Unitarity constraints on the ratio of shear viscosity to entropy density in higher derivative gravity

We discuss corrections to the ratio of shear viscosity to entropy density $\eta/s$ in higher-derivative gravity theories. Generically, these theories contain ghost modes with Planck-scale masses. Motivated by general considerations about unitarity, we propose new boundary conditions for the equations of motion of the graviton perturbations that force the amplitude of the ghosts modes to vanish. We analyze explicitly four-derivative perturbative corrections to Einstein gravity which generically lead to four-derivative equations of motion, compare our choice of boundary conditions to previous proposals and show that, with our new prescription, the ratio $\eta/s$ remains at the Einstein-gravity value of $1/4\pi$ to leading order in the corrections. It is argued that, when the new boundary conditions are imposed on six and higher-derivative equations of motion, $\eta/s$ can only increase from the Einstein-gravity value. We also recall some general arguments that support the validity of our results to all orders in the strength of the corrections to Einstein gravity. We then discuss the particular case of Gauss-Bonnet gravity, for which the equations of motion are only of two-derivative order and the value of $\eta/s$ can decrease below $1/4\pi$ when treated in a nonperturbative way. Our findings provide further evidence for the validity of the KSS bound for theories that can be viewed as perturbative corrections to Einstein Gravity.Comment: Sign error in the equations of motion corrected, leading to several numerical changes. Clarifications added, references added. Main results and cnclusions essentially unchanged. V3 published version. Clarifications added, discussion of Gauss-Bonnet moved to main tex

Optimal control of the state statistics for a linear stochastic system

We consider a variant of the classical linear quadratic Gaussian regulator (LQG) in which penalties on the endpoint state are replaced by the specification of the terminal state distribution. The resulting theory considerably differs from LQG as well as from formulations that bound the probability of violating state constraints. We develop results for optimal state-feedback control in the two cases where i) steering of the state distribution is to take place over a finite window of time with minimum energy, and ii) the goal is to maintain the state at a stationary distribution over an infinite horizon with minimum power. For both problems the distribution of noise and state are Gaussian. In the first case, we show that provided the system is controllable, the state can be steered to any terminal Gaussian distribution over any specified finite time-interval. In the second case, we characterize explicitly the covariance of admissible stationary state distributions that can be maintained with constant state-feedback control. The conditions for optimality are expressed in terms of a system of dynamically coupled Riccati equations in the finite horizon case and in terms of algebraic conditions for the stationary case. In the case where the noise and control share identical input channels, the Riccati equations for finite-horizon steering become homogeneous and can be solved in closed form. The present paper is largely based on our recent work in arxiv.org/abs/1408.2222, arxiv.org/abs/1410.3447 and presents an overview of certain key results.Comment: 7 pages, 4 figures. arXiv admin note: substantial text overlap with arXiv:1410.344

D0-branes with non-zero angular momentum

In my talk I shall consider the mechanism of self-expansion of a system of N D0-branes into high-dimensional non-commutative world-volume investigated by Harmark and Savvidy. Here D2-brane is formed due to the internal angular momentum of D0-brane system. The idea is that attractive force of tension should be cancelled by the centrifugal motion preventing a D-brane system from collapse to a lower-dimensional one. I shall also present a new extended solution where a total of 9 space dimensions is used to embed a D0-brane system. In the last section, by performing linear analysis, the stability of the system is demonstrated.Comment: 10 pages, Latex, aipxfm.sty, fix2col.sty; Based on talk given at 10th Tohwa International Symposium on String Theory, Tohwa Univ., Fukuoka, (Japan), July 3-7, 200

Curvature terms in D-brane actions and their M-theory origin

We derive the complete $(curvature)^2$ terms of effective D-brane actions, for arbitrary ambient geometries and world-volume embeddings, at lowest order (disk-level) in the string-loop expansion. These terms reproduce the $o(\alpha'^2)$ corrections to string scattering amplitudes, and are consistent with duality conjectures. In the particular case of the D3-brane with trivial normal bundle, considerations of $SL(2,\mathbb{Z})$ invariance lead to a complete sum of D-instanton corrections for both the parity-conserving and the parity-violating parts of the effective action. These corrections are required for the cancellation of the modular anomalies of massless modes, and are consistent with the absence of chiral anomalies in the intersection domain of pairs of D-branes. We also show that the parity-conserving part of the non-perturbative R^2 action follows from a one-loop quantum calculation in the six-dimensional world-volume of the M5-brane compactified on a two-torus.Comment: tex file, 31 pages, uses harvmac. Some rewriting of section 2, conclusions and appendix B, in particular in what concerns the discussion of seven-branes in the conclusions and the structure of $\alpha'^2$ terms in appendix B. Other minor corrections plus added reference

A Century of Gravity: 1901--2000 (plus some 2001)

This lecture consists of two parts. The first is a (totally unsystematic) survey of some of the high points in the evolution of gravity and its successors, primarily in the course of the past century. The second summarizes some new work on surprising properties of higher $(> 1)$ spin fields in cosmological backgrounds: the presence of \L gives rise to discrete sets of massive models endowed with gauge invariances, that divide the (m^2, \L) plane into unitary and non-unitary phases. The unitary region common to fermions and bosons shrinks to flat space ( \L \to 0 ) as their spins increase.Comment: 12 pages, 1 eps Fig. Invited Lecture at 2001: A Spacetime Odyssey, Ann Arbor, May 200