Breaking rotations without violating the KSS viscosity bound

We revisit the computation of the shear viscosity to entropy ratio in a holographic p-wave superfluid model, focusing on the role of rotational symmetry breaking. We study the interplay between explicit and spontaneous symmetry breaking and derive a simple horizon formula for $\eta/s$, which is valid also in the presence of explicit breaking of rotations and is in perfect agreement with the numerical data. We observe that a source which explicitly breaks rotational invariance suppresses the value of $\eta/s$ in the broken phase, competing against the effects of spontaneous symmetry breaking. However, $\eta/s$ always reaches a constant value in the limit of zero temperature, which is never smaller than the Kovtun-Son-Starinets (KSS) bound, $1/4\pi$. This behavior appears to be in contrast with previous holographic anisotropic models which found a power-law vanishing of $\eta/s$ at small temperature. This difference is shown to arise from the properties of the near-horizon geometry in the extremal limit. Thus, our construction shows that the breaking of rotations itself does not necessarily imply a violation of the KSS bound.Comment: 20 pages, 7 figure

On the Economic Value and Price-Responsiveness of Ramp-Constrained Storage

The primary concerns of this paper are twofold: to understand the economic value of storage in the presence of ramp constraints and exogenous electricity prices, and to understand the implications of the associated optimal storage management policy on qualitative and quantitative characteristics of storage response to real-time prices. We present an analytic characterization of the optimal policy, along with the associated finite-horizon time-averaged value of storage. We also derive an analytical upperbound on the infinite-horizon time-averaged value of storage. This bound is valid for any achievable realization of prices when the support of the distribution is fixed, and highlights the dependence of the value of storage on ramp constraints and storage capacity. While the value of storage is a non-decreasing function of price volatility, due to the finite ramp rate, the value of storage saturates quickly as the capacity increases, regardless of volatility. To study the implications of the optimal policy, we first present computational experiments that suggest that optimal utilization of storage can, in expectation, induce a considerable amount of price elasticity near the average price, but little or no elasticity far from it. We then present a computational framework for understanding the behavior of storage as a function of price and the amount of stored energy, and for characterization of the buy/sell phase transition region in the price-state plane. Finally, we study the impact of market-based operation of storage on the required reserves, and show that the reserves may need to be expanded to accommodate market-based storage

Conformal Tightness of Holographic Scaling in Black Hole Thermodynamics

The near-horizon conformal symmetry of nonextremal black holes is shown to be a mandatory ingredient for the holographic scaling of the scalar-field contribution to the black hole entropy. This conformal tightness is revealed by semiclassical first-principle scaling arguments through an analysis of the multiplicative factors in the entropy due to the radial and angular degrees of freedom associated with a scalar field. Specifically, the conformal SO(2,1) invariance of the radial degree of freedom conspires with the area proportionality of the angular momentum sums to yield a robust holographic outcome.Comment: 23 pages, 1 figure. v2 & v3: expanded explanations and proofs, references added, typos corrected; v3: published versio

The phases of 2D NCOS

We study the phases of the 1+1 dimensional Non-Commutative Open String theory on a circle. We find that the length scale of non-commutativity increases at strong coupling, the coupling in turn being dressed by a power of D-string charge. The system is stringy at around this length scale, with dynamics involving an interplay between the open and wrapped closed strings sectors. Above this energy scale and at strong coupling, and below it at weak coupling, the system acquires a less stringy character. The near horizon geometry of the configuration exhibits several intriguing features, such as a flip in the dilaton field and the curvature scale, reflecting UV-IR mixing in non-commutative dynamics. Two special points in the parameter measuring the size of the circle are also identified.Comment: 27 pages, 4 figures; v2: reference added; v3: error in argument on page 6 correcte

Cosmological horizons and reconstruction of quantum field theories

As a starting point, we state some relevant geometrical properties enjoyed by the cosmological horizon of a certain class of Friedmann-Robertson-Walker backgrounds. Those properties are generalised to a larger class of expanding spacetimes $M$ admitting a geodesically complete cosmological horizon \scrim common to all co-moving observers. This structure is later exploited in order to recast, in a cosmological background, some recent results for a linear scalar quantum field theory in spacetimes asymptotically flat at null infinity. Under suitable hypotheses on $M$, encompassing both the cosmological de Sitter background and a large class of other FRW spacetimes, the algebra of observables for a Klein-Gordon field is mapped into a subalgebra of the algebra of observables \cW(\scrim) constructed on the cosmological horizon. There is exactly one pure quasifree state $\lambda$ on \cW(\scrim) which fulfils a suitable energy-positivity condition with respect to a generator related with the cosmological time displacements. Furthermore $\lambda$ induces a preferred physically meaningful quantum state $\lambda_M$ for the quantum theory in the bulk. If $M$ admits a timelike Killing generator preserving \scrim, then the associated self-adjoint generator in the GNS representation of $\lambda_M$ has positive spectrum (i.e. energy). Moreover $\lambda_M$ turns out to be invariant under every symmetry of the bulk metric which preserves the cosmological horizon. In the case of an expanding de Sitter spacetime, $\lambda_M$ coincides with the Euclidean (Bunch-Davies) vacuum state, hence being Hadamard in this case. Remarks on the validity of the Hadamard property for $\lambda_M$ in more general spacetimes are presented.Comment: 32 pages, 1 figure, to appear on Comm. Math. Phys., dedicated to Professor Klaus Fredenhagen on the occasion of his 60th birthda

Radio Galaxies at VHE energies

Radio Galaxies have by now emerged as a new $\gamma$-ray emitting source class on the extragalactic sky. Given their remarkable observed characteristics, such as unusual gamma-ray spectra or ultrafast VHE variability, they represent unique examples to probe into the nature and physics of AGN in general. This review provides a compact summary of their observed characteristics at very high $\gamma$-ray energies (VHE; $> 100$ GeV) along with a discussion of their possible physics implications. A particular focus is given to a concise overview of fundamental concepts concerning the origin of variable VHE emission, including recent developments in black hole gap physics.Comment: Invited review article, submitted to Galaxies; review, 21 pages, 14 figures; small typos corrected and references fixed to match accepted versio