Papers by Yoshihisa Kitazawa
We perform the resummation of the infrared logarithms in the inflationary universe. Applying the ... more We perform the resummation of the infrared logarithms in the inflationary universe. Applying the renormalization group, we derive the stochastic equations as the effective theory at the horizon. We focus on the conformal zero mode to respect local Lorentz symmetry. Under Gaussian approximation, we derive the fundamental equation for the Universe (EqU). We also derive the identical equation from the first law of thermodynamics in a dual geometric picture. We believe it is a convincing evidence for de Sitter duality between quantum stochastic physics on the boundary and classical thermodynamics in the bulk. The equation for the Universe (EqU) possesses the solution with the ultraviolet fixed point. It also contains the inflationary universe with the power potentials. We discuss possible scenarios for the very early universe with decreasing epsilon. We argue inflationary universe subsequently dominates to maximize the entropy and epsilon problem is naturally solved.
Oxford University Press (OUP), Oct 7, 2021
We investigate the history of dark energy to explain the present magnitude. We assume the dark en... more We investigate the history of dark energy to explain the present magnitude. We assume the dark energy is the residual cosmological constant. The most important channel in the reheating process is gluon pair production by the quantumchromodynamic trace anomaly. We argue that dark energy decays rapidly by gluon pair emissions during the reheating and after the big bang. The reheating temperature is determined by the decay width of dark energy, , and the Planck mass, M p , as √ M P ∼ 10 6 GeV. This is a consequence of Friedmann's equation and the equilibrium condition ∼ H. As the Universe cools below the hadronic scale, the dark energy density is almost frozen. Nevertheless, the dark energy further decreases by emitting two photons. We have estimated the current decay rate of dark energy from the quantum electrodynamic trace anomaly. The consistent solution of the Friedmann equation is in excellent agreement with the observations. The suppression factor of the dark energy scale is the product of the fine structure constant, α, and the curvature perturbation, P: 10 −30 = (α 2 P/4π) 2. We argue that the conformal symmetry breaking in both ultraviolet and infrared are necessary unless dark energy is subtracted. We also investigate leptogenesis by adding massive right-handed neutrinos: realistic leptogenesis takes place during the reheating process.
We investigate the history of dark energy to explain the present magnitude. We assume the dark en... more We investigate the history of dark energy to explain the present magnitude. We assume the dark energy is the residual cosmological constant. The most important channel in the reheating process is the gluon pair productions by QCD trace anomaly. We argue dark energy decays rapidly by gluon pair emissions during the reheating and after the big bang. The reheating temperature is determined by the decay width of dark energy Gamma and the Planck mass M_p as sqrtM_P Gamma 10^6GeV. It is the consequence of Friedmann's equation and an equilibrium condition Gamma H. As the Universe cools below the hadronic scale, dark energy density is almost frozen. Nevertheless the dark energy further decreases by emitting two photons. We have estimated the current decay rate of dark energy from the QED trace anomaly. The consistent solution of Friedmann equation is in an excellent agreement with the observations. We also investigated lepto-genesis by adding massive right handed neutrinos. The reali...
We extend our investigation of the IR effects on the local dynamics of matter fields in quantum g... more We extend our investigation of the IR effects on the local dynamics of matter fields in quantum gravity. Specifically we clarify how the IR effects depend on the change of the quantization scheme: different parametrization of the metric and the matter field redefinition. Conformal invariance implies effective Lorentz invariance of the matter system in de Sitter space. An arbitrary choice of the parametrization of the metric and the matter field redefinition does not preserve the effective Lorentz invariance of the local dynamics. As for the effect of different parametrization of the metric alone, the effective Lorentz symmetry breaking term can be eliminated by shifting the background metric. In contrast, we cannot compensate the matter field redefinition dependence by such a way. The effective Lorentz invariance can be retained only when we adopt the specific matter field redefinitions where all dimensionless couplings become scale invariant at the classical level. This scheme is a...
We investigate the large N reduced model of gauge theory on a curved spacetime through the plane ... more We investigate the large N reduced model of gauge theory on a curved spacetime through the plane wave matrix model. We formally derive the action of the N=4 supersymmetric Yang-Mills theory on R \times S^3 from the plane wave matrix model in the large N limit. Furthermore, we evaluate the effective action of the plane wave matrix model up to the two-loop level at finite temperature. We find that the effective action is consistent with the free energy of the N=4 supersymmetric Yang-Mills theory on S^3 at high temperature limit where the planar contributions dominate. We conclude that the plane wave matrix model can be used as a large N reduced model to investigate nonperturbative aspects of the N=4 supersymmetric Yang-Mills theory on R \times S^3.
We study how the introduction of a 2-form field flux modify the dynamics of a T-duality invariant... more We study how the introduction of a 2-form field flux modify the dynamics of a T-duality invariant string gas cosmology model of Greene, Kabat and Marnerides. It induces a repulsive potential term in the effective action for the scale factor of the spacial dimensions. Without the 2-form field flux, the universe fails to expand when the pressure due to string modes vanishes. With the presence of a homogeneous 2-form field flux, it propels 3 spacial dimensions to grow into a macroscopic 4 dimensional space-time. We find that it triggers an expansion of a universe away from the oscillating phase around the self-dual radius. We also investigate the effects of a constant 2-form field. We can obtain an expanding 4 dimensional space-time by tuning it at the critical value.
We perform the two loop level renormalization of quantum gravity in 2+ϵ dimensions. We work in th... more We perform the two loop level renormalization of quantum gravity in 2+ϵ dimensions. We work in the background gauge whose manifest covariance enables us to use the short distance expansion of the Green's functions. We explicitly show that the theory is renormalizable to the two loop level in our formalism. We further make a physical prediction for the scaling relation between the gravitational coupling constant and the cosmological constant which is expected to hold at the short distance fixed point of the renormalization group. It is found that the two loop level calculation is necessary to determine the scaling exponent to the leading order in ϵ.
We extend our investigation of soft graviton effects on the microscopic dynamics of matter fields... more We extend our investigation of soft graviton effects on the microscopic dynamics of matter fields in de Sitter space. We evaluate the quantum equation of motion in generic gauge theories. We find that the Lorentz invariance can be respected and the velocity of light is not renormalized at the one-loop level. The gauge coupling constant is universally screened by soft gravitons and diminishes with time. These features are in common with other four dimensional field theories with dimensionless couplings. In particular the couplings scale with time with definite scaling exponents. Although individual scaling exponents are gauge dependent, we argue that the relative scaling exponents are gauge independent and should be observable. We also mention soft graviton effects on cosmic microwave background.
S^3 is a simple principle bundle which is locally S^2 \times S^1. It has been shown that such a s... more S^3 is a simple principle bundle which is locally S^2 \times S^1. It has been shown that such a space can be constructed in terms of matrix models. It has been also shown that such a space can be realized by a generalized compactification procedure in the S^1 direction. We investigate the effective action of supersymmetric gauge theory on S^3 with an angular momentum cutoff and that of a matrix model compactification. The both cases can be realized in a deformed IIB matrix model with a Myers Term. We find that the highly divergent contributions at the tree and one loop level are sensitive to the uv cutoff. However the two loop level contributions are universal since they are only logarithmically divergent. We expect that the higher loop contributions are insensitive to the uv cutoff since 3d gauge theory is super renormalizable.
The scale invariance of the quantum fluctuations in de Sitter space leads to the appearance of de... more The scale invariance of the quantum fluctuations in de Sitter space leads to the appearance of de Sitter symmetry breaking infra-red logarithms in the graviton propagator. We investigate physical effects of soft gravitons on the local dynamics of matter fields well inside the cosmological horizon. We show that the IR logarithms do not spoil Lorentz invariance in scalar and Dirac field theory. The leading IR logarithms can be absorbed by a time dependent wave function renormalization factor in the both cases. In the interacting field theory with λϕ^4 and Yukawa interaction, we find that the couplings become time dependent with definite scaling exponents. We argue that the relative scaling exponents of the couplings are gauge invariant and physical as we can use the evolution of a coupling as a physical time.
We show that correlation functions for branched polymers correspond to those for ϕ^3 theory with ... more We show that correlation functions for branched polymers correspond to those for ϕ^3 theory with a single mass insertion, not those for the ϕ^3 theory themselves, as has been widely believed. In particular, the two-point function behaves as 1/p^4, not as 1/p^2. This behavior is consistent with the fact that the Hausdorff dimension of the branched polymer is four.
We construct Green-Schwarz (GS) light-cone closed superstring theory from type IIB matrix model. ... more We construct Green-Schwarz (GS) light-cone closed superstring theory from type IIB matrix model. A GS light-cone string action is derived from two dimensional N=8 U(n) noncommutative Yang-Mills (NCYM) by identifying noncommutative scale with string scale. Supersymmetry transformation for the light-cone gauge action is also derived from supersymmetry transformation for IIB matrix model. By identifying the physical states and interaction vertices, string theory is perturbatively reproduced.
Scale invariant fluctuations of metric are universal feature of quantum gravity in de Sitter spac... more Scale invariant fluctuations of metric are universal feature of quantum gravity in de Sitter spacetime. We construct an effective Lagrangian which summarizes their implications on local physics by integrating super-horizon metric fluctuations. It shows infrared quantum effects are local and render fundamental couplings time dependent. We impose Lorenz invariance on the effective Lagrangian as it is required by the principle of general covariance. We show that such a requirement leads to unique physical predictions by fixing the quantization ambiguities. We explain how the gauge parameter dependence of observables is canceled. In particular the relative evolution speed of the couplings are shown to be gauge invariant.
It is known that noncommutative Yang-Mills is equivalent to IIB matrix model with a noncommutativ... more It is known that noncommutative Yang-Mills is equivalent to IIB matrix model with a noncommutative background, which is interpreted as a twisted reduced model. In noncommutative Yang-Mills, long range interactions can be seen in nonplanar diagrams after integrating high momentum modes. These interactions can be understood as block-block interactions in the matrix model. Using this relation, we consider long range interactions in noncommutative Yang-Mills associated with fermionic backgrounds. Exchanges of gravitinos, which couple to a supersymmetry current, are examined.
We investigate a solution of the exactly renormalized Liouville action to foresee the fate of the... more We investigate a solution of the exactly renormalized Liouville action to foresee the fate of the two-dimensional de Sitter space. We work in the semiclassical region with a large matter central charge c. Instead of de Sitter expansion, it performs a slow-roll inflation with the parameters ϵ=(1/2)η =6/c. An inflaton field is induced in the effective theory to describe quantum effects of the Liouville theory. The geometric entropy increases logarithmically with the Hubble radius. We propose that de Sitter entropy is carried by superhorizon modes of the metric. It can be directly estimated from the partition function as S= Z in Liouville gravity. We formulate a gravitational Fokker-Planck equation to elucidate the Brownian process at the horizon: the superhorizon modes are constantly jolted by newcomers. We show that such a built-in entropy-generating process diffuses the cosmological constant. We evaluate von Neumann entropy associated with the distribution function of superhorizon m...
We extend our investigation on a possible de Sitter symmetry breaking mechanism in non-linear sig... more We extend our investigation on a possible de Sitter symmetry breaking mechanism in non-linear sigma models. The scale invariance of the quantum fluctuations could make the cosmological constant time dependent signaling the de Sitter symmetry breaking. To understand such a symmetry breaking mechanism, we investigate the energy-momentum tensor. We show that the leading infra-red logarithms cancel to all orders in perturbation theory in a generic non-linear sigma model. When the target space is an N sphere, the de Sitter symmetry is preserved in the large N limit. For a less symmetric target space, the infra-red logarithms appear at the three loop level. However there is a counter term to precisely cancel it. The leading infra-red logarithms do not cancel for higher derivative interactions. We investigate such a model in which the infra-red logarithms first appear at the three loop level. A nonperturbative investigation in the large N limit shows that they eventually grow as large as t...
We study the stability of fuzzy S^2 x S^2 x S^2 backgrounds in three different IIB type matrix mo... more We study the stability of fuzzy S^2 x S^2 x S^2 backgrounds in three different IIB type matrix models with respect to the change of the spins of each S^2 at the two loop level. We find that S^2 x S^2 x S^2 background is metastable and the effective action favors a single large S^2 in comparison to the remaining S^2 x S^2 in the models with Myers term. On the other hand, we find that a large S^2 x S^2 in comparison to the remaining S^2 is favored in IIB matrix model itself. We further study the stability of fuzzy S^2 x S^2 background in detail in IIB matrix model with respect to the scale factors of each S^2 as well. In this case, we find unstable directions which lower the effective action away from the most symmetric fuzzy S^2 x S^2 background.
We evaluate the quantum corrections of the Einstein-Hilbert action with boundaries in the 2+ϵ dim... more We evaluate the quantum corrections of the Einstein-Hilbert action with boundaries in the 2+ϵ dimensional expansion approach. We find the Einstein-Hilbert action with boundaries to be renormalizable to the one loop order. We compute the geometric entropy beyond the semiclassical approximation. It is found that the exact geometric entropy is related to the string succeptibility by the analytic continuation in the central charge. Our results also show that we can renormalize the divergent quantum corrections for the Bekenstein-Hawking entropy of blackholes by the gravitational coupling constant renormalization beyond two dimensions.
We study the correlation functions of the Wilson loops in noncommutative Yang-Mills theory based ... more We study the correlation functions of the Wilson loops in noncommutative Yang-Mills theory based upon its equivalence to twisted reduced models. We point out that there is a crossover at the noncommutativity scale. At large momentum scale, the Wilson loops in noncommmutative Yang-Mills represent extended objects. They coincide with those in ordinary Yang-Mills theory in low energy limit. The correlation functions on D-branes in IIB matrix model exhibit the identical crossover behavior. It is observed to be consistent with the supergravity description with running string coupling. We also explain that the results of Seiberg and Witten can be simply understood in our formalism.
We clarify the relation between the vertex operators in type IIB matrix model and superstring. Gr... more We clarify the relation between the vertex operators in type IIB matrix model and superstring. Green-Schwarz light-cone closed superstring theory is obtained from IIB matrix model on two dimensional noncommutative backgrounds. Superstring vertex operators should be reproduced from those of IIB matrix model through this connection. Indeed, we confirm that supergravity vertex operators in IIB matrix model on the two dimensional backgrounds reduce to those in superstring theory. Noncommutativity plays an important role in our identification. Through this correspondence, we can reproduce superstring scattering amplitudes from IIB matrix model.
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Papers by Yoshihisa Kitazawa