arXiv subjects

Hikaru Kawai

Publications and source records attributed to Hikaru Kawai.

At least 73 records · Page 4Linked to original sources

arXiv2013

Spacetime Structure of the Black Hole Evaporation

We study a self-consistent solution of the semi-classical Einstein equation including the back reaction from the Hawking radiation. Our geometry is constructed by connecting flat space and the outgoing Vaidya metric at the locus of the shock wave. In order to prove that this is the self-consistent solution, we first show that the Weyl anomaly is canceled if we take the effects of the fluctuations of the metric into account. We further demonstrate that the Hawking radiation occurs even if the geometry has no horizon. Then, the energy-momentum tensor is found to be consistent with the semi-classical Einstein equation. Since our geometry has neither horizon nor singularity, all matters inside the black hole finally come back to infinity. Therefore, no information is lost by the black hole evaporation. Furthermore, we take into account the gray-body factor. We construct a stationary solution for a black hole in the heat bath and estimate the entropy. The entropy-area law is reproduced by the volume integration of the entropy density over the inside of the horizon, and the black hole can be treated as an ordinary thermodynamic object.

hep-th↗

arXiv2012

Possible origin of CMB temperature fluctuations: Vacuum fluctuations of Kaluza-Klein and string states during inflationary era

We point out that the temperature fluctuations of cosmic microwave background (CMB) can be generated in a way that is different from the one usually assumed in slow-roll inflation. Our mechanism is based on vacuum fluctuations of fields which are at rest at the bottom of the potential, such as Kaluza-Klein modes or string excited states. When there are a large number (typically of order $N\sim 10^{14}$) of fields with small mass in unit of Hubble parameter during the inflationary era, this effect can give significant contributions to the CMB temperature fluctuations. This number $N$ makes it possible to enhance scalar perturbation relative to tensor perturbation. Comparison with the observed amplitudes suggests that models with string scale of order $10^{-5}$ of 4D Planck scale are favorable.

hep-th↗

arXiv2012

Factorization of the Effective Action in the IIB Matrix Model

We study the low-energy effective action of the IIB matrix model in the derivative interpretation, where the diffeomorphism invariance is manifest and arbitrary manifolds are described by matrices. We show that it is expressed as a sum of terms, each of which is factorized into a product of diffeomorphism invariant action functionals: $S=\sum_{i}c_is_i+\sum_{i,j}c_{ij}s_is_j+\sum_{i,j,k}c_{ijk}s_is_js_k+\...$. Each action functional $s_i$ is an ordinary local action of the form $s_i=\int d^Dx\sqrt{-g} O_i(x)$, where $O_i(x)$ is a scalar operator. This is also true for the background consisting of block diagonal matrices. In this case, the effective action can be interpreted as describing a multiverse where the universes described by the blocks are connected by wormholes.

hep-th↗

arXiv2012

Solving the Naturalness Problem by Baby Universes in the Lorentzian Multiverse

We propose a solution of the naturalness problem in the context of the multiverse wavefunction without the anthropic argument. If we include microscopic wormhole configurations in the path integral, the wave function becomes a superposition of universes with various values of the coupling constants such as the cosmological constant, the parameters in the Higgs potential, and so on. We analyze the quantum state of the multiverse, and evaluate the density matrix of one universe. We show that the coupling constants induced by the wormholes are fixed in such a way that the density matrix is maximized. In particular, the cosmological constant, which is in general time-dependent, is chosen such that it takes an extremely small value in the far future. We also discuss the gauge hierarchy problem and the strong CP problem in this context. Our study predicts that the Higgs mass is 140\pm20 GeV and θ=0.

hep-th↗

arXiv2011

CMB Fluctuations and String Compactification Scales

We propose a mechanism for the generation of temperature fluctuations of cosmic microwave background. We consider a large number of fields, such as Kaluza-Klein modes and string excitations. Each field contributes to the gravitational potential by a small amount, but an observable level of temperature fluctuations is achieved by summing up the contribution of typically of order 10^{14} fields. Tensor fluctuations are hardly affected by these fields. Our mechanism is based on purely quantum effects, and is different from the "slow-roll" or "curvaton" scenario. Using the observed data, we find constraints on the parameters of this model, such as the size of the extra dimensions and the string scale. Our model predicts a particular pattern of non-gaussianity with a small magnitude.

hep-th↗

arXiv2011

Gravitational string-membrane hedgehog and internal structure of black holes

We investigate charged Nambu-Goto strings/membrane systems in the Einstein-Maxwell theory in 3+1 dimensions. We first construct a charged string hedgehog solution that has a single horizon and conical singularity. Then we examine a charged membrane system, and give a simple derivation of its self energy. We find that the membrane may form an extremal Reissner-Nordstrom black hole, but its interior is a flat spacetime. Finally by combining the charged strings and the membrane we construct black hole solutions that have no singularities inside the horizons. We study them in detail by varying the magnitude of the two parameters, namely, the charge times the membrane tension and the string tension. We also argue that the strings have, due to the large redshift inside the system, a fair amount of degrees of freedom that may explain the entropy of the corresponding black holes.

gr-qc↗

arXiv2011

Asymptotically Vanishing Cosmological Constant in the Multiverse

We study the problem of the cosmological constant in the context of the multiverse in Lorentzian spacetime, and show that the cosmological constant will vanish in the future. This sort of argument was started from Coleman in 1989, and he argued that the Euclidean wormholes make the multiverse partition a superposition of various values of the cosmological constant $Λ$, which has a sharp peak at $Λ=0$. However, the implication of the Euclidean analysis to our Lorentzian spacetime is unclear. With this motivation, we analyze the quantum state of the multiverse in Lorentzian spacetime by the WKB method, and calculate the density matrix of our universe by tracing out the other universes. Our result predicts vanishing cosmological constant. While Coleman obtained the enhancement at $Λ=0$ through the action itself, in our Lorentzian analysis the similar enhancement arises from the front factor of $e^{iS}$ in the universe wave function, which is in the next leading order in the WKB approximation.

hep-th↗

arXiv2010

Large N reduction on group manifolds

We show that the large N reduction holds on group manifolds. Large N field theories defined on group manifolds are equivalent to some corresponding matrix models. For instance, gauge theories on S^3 can be regularized in a gauge invariant and SO(4) invariant manner.

hep-th↗

arXiv2010

Large N reduction on coset spaces

As an extension of our previous work concerning the large N reduction on group manifolds, we study the large N reduction on coset spaces. We show that large N field theories on coset spaces are described by certain corresponding matrix models. We also construct Chern-Simons-like theories on group manifolds and coset spaces, and give their reduced models.

hep-th↗

arXiv2010

Universal description of viscoelasticity with foliation preserving diffeomorphisms

We review our recent proposal for a universal description of generic single-component viscoelastic systems with a single relaxation time. Foliation preserving diffeomorphisms are introduced as an underlying symmetry which naturally interpolates between the two extreme characters of elasticity and fluidity. The symmetry is found to be powerful enough to determine the dynamics in the first order of strains.

hep-th↗

arXiv2009

Universal description of viscoelasticity with foliation preserving diffeomorphisms

A universal description is proposed for generic viscoelastic systems with a single relaxation time. Foliation preserving diffeomorphisms are introduced as an underlying symmetry which naturally interpolates between the two extreme limits of elasticity and fluidity. The symmetry is found to be powerful enough to determine the dynamics in the first order of strains.

hep-th↗

arXiv2008

Worldsheet Analysis of Gauge/Gravity Dualities

Gauge/gravity dualities are investigated from the worldsheet point of view. In [arXiv:0706.1163] and [arXiv:0708.2463], a duality between 4d SYM and supergravity on AdS_5xS^5 has been partly explained by using an anisotropic scale invariance of worldsheet theory. In this paper, we refine the argument and generalize it to lower dimensional cases. We show the correspondence between the Wilson loops in (p+1)-d SYM and the minimal surface in the black p-brane background. Although the scale invariance does not exist in these cases, the generalized scale transformation can be utilized. We also find that the energy density of open strings can be related to the ADM mass of the p-brane without relying on this symmetry.

hep-th↗

arXiv2007

Perturbative Vacua from IIB Matrix Model

It has not been clarified whether a matrix model can describe various vacua of string theory. In this paper, we show that the IIB matrix model includes type IIA string theory. In the naive large N limit of the IIB matrix model, configurations consisting of simultaneously diagonalizable matrices form a moduli space, although the unique vacuum would be determined by complicated dynamics. This moduli space should correspond to a part of perturbatively stable vacua of string theory. Actually, one point on the moduli space represents type IIA string theory. Instead of integrating over the moduli space in the path-integral, we can consider each of the simultaneously diagonalizable configurations as a background and set the fluctuations of the diagonal elements to zero. Such procedure is known as quenching in the context of the large N reduced models. By quenching the diagonal elements of the matrices to an appropriate configuration, we show that the quenched IIB matrix model is equivalent to the two-dimensional large N N=8 super Yang-Mills theory on a cylinder. This theory is nothing but matrix string theory and is known to be equivalent to type IIA string theory. As a result, we find the manner to take the large N limit in the IIB matrix model.

hep-th↗

arXiv2007

AdS/CFT Correspondence as a Consequence of Scale Invariance

We study an anisotropic scale transformation in the worldsheet description of D3-branes in Type IIB theory, and show that the transformation is really a symmetry in a region near D3-branes. AdS/CFT correspondence follows from this symmetry. We will explicitly show that Wilson loops in N=4 supersymmetric Yang-Mills theory and minimal surfaces in AdS_5 are related by the symmetry. The functional form of a supersymmetric Wilson loop operator is naturally derived from our worldsheet point of view.

hep-th↗

arXiv2007

Phase structure of the large-N reduced gauge theory and generalized Weingarten model

We study a generalization of Weingarten model reduced to a point, which becomes the large-N reduced U(N) gauge theory in a special limit. We find that the U(1)^d symmetry is broken one by one, and restored simultaneously as U(1)^d -> U(1)^{d-1} -> ... -> U(1) -> 1 -> U(1)^d as we change the coupling constants. In this model we can develop an efficient algorithm and we can see the phase structure of large-N reduced model clearly, and therefore this model would be useful for the study of the unitary model.

hep-th↗

arXiv2006

Field Equations of Massless Fields in the New Interpretation of the Matrix Model

Recently, some of the authors have introduced a new interpretation of matrix models in which covariant derivatives on any curved space can be expressed by large-N matrices. It has been shown that the Einstein equation follows from the equation of motion of IIB matrix model in this interpretation. In this paper, we generalize this argument to covariant derivatives with torsion. We find that some components of the torsion field can be identified with the dilaton and the $B$-field in string theory. However, the other components do not seem to have string theory counterparts. We also consider the matrix model with a mass term or a cubic term, in which the equation of motion of string theory is exactly satisfied.

hep-th↗

arXiv2006

Describing Curved Spaces by Matrices

It is shown that a covariant derivative on any d-dimensional manifold M can be mapped to a set of d operators acting on the space of functions on the principal Spin(d)-bundle over M. In other words, any d-dimensional manifold can be described in terms of d operators acting on an infinite dimensional space. Therefore it is natural to introduce a new interpretation of matrix models in which matrices represent such operators. In this interpretation the diffeomorphism, local Lorentz symmetry and their higher-spin analogues are included in the unitary symmetry of the matrix model. Furthermore the Einstein equation is obtained from the equation of motion, if we take the standard form of the action S=-tr([A_{a},A_{b}][A^{a},A^{b}]).

hep-th↗

arXiv2006

Curved Superspaces and Local Supersymmetry in Supermatrix Model

In a previous paper, we introduced a new interpretation of matrix models, in which any d-dimensional curved space can be realized in terms of d matrices, and the diffeomorphism and the local Lorentz symmetries are included in the ordinary unitary symmetry of the matrix model. Furthermore, we showed that the Einstein equation is naturally obtained, if we employ the standard form of the action, S=-tr([A_a,A_b][A^a,A^b])+.... In this paper, we extend this formalism to include supergravity. We show that the supercovariant derivatives on any d-dimensional curved space can be expressed in terms of d supermatrices, and the local supersymmetry can be regarded as a part of the superunitary symmetry. We further show that the Einstein and Rarita-Schwinger equations are compatible with the supermatrix generalization of the standard action.

hep-th↗