Soonkeon Nam

Area spectra of the rotating BTZ black hole from quasinormal modes

Following Bekensteins suggestion that the horizon area of a black hole should be quantized, the discrete spectrum of the horizon area has been investigated in various ways. By considering the quasinormal mode of a black hole, we obtain the transition frequency of the black hole, analogous to the case of a hydrogen atom, in the semiclassical limit. According to Bohrs correspondence principle, this transition frequency at a large quantum number is equal to the classical oscillation frequency. For the corresponding classical system of periodic motion with this oscillation frequency, an action variable is identified and quantized via the Bohr–Sommerfeld quantization, from which the quantized spectrum of the horizon area is obtained. This method can be applied for black holes with discrete quasinormal modes. As an example, we apply the method for both non-rotating and rotating BTZ black holes and obtain that the spectrum of the horizon area is equally spaced and independent of the cosmological constant for both cases.

Mass and angular momentum of black holes in a new massive gravity

We obtain mass and angular momentum of black holes as conserved charges in three dimensional new massive gravity, after presenting the explicit expression for the potential of the conserved charges. This confirms the expression of those charges obtained in several ways, in particular through AdS/CFT correspondence, and shows us that the first law of black hole thermodynamics is valid in these black holes. We also comment about conserved charges in new type black holes with the emphasis on the AdS/CFT correspondence as guiding principle.

AdS black hole solutions in the extended new massive gravity

We have obtained (warped) AdS black hole solutions in the three dimensional extended new massive gravity. We investigate some properties of black holes and obtain central charges of the two dimensional dual CFT. To obtain the central charges, we use the relation between entropy and temperature according to the AdS/CFT dictionary. For AdS black holes, one can also use the central charge function formalism which leads to the same results.

Quasi-normal modes for new type black holes in new massive gravity

We obtain the quasi-normal mode (QNM) frequencies of scalar perturbation on new type black holes in three-dimensional new massive gravity. In some special cases, the exact QNM frequencies are obtained by solving scalar field equations exactly. On some parameter regions, the highly damped QNM frequencies are obtained in an analytic form by the so-called Stokes line method. This study on QNMs sheds some light on the mysterious nature of these black holes. We also comment about the AdS/CFT correspondence and the entropy/area spectrum for new type black holes.

Superpotentials of N=1 supersymmetric gauge theories from M-theory

Abstract We consider brane configurations in M-theory describing N =1 supersymmetric gauge theories and using the parametric representation of the brane configurations, we calculate the superpotentials for various cases including multiple gauge groups or fermions. For SU ( n ) N =1 SQCD with N f fermion case ( N f N c ), we find that the superpotential from M-theory and the gauge theory agree precisely. This gives a direct evidence of the validity of Wittens M-theory method for calculating the superpotential.

Entropy spectra of black holes from resonance modes in scattering by the black holes

Since Bekensteins proposal that a black hole has an equally spaced area spectrum, the quasinormal modes (QNM) as the characteristic modes of a black hole have been used for obtaining the horizon area spectrum of the black hole. However, the area spectrum of the Kerr black hole in some previous works was inconsistent with Bekensteins proposal. In this paper, noting that black holes can have three types of resonance modes which are QNM, total transmission modes (TTM), and total reflection modes (TRM), we propose that all of these modes in a highly damped regime should be used in quantizing the black hole. Although the QNM and the TTM of the Kerr black hole give us complicated quantization conditions from the Bohr–Sommerfeld quantization of an action variable, we find a very simple result from the TRM. It gives an equally spaced outer horizon area. Therefore, by the Bekenstein–Hawking area law, we find that the Kerr black hole has universal behavior of the equally spaced entropy spectrum. With the same argument, we find that the Reissner–Nordstrom black hole also has the equally spaced entropy spectrum.

Supersymmetric SO(Nc) gauge theory and matrix model

Abstract By applying the method of Dijkgraaf and Vafa, we study matrix model related to supersymmetric SO ( N c ) gauge theory with N f flavors of quarks in the vector representation found by Intriligator and Seiberg. By performing the matrix integral over tree level superpotential characterized by light meson fields (mass deformation) in electric theory, we reproduce the exact effective superpotential in the gauge theory side. Moreover, we do similar analysis in magnetic theory. It turns out the matrix descriptions of both electric and magnetic theories are the same: Seiberg duality in the gauge theory side.

Non-supersymmetric attractor with the cosmological constant

As a test for the non-supersymmetric attractor mechanism, we consider extremal Reissner-Nordstrom-(anti-)de Sitter black holes. Based on the simple observation that the near-horizon geometry of a generic extremal black hole contains two-dimensional anti-de Sitter factor even in the presence of the positive cosmological constant, we apply Ashoke Sens entropy function method to compute the entropy of these black holes. We find the results which exactly agree with the Bekenstein-Hawking entropy. We also obtain the constant higher-order correction to the entropy due to the Gauss-Bonnet term.

Holographic renormalization and stress tensor in new massive gravity

A bstractWe obtain holographically renormalized boundary stress tensor with the em- phasis on a special point in the parameter space of three dimensional new massive gravity, using the so-called Fefferman-Graham coordinates with relevant counter terms. Through the linearized equations of motion with a standard prescription, we also obtain correlators among these stress tensors. We argue that the self-consistency of holographic renormaliza- tion determines counter terms up to unphysical ambiguities. Using this renormalized stress tensor in Fefferman-Graham coordinates, we obtain the central charges of dual CFT, and mass and angular momentum of some AdS black hole solutions. These results are consistent with the previous ones obtained by other methods. In this study on the Fefferman-Graham expansion of new massive gravity, some aspects of higher curvature gravity are revealed.

N=2 supersymmetric SO(N) / Sp(N) gauge theories from matrix model

We use the matrix model to describe the N=2 SO(N)/Sp(N) supersymmetric gauge theories with massive hypermultiplets in the fundamental representation. By taking the tree level superpotential perturbation made of a polynomial of a scalar chiral multiplet, the effective action for the eigenvalues of chiral multiplet can be obtained. By varying this action with respect to an eigenvalue, a loop equation is obtained. By analyzing this equation, we derive the Seiberg-Witten curve within the context of matrix model.