Yasuhiro Sekino

Holographic framework for eternal inflation

In this paper we provide some circumstantial evidence for a holographic duality between bubble nucleation in an eternally inflating universe and a Euclidean conformal field theory (CFT). The holographic correspondence (which is different than Stromingers de Sitter (dS)/CFT duality) relates the decay of (3+1)-dimensional de Sitter space to a two-dimensional CFT. It is not associated with pure de Sitter space, but rather with Coleman-De Luccia bubble nucleation. Alternatively, it can be thought of as a holographic description of the open, infinite, Friedmann-Robertson-Walker (FRW) cosmology that results from such a bubble. The conjectured holographic representation is of a new type that combines holography with the Wheeler-DeWitt formalism to produce a Wheeler-DeWitt theory that lives on the spatial boundary of a k=-1 FRW cosmology. We also argue for a more ambitious interpretation of the Wheeler-DeWitt CFT as a holographic dual of the entire Landscape.

Monte Carlo Studies of Matrix Theory Correlation Functions

We study correlation functions in (0+1)-dimensional maximally supersymmetric U(N) gauge theory, which represents the low-energy effective theory of D0-branes. In the large-N limit, the gauge-gravity duality predicts power-law behaviors in the infrared region for the two-point correlation functions of operators corresponding to supergravity modes. We evaluate such correlation functions on the gauge theory side by the Monte Carlo method. Clear power-law behaviors are observed at N=3, and the predicted exponents are confirmed consistently. Our results suggest that the agreement extends to the M-theory regime, where the supergravity analysis in 10 dimensions may not be justified a priori.

Direct test of the gauge-gravity correspondence for Matrix theory correlation functions

A bstractWe study correlation functions in (0 + 1)-dimensional maximally supersym-metric U(N ) Yang-Mills theory, which was proposed by Banks et al. as a non-perturbative definition of 11-dimensional M-theory in the infinite-momentum frame. We perform first-principle calculations using Monte Carlo simulations, and compare the results against the predictions obtained previously based on the gauge-gravity correspondence from 10 dimensions. After providing a self-contained review on these predictions, we present clear evidence that the predictions in the large-N limit actually hold even at small N such as N =2 and 3. The predicted behavior seems to continue to the far infrared regime, which goes beyond the naive range of validity of the 10D supergravity analysis. This suggests that the correlation functions also contain important information on the M-theory limit.

PP-wave holography for Dp-brane backgrounds

As an extension of the so-called BMN conjecture, we investigate the plane-wave limit for possible holographic connection between bulk string theories in nonconformal backgrounds of Dp-branes and the corresponding supersymmetric gauge theories for p<5. Our work is based on the tunneling picture for dominant null trajectories of strings in the limit of large angular momentum. The tunneling null trajectories start from the near-horizon boundary and return to the boundary, and the resulting backgrounds are time-dependent for general Dp-branes except for p=3. We develop a general method for extracting diagonalized two-point functions for boundary theories as Euclidean (bulk) S-matrix in the time-dependent backgrounds. For the case of D0-brane, two-point functions of supergravity modes are shown to agree with the results derived previously by the perturbative analysis of supergravity. We then discuss the implications of the holography for general cases of Dp-branes including the stringy excitations. All the cases (p≠3, p<5) exhibit interesting infra-red behaviors, which are different from free-field theories, suggesting the existence of quite nontrivial fixed-points in dual gauge theories.

Future foam: Nontrivial topology from bubble collisions in eternal inflation

We study pocket universes which have zero cosmological constant and nontrivial boundary topology. These arise from bubble collisions in eternal inflation. Using a simplified dust model of collisions we find that boundaries of any genus can occur. Using a radiation shell model we perform analytic studies in the thin-wall limit to show the existence of geometries with a single toroidal boundary. We give plausibility arguments that higher genus boundaries can also occur. In geometries with one boundary of any genus a timelike observer can see the entire boundary. Geometries with multiple disconnected boundaries can also occur. In the spherical case with two boundaries the boundaries are separated by a horizon. Our results suggest that the holographic dual description for eternal inflation, proposed by Freivogel, Sekino, Susskind and Yeh, should include summation over the genus of the base space of the dual conformal field theory. We point out peculiarities of this genus expansion compared to the string perturbation series.

Large N limit of SYM theories with 16 supercharges from superstrings on Dp-brane backgrounds

Abstract We investigate the holographic correspondence between ( p + 1 ) -dimensional ( 0 ⩽ p ⩽ 4 ) SYM theories with 16 supercharges and superstring theories on the near-horizon limit of D p -brane backgrounds. We take an approach to holography based on the tunneling picture and study superstring with Euclidean world-sheet. We obtain the amplitude in a semi-classical approximation around a null geodesic which connects two-points on the boundary of the spacetime. As an extension of the analysis of hep-th/0308024 , we study the fermionic sector of the superstring. For p ≠ 3 , we do not have world-sheet supersymmetry, and the energies of bosonic and fermionic fluctuations do not match. By interpreting the superstring amplitudes as correlators of gauge theory operators with large R-charge J , we obtain gauge theory two-point functions including those of fermionic operators. Our approach yields results consistent with the previous supergravity analysis for the D0-branes, including the subleading part in J . Our prediction from holography is that the two-point functions for the supergravity modes are power-law behaved, even for the non-conformal ( p ≠ 3 ) SYM theories.

Evolution of vacuum fluctuations generated during and before inflation

We calculate the time evolution of the expectation value of the energy-momentum tensor for a minimally coupled massless scalar field in cosmological spacetimes, with an application to dark energy in mind. We first study the evolution from inflation until the present, fixing the Bunch-Davies initial condition. The energy density of a quantum field evolves as ρ ∼ 3 ( H I H ) 2 / 32 π 2 in the matter-dominated (MD) period, where H I and H are the Hubble parameters during inflation and at each moment. Its equation of state, w = ρ / p , changes from a negative value to w = 1 / 3 in the radiation-dominated (RD) period, and from 1 / 3 to w = 0 in the MD period. We then consider possible effects of a Planckian universe, which may have existed before inflation, by assuming there was another inflation with the Hubble parameter H P ( > H I ) . In this case, modes with wavelengths longer than the current horizon radius are mainly amplified, and the energy density of a quantum field grows with time as ρ ∼ ( a / a 0 ) ( H P H ) 2 / 32 in the MD period, where a and a 0 are the scale factors at each time and at present. Hence, if H P is of the order of the Planck scale M P , ρ becomes comparable to the critical density 3 ( M P H ) 2 at the present time. The contribution to ρ from the long wavelength fluctuations generated before the ordinary inflation has w = - 1 / 3 in the free field approximation. We mention a possibility that interactions further amplify the energy density and change the equation of state.

Equilibration in low-dimensional quantum matrix models

A bstractMatrix models play an important role in studies of quantum gravity, being candidates for a formulation of M-theory, but are notoriously difficult to solve. In this work, we present a fresh approach by introducing a novel exact model, provably equivalent with a low-dimensional bosonic matrix model, which is on its own a well-known, unsolved model of quantum chaos. In our equivalent reformulation local structure becomes apparent, facilitating analytical and precise numerical study. We derive a substantial part of the low energy spectrum, find a conserved charge, and are able to derive numerically the Regge trajectories. To exemplify the usefulness of the approach, we address questions of equilibration starting from a non-equilibrium situation, building upon an intuition from quantum information. We finally discuss possible generalisations of the approach.

CMB Fluctuations and String Compactification Scales

Abstract 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 1014 fields. Tensor fluctuations are hardly affected by these fields. Our mechanism is based on purely quantum effects of the fields which are classically at rest, and is different from the one in slow-roll inflation. 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.

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