Holographic renormalization as a canonical transformation

The gauge/string dualities have drawn attention to a class of variational problems on a boundary at infinity, which are not well defined unless a certain boundary term is added to the classical action. In the context of supergravity in asymptotically AdS spaces these problems are systematically addressed by the method of holographic renormalization. We argue that this class of a priori ill defined variational problems extends far beyond the realm of holographic dualities. As we show, exactly the same issues arise in gravity in non asymptotically AdS spaces, in point particles with certain unbounded from below potentials, and even fundamental strings in flat or AdS backgrounds. We show that the variational problem in all such cases can be made well defined by the following procedure, which is intrinsic to the system in question and does not rely on the existence of a holographically dual theory: (i) The first step is the construction of the space of the most general asymptotic solutions of the classical equations of motion that inherits a well defined symplectic form from that on phase space. The requirement of a well defined symplectic form is essential and often leads to a necessary repackaging of the degrees of freedom. (ii) Once the space of asymptotic solutions has been constructed in terms of the correct degrees of freedom, then there exists a boundary term that is obtained as a certain solution of the Hamilton-Jacobi equation which simultaneously makes the variational problem well defined and preserves the symplectic form. This procedure is identical to holographic renormalization in the case of asymptotically AdS gravity, but it is applicable to any Hamiltonian system.Comment: 37 pages; v2 minor corrections in section 2, 2 references and a footnote on Palatini gravity added. Version to appear in JHE

Sequencing and timing of strategic responses after industry disruption: evidence from post-deregulation competition in the U.S. railroad industry

This paper examines the sequencing and timing of firms’ strategic responses after significant industry disruption. We show that it is not the single strategic choice or response per se, but the sequencing and patterns of consecutive strategic responses that drive a firm’s adaptation and survival in the aftermath of a shift in the industry. We find that firms’ renewal efforts involved differential adaptability in finding balance at the juxtaposition of responding to demand-side pressures and choosing a path of new capability acquisition efficiently. Our study underscores the importance of taking a sequencing approach to studying strategic responses to industry disruption

Casual Compressive Sensing for Gene Network Inference

We propose a novel framework for studying causal inference of gene interactions using a combination of compressive sensing and Granger causality techniques. The gist of the approach is to discover sparse linear dependencies between time series of gene expressions via a Granger-type elimination method. The method is tested on the Gardner dataset for the SOS network in E. coli, for which both known and unknown causal relationships are discovered

Conformal higher spin scattering amplitudes from twistor space

We use the formulation of conformal higher spin (CHS) theories in twistor space to study their tree-level scattering amplitudes, finding expressions for all three-point anti-MHV amplitudes and all MHV amplitudes involving positive helicity conformal gravity particles and two negative helicity higher spins. This provides the on-shell analogue for the covariant coupling of CHS fields to a conformal gravity background. We discuss the restriction of the theory to a ghost-free unitary subsector, analogous to restricting conformal gravity to general relativity with a cosmological constant. We study the flat-space limit and show that the restricted amplitudes vanish, supporting the conjecture that in the unitary sector the S-matrix of CHS theories is trivial. However, by appropriately rescaling the amplitudes we find non-vanishing results which we compare with chiral flat-space higher spin theories.Comment: 31 pages, no figures. v2: comments added, published versio

Scattering of conformal higher spin fields

We develop a formalism for describing the most general notion of tree-level scattering amplitudes in 4d conformal higher spin theory. As conformal higher spin fields obey higher-derivative equations of motion, there are many distinct on-shell external states which may contribute to their scattering, some of which grow polynomially with time, leading to ill-defined amplitudes. We characterize the set of admissible scattering states which produce finite tree amplitudes, noting that there are more such states than just standard massless higher spins obeying two-derivative equations of motion. We use conformal gravity as a prime example, where the set of scattering states includes the usual Einstein graviton and a `ghost' massless spin 1 particle. An extension of the usual spinor helicity formalism allows us to encode these scattering states efficiently in terms of `twistor-spinors'. This leads to compact momentum space expressions for all finite tree-level 3-point amplitudes of conformal higher spin theory. While some of these 3-point amplitudes vanish (including all those with only standard two-derivative higher spin external states), there are many others which are non-vanishing. We also comment on the generalization to scattering of conformal higher spins in AdS$_4$.Comment: 40 pages, no figures. v2: references adde

Black hole spin: theory and observation

In the standard paradigm, astrophysical black holes can be described solely by their mass and angular momentum - commonly referred to as `spin' - resulting from the process of their birth and subsequent growth via accretion. Whilst the mass has a standard Newtonian interpretation, the spin does not, with the effect of non-zero spin leaving an indelible imprint on the space-time closest to the black hole. As a consequence of relativistic frame-dragging, particle orbits are affected both in terms of stability and precession, which impacts on the emission characteristics of accreting black holes both stellar mass in black hole binaries (BHBs) and supermassive in active galactic nuclei (AGN). Over the last 30 years, techniques have been developed that take into account these changes to estimate the spin which can then be used to understand the birth and growth of black holes and potentially the powering of powerful jets. In this chapter we provide a broad overview of both the theoretical effects of spin, the means by which it can be estimated and the results of ongoing campaigns.Comment: 55 pages, 5 figures. Published in: "Astrophysics of Black Holes - From fundamental aspects to latest developments", Ed. Cosimo Bambi, Springer: Astrophysics and Space Science Library. Additional corrections mad

Darwinism, organizational evolution and survival: key challenges for future research

How do social organizations evolve? How do they adapt to environmental pressures? What resources and capabilities determine their survival within dynamic competition? Charles Darwin’s seminal work The Origin of Species (1859) has provided a significant impact on the development of the management and organization theory literatures on organizational evolution. This article introduces the JMG Special Issue focused on Darwinism, organizational evolution and survival. We discuss key themes in the organizational evolution research that have emerged in recent years. These include the increasing adoption of the co-evolutionary approach, with a particular focus on the definition of appropriate units of analysis, such as routines, and related challenges associated with exploring the relationship between co-evolution, re-use of knowledge, adaptation, and exaptation processes. We then introduce the three articles that we have finally accepted in this Special Issue after an extensive, multi-round, triple blind-review process. We briefly outline how each of these articles contributes to understanding among scholars, practitioners and policy makers of the continuous evolutionary processes within and among social organizations and systems