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.Comment: 4 pages, 2 figures; v2: Corrected a mistake in eq. (11), which does not affect the subsequent context. Added a comment on inflaton fluctuations at the end of the paper. Final version to appear in Phys. Lett.

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

We investigate the holographic correspondence between (p+1)-dimensional ($0\le p\le 4$) SYM theories with 16 supercharges and superstring theories on the near-horizon limit of Dp-brane backgrounds. Following an approach based on the tunneling picture, we study Euclidean superstring semi-classically along null geodesics which connect two points on the boundary of the spacetime. We extend the analysis of hep-th/0308024 and study the fermionic sector of the superstring. For $p\ne 3$, 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 ($p\ne 3$) SYM theories.Comment: 31 pages, 1 figure; v2: discussion on the consistency with a known result of supergravity analysis adde

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 non-conformal backgrounds of D$p$-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 D$p$-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 D$p$-branes including the stringy excitations. All the cases ($p\ne 3, p<5$) exhibit interesting infra-red behaviors, which are different from free-field theories, suggesting the existence of quite nontrivial fixed-points in dual gauge theories.Comment: 43 pages, corrected typos, version to be published in Nucl. Phys.