 2- and 3- point functions of the $Δ=3$ scalar operators as expected in previous literature. It makes sense since 2- and 3- point functions are determined by global conformal symmetry not being dependent on the details of the conformal theory. We also get 4-point function from this holographic model. In fact, it turns out that the 4-point correlation function is not conformal because it does not satisfy the special conformal Ward identity although it does dilation Ward identity and respect $SO(5)$ rotation symmetry. However, in the co-linear limit that all the external momenta are in a same direction, the 4-point function is conformal which means that it satisfy the special conformal Ward identity. We inspect holographic $n$-point functions of this theory which can be obtained by employing a certain Feynman-like rule. This rule is a construction of $n$-point function by connecting $l$-point functions each other where $l<n$. In the co-linear limit, these $n$-point functions reproduce the conformal $n$-point functions of $Δ=3$ scalar operators in $d=5$ Euclidean space addressed in arXiv:2001.05379.

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arXiv2016

Phase transition in anisotropic holographic superfluids with arbitrary $z$ and $α$

Einstein-dilaton-$U(2)$ gauge field theory is considered in a spacetime characterised by $α$ and $z$, which are the hyperscaling violation factor and the dynamical critical exponent respectively. We obtain the critical values of chemical potential $μ_c$ that is defined on its boundary dual fluid and derives phase transition from spatially isotropic to anisotropic phase for the various values of the $α$ and $z$. To do so, we first apply Sturm-Liouville theory and estimate the upper bounds of the critical values of the chemical potential. We also employ a numerical method in the ranges of $1 \leq z \leq 4$ and $0 \leq α\leq 4$ to check if the Sturm-Liouville method correctly estimates the critical values of the chemical po10 percent error ranges. Finally, we compute free energy density of the dual fluid by using its gravity dual and check if the system shows phase transition at the critical values of the chemical potential $μ_c$ for the given parameter region of $α$ and $z$. Interestingly, it is observed that the anisotropic phase is more favoured than the isotropic phase for small values of $z$ and $α$. However, for large values of $z$ and $α$, the anisotropic phase is not favoured.tential. It turns out that the two methods are agreed within

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arXiv2015

Boundary conditions for conformally coupled scalar in AdS$_4$

We consider conformally coupled scalar with $ϕ^4$ coupling in AdS$_4$ and study its various boundary conditions on AdS boundary. We have obtained perturbative solutions of equation of motion of the conformally coupled scalar with power expansion order by order in $ϕ^4$ coupling $λ$ up to $λ^2$ order. In its dual CFT, we get 2,4 and 6 point functions by using this solution with Dirichlet and Neumann boundary conditions via AdS/CFT dictionary. We also consider marginal deformation on AdS boundary and get its on-shell and boundary effective actions.

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arXiv2014

Electric-magnetic duality implies (global) conformal invariance

We have examined quantum theories of electric magnetic duality invariant vector fields enjoying classical conformal invariance in 4-dimensional flat spacetime. We extend Dirac's argument about "the conditions for a quantum field theory to be relativistic" to "those for a quantum theory to be conformal". We realize that electric magnetic duality invariant vector theories together with classical conformal invariance defined in 4-$d$ flat spacetime are still conformally invariant theories when they are quantized in a way that electric magnetic duality is manifest.

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arXiv2013

Stochastic quantization and holographic Wilsonian renormalization group of massless fermions in AdS

We have studied holographic Wilsonian renormalization group (HWRG) of free massless fermionic fields in AdS space and its stochastic quantization(SQ) by identifying the Euclidean action with its boundary on-shell action. The natural extension of the relation between stochastic 2-point correlation function and double trace coupling obtained from HWRG computation conjectured in arXiv:1209.2242 to fermionic fields is established. We have confirmed that the stochastic 2-point function precisely captures the radial flow of the double trace coupling via this relation.

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arXiv2013

Stochastic quantization of conformally coupled scalar in AdS

We explore the relation between stochastic quantization and holographic Wilsonian renormalization group flow further by studying conformally coupled scalar in $AdS_{d+1}$. We establish one to one mapping between the radial flow of its double trace deformation and stochastic 2-point correlation function. This map is shown to be identical, up to a suitable field re-definition of the bulk scalar, to the original proposal in arXiv:1209.2242.

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arXiv2013

Transport in non-conformal holographic fluids

We have considered non-conformal fluid dynamics whose gravity dual is a certain Einstein dilaton system with Liouville type dilaton potential, characterized by an intrinsic parameter $η$. We have discussed the Hawking-Page transition in this framework using hard-wall model and it turns out that the critical temperature of the Hawking-Page transition encapsulates a non-trivial dependence on $η$. We also obtained transport coefficients such as AC conductivity, shear viscosity and diffusion constant in the hydrodynamic limit, which show non-trivial $η$ dependent deviations from those in conformal fluids, although the ratio of the shear viscosity to entropy density is found to saturate the universal bound. Some of the retarded correlators are also computed in the high frequency limit for case study.

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