arXiv subjects

Hyunsoo Min

Publications and source records attributed to Hyunsoo Min.

At least 19 recordsLinked to original sources

arXiv2018

Patterns of Gravitational Cooling in Schrodinger Newton System

We study time evolution of Schrodinger-Newton system using the self-consistent Crank-Nicolson method to understand the dynamical characteristics of nonlinear systems. Compactifying the radial coordinate by a new one, which brings the spatial infinity to a finite value, we are able to impose the boundary condition at infinity allowing for a numerically exact treatment of the Schrodinger-Newton equation. We study patterns of gravitational cooling starting from exponentially localized initial states. When the gravitational attraction is strong enough, we find that a small-sized oscillatory solitonic core is forming quickly, which is surrounded by a growing number of temporary halo states. In addition a significant fraction of particles escape to asymptotic regions. The system eventually settles down to a stable solitonic core state while all the excess kinetic energy is carried away by the escaping particles, which is a phenomenon of gravitational cooling.

gr-qc↗

arXiv2016

Geometric Monte Carlo and Black Janus Geometries

We describe an application of the Monte Carlo method to the Janus deformation of the black brane background. We present numerical results for three and five dimensional black Janus geometries with planar and spherical interfaces. In particular, we argue that the 5D geometry with a spherical interface has an application in understanding the finite temperature bag-like QCD model via the AdS/CFT correspondence. The accuracy and convergence of the algorithm are evaluated with respect to the grid spacing. The systematic errors of the method are determined using an exact solution of 3D black Janus. This numerical approach for solving linear problems is unaffected initial guess of a trial solution and can handle an arbitrary geometry under various boundary conditions in the presence of source fields.

hep-th↗

arXiv2014

Multi-faced Black Janus and Entanglement

To the second order of the deformation parameter, we construct the black brane solutions, which are dual to the multiple interface deformations of conformal field theories. We compute their thermodynamic quantities from the gravity and the field theory sides, and find a precise agreement, confirming the validity of the AdS/CFT correspondence. The correlation of two separate interfaces induces a Casimir energy and an interesting form of correlated entropy contribution. We comment on the properties of the interface lattice system too.

hep-th↗

arXiv2013

Duality-symmetric Action for Electromagnetic Theory with Electric and Magnetic Sources

For the SL(2,\textbf{R}) duality-invariant generalization of Maxwell electrodynamics in the presence of both electric and magnetic sources, we formulate a local, manifestly duality-symmetric, Zwanziger-type action by introducing a pair of four-potentials $A^μ$ and $B^μ$ in a judicious way. On the two potentials $A^μ$ and $B^μ$ the SL(2,\textbf{R}) duality transformation acts in a simple linear manner. In quantum theory including charged source fields, this action can be recast as a SL(2,\textbf{Z})-invariant action. Also given is a Zwanziger-type action for SL(2,\textbf{R}) duality-invariant Born-Infeld electrodynamics which can be important for D-brane dynamics in string theory.

hep-th↗

arXiv2011

Calculation of renormalized fermion effective actions in radially symmetric non-Abelian backgrounds

Our recent method to calculate renormalized functional determinants, the partial wave cutoff method, is extended for the evaluation of 4-D fermion one-loop effective action with arbitrary mass in certain types of radially symmetric, non-Abelian, background gauge fields (including instanton-like and instanton-antiinstanton-like configurations). A detailed study on functional determinants for matrix-valued radial differential operators is presented, explicating both our analytic treatment on the high partial wave contribution and the application of the generalized Gel'fand-Yaglom formula to determine the low partial wave contribution. In general, some numerical work is needed for the low partial wave part. In the massless limit, however, the factorizable nature of our partial-wave radial differential operators can be exploited to evaluate semi-analytically even the low partial wave part, and we thus have the full fermion effective action calculated explicitly in a class of non-Abelian background gauge fields. With nonzero mass, we also perform necessary numerical analysis as regards the low partial wave contribution to produce numerically exact results for the massive effective action. Comparing these against the results of the large mass expansion, the validity range of the large mass expansion is addressed. Also studied is the fermion mass dependence of the effective instanton-antiinstanton interaction.

hep-th↗

arXiv2011

The Derivative Expansion at Small Mass for the Spinor Effective Action

We study the small mass limit of the one-loop spinor effective action, comparing the derivative expansion approximation with exact numerical results that are obtained from an extension to spinor theories of the partial-wave-cutoff method. In this approach one can compute numerically the renormalized one-loop effective action, for radially separable gauge field background fields in spinor QED. We highlight an important difference between the small mass limit of the derivative expansion approximation for spinor and scalar theories.

hep-th↗

arXiv2010

Some chirality-related properties of the 4-D massive Dirac propagator and determinant in an arbitrary gauge field

For a 4-D massive Dirac field in the background of arbitrary gauge fields, we show that the Dirac propagator and functional determinant are completely determined by knowledge of the corresponding quantities for just one of the chirality sectors of the second-order Dirac operator. This generalizes the related, previously known, statements in (anti-)self-dual background gauge fields. The logarithms of the (renormalized) functional determinants from the two chirality sectors are shown to be different only by a term reflecting the integrated chiral anomaly.

hep-th↗

arXiv2010

Static Length Scales of N=6 Chern-Simons Plasma

Using gravity description, we compute various static length scales of N=6 Chern Simons plasma in a strongly coupled regime. For this, we consider the CP3 compactification of the type IIA supergravity down to four dimensions, and identify all the low-lying bosonic modes up to masses corresponding to the operator dimension 3 together with all the remaining CP3 invariant modes. We find the true mass gap, the Debye screening mass and the corresponding dual operators to be probed in the field theory side.

hep-th↗

arXiv2010

Integrability of N=6 Chern-Simons Theory at Six Loops and Beyond

We study issues concerning perturbative integrability of N=6 Chern-Simons theory at planar and weak `t Hooft coupling regime. By Feynman diagrammatics, we derive so called maximal-ranged interactions in the quantum dilatation generator, originating from homogeneous and inhomogeneous diagrams. These diagrams require proper regularization of not only ultraviolet but also infrared divergences. We first consider standard operator mixing method. We show that homogeneous diagrams are obtainable by recursive method to all orders. The method, however, is not easily extendable to inhomogeneous diagrams. We thus consider two-point function method and study both operator contents and spectrum of the quantum dilatation generator up to six loop orders. We show that, of two possible classes of operators, only one linear combination actually contributes. Curiously, this is exactly the same combination as in N=4 super Yang-Mills theory. We then study spectrum of anomalous dimension up to six loops. We find that the spectrum agrees perfectly with the prediction based on quantum integrability. In evaluating the six loop diagrams, we utilized remarkable integer-relation algorithm (PSLQ) developed by Ferguson, Baily and Arno.

hep-th↗

arXiv2010

Generalized Dynamical Spin Chain and 4-Loop Integrability in N=6 Superconformal Chern-Simons Theory

We revisit unitary representation of centrally extended (2 | 2) excitation superalgebra. We find most generally that `pseudo-momentum', not lattice momentum, diagonalizes spin chain Hamiltonian and leads to generalized dynamic spin chain. All known results point to lattice momentum diagonalization for N=4 super Yang-Mills theory. Having different interacting structure, we ask if N=6 superconformal Chern-Simons theory provides an example of pseudo-momentum diagonalization. For SO(6) sector, we study maximal shuffling and next-to-maximal shuffling terms in the dilatation operator and compare them with results expected from psu(2|2) superalgebbra and integrability. At two loops, we rederive maximal shuffling term (3-site) and find perfect agreement with known results. At four loops, we first find absence of next-to-maximal shuffling term (4-site), in agreement with prediction based on integrability. We next extract maximal shuffling term (5-site), the most relevant term for checking the possibility of pseudo-momentum diagonalization. Curiously, we find that result agrees with integraility prediction based on lattice momentum, as in N=4 super Yang-Mills theory. Consistency of our results is fully ensured by checks of renormalizability up to six loops.

hep-th↗

arXiv2009

Efficient Evaluation of Effective Action in Radial Backgrounds

Recently a new caculational scheme for effective actions in radial background fields was developed. The effective action is expressed as an infinite sum of partial-wave contributions, using the rotational symmetry of the system. The sum becomes convergent after proper regularization and renormalization, but the rate of convergence is rather slow. We introduce a systematic way of accelerating the rate of convergence. This method is based on a radial WKB series in the angular momentum cut-off. We demonstrate the power of this scheme by applying it to the calculation of instanton determinant in QCD.

hep-th↗

arXiv2009

Fermion Zero Modes in Odd Dimensions

We study the zero modes of the Abelian Dirac operator in any odd dimension. We use the stereographic projection between a $(2n-1)$ dimensional space and a $(2n-1)$ sphere embedded in a $2n$ dimensional space. It is shown that the Dirac operator with a gauge field of uniform field strengths in $S^{2n-1}$ has symmetries of SU($n$)$\times$U(1) which is a subgroup of SO($2n$). Using group representation theory, we obtain the number of fermion zero modes, as well as their explicit forms, in a simple way.

hep-th↗

arXiv2009

Analytic Form of the QCD Instanton Determinant for Small Quark Mass

We use a novel method to calculate analytically the QCD instanton prefactor due to a quark field carrying a small mass parameter $m$. In the SU(2) instanton background of size $ρ$, the spinor effective action $Γ^F$ (in the minimal subtraction scheme), which gives rise to the prefactor $\exp (-Γ^F)$, is shown to have the small-$m ρ$ behavior Γ^F = -\ln (m /μ) - \ln (μρ)/3 -2 α(1/2) -(m ρ)^2 \{\ln (m ρ/2) +γ+1/2\} -2 (m ρ)^4 \{-\ln ^2(m ρ)/4+\ln (m ρ) (1/2-γ+\ln 2)/2+C \} +O((m ρ)^6), where $γ=0.577216...$, $α(1/2)=0.145873...$, and our numerically evaluated value for the constant $C$ is $C=-0.382727...$. A good agreement between this form and the numerically exact calculation is found if $(m ρ) \lesssim 0.8$.

hep-th↗

arXiv2008

Abelian Zero Modes in Odd Dimensions

We show that the Loss-Yau zero modes of the 3d abelian Dirac operator may be interpreted in a simple manner in terms of a stereographic projection from a 4d Dirac operator with a constant field strength of definite helicity. This is an alternative to the conventional viewpoint involving Hopf maps from S^3 to S^2. Furthermore, our construction generalizes in a straightforward way to any odd dimension. The number of zero modes is related to the Chern-Simons number in a nonlinear manner.

hep-th↗

arXiv2008

A Fast Way to Compute Functional Determinants of Radially Symmetric Partial Differential Operators in General Dimensions

Recently the partial wave cutoff method was developed as a new calculational scheme for a functional determinant of quantum field theory in radial backgrounds. For the contribution given by an infinite sum of large partial waves, we derive explicitly radial WKB series in the angular momentum cutoff for $d=2,3,4$ and 5 ($d$ is the spacetime dimension), which has uniform validity irrespectively of any specific values assumed for other parameters. Utilizing this series, precision evaluation of the renormalized functional determinant is possible with a relatively small number of low partial wave contributions determined separately. We illustrate the power of this scheme in numerically exact evaluation of the prefactor (expressed as a functional determinant) in the case of the false vacuum decay of 4D scalar field theory.

hep-th↗

arXiv2007

Renormalized Effective Actions in Radially Symmetric Backgrounds: Exact Calculations Versus Approximation Methods

Our previously-developed calculational method (the partial wave cutoff method) is employed to evaluate explicitly scalar one-loop effective actions in a class of radially symmetric background gauge fields. Our method proves to be particularly effective when it is used in conjunction with a systematic WKB series for the large partial wave contribution to the effective action. By comparing these numerically exact calculations against the predictions based on the large mass expansion and derivative expansion, we discuss the validity ranges of the latter approximation methods.

hep-th↗

arXiv2005

Beyond the thin-wall approximation : precise numerical computation of prefactors in false vacuum decay

We present a general numerical method for computing precisely the false vacuum decay rate, including the prefactor due to quantum fluctuations about the classical bounce solution, in a self-interacting scalar field theory modeling the process of nucleation in four dimensional spacetime. This technique does not rely on the thin-wall approximation. The method is based on the Gelfand-Yaglom approach to determinants of differential operators, suitably extended to higher dimensions using angular momentum cutoff regularization. A related approach has been discussed recently by Baacke and Lavrelashvili, but we implement the regularization and renormalization in a different manner, and compare directly with analytic computations made in the thin-wall approximation. We also derive a simple new formula for the zero mode contribution to the fluctuation prefactor, expressed entirely in terms of the asymptotic behavior of the classical bounce solution.

hep-th↗

arXiv2005

Calculation of QCD Instanton Determinant with Arbitrary Mass

The precise quark mass dependence of the one-loop effective action in an instanton background has recently been computed [arXiv:hep-th/0410190]. The result interpolates smoothly between the previously known extreme small and large mass limits. The computational method makes use of the fact that the single instanton background has radial symmetry, so that the computation can be reduced to a sum over partial waves of logarithms of radial determinants, each of which can be computed numerically in an efficient manner. The bare sum over partial waves is divergent and must be regulated and renormalized. In this paper we provide more details of this computation, including both the renormalization procedure and the numerical approach. We conclude with comparisons of our precise numerical results with a simple interpolating function that connects the small and large mass limits, and with the leading order of the derivative expansion.

hep-th↗