GIT Constructions of Moduli Spaces of Stable Curves and Maps

This largely expository paper first gives an introduction to Hilbert stability and its use in Gieseker's GIT construction of $\overline{M}_g$. Then I review recent work in this area--variants for unpointed curves that arise in Hassett's log minimal model program, starting with Schubert's moduli space of pseudostable curves, and constructions for weighted pointed stable curves and for pointed stable maps due to Swinarski and to Baldwin and Swinarski respectively. The focus is on the steps at which new ideas are needed. Finally, I list open problems in the area, particularly some arising in the log minimal model program that seem inaccessible to current techniques.Comment: 46 pages, 3 figures, written for Surveys in Differential Geometr

The IR stability of de Sitter QFT: Physical initial conditions

This work uses Lorentz-signature in-in perturbation theory to analyze the late-time behavior of correlators in time-dependent interacting massive scalar field theory in de Sitter space. We study a scenario recently considered by Krotov and Polyakov in which the coupling $g$ turns on smoothly at finite time, starting from $g=0$ in the far past where the state is taken to be the (free) Bunch-Davies vacuum. Our main result is that the resulting correlators (which we compute at the one-loop level) approach those of the interacting Hartle-Hawking state at late times. We argue that similar results should hold for other physically-motivated choices of initial conditions. This behavior is to be expected from recent quantum "no hair" theorems for interacting massive scalar field theory in de Sitter space which established similar results to all orders in perturbation theory for a dense set of states in the Hilbert space. Our current work i) indicates that physically motivated initial conditions lie in this dense set, ii) provides a Lorentz-signature counter-part to the Euclidean techniques used to prove such theorems, and iii) provides an explicit example of the relevant renormalization techniques.Comment: 32 pages, 3 figure

The IR stability of de Sitter: Loop corrections to scalar propagators

We compute 1-loop corrections to Lorentz-signature de Sitter-invariant 2-point functions defined by the interacting Euclidean vacuum for massive scalar quantum fields with cubic and quartic interactions. Our results apply to all masses for which the free Euclidean de Sitter vacuum is well-defined, including values in both the complimentary and the principal series of SO(D,1). In dimensions where the interactions are renormalizeable we provide absolutely convergent integral representations of the corrections. These representations suffice to analytically extract the leading behavior of the 2-point functions at large separations and may also be used for numerical computations. The interacting propagators decay at long distances at least as fast as one would naively expect, suggesting that such interacting de Sitter invariant vacuua are well-defined and are well-behaved in the IR. In fact, in some cases the interacting propagators decay faster than any free propagator with any value of $M^2> 0$.Comment: To appear in Phys. Rev.

On higher spin symmetries in de Sitter QFTs

We consider the consequences of global higher-spin symmetries in quantum field theories on a fixed de Sitter background of spacetime dimension $D \ge 3$. These symmetries enhance the symmetry group associated with the isometries of the de Sitter background and thus strongly constrain the dynamics of the theory. In particular, we consider the case when a higher spin charge acts linearly on a scalar operator to leading order in a Fefferman-Graham expansion near the future/past conformal boundaries. We show that this implies that the expectation values of the operator inserted near the boundaries are asymptotically Gaussian. Thus, these operators have trivial cosmological spectra, and on global de Sitter these operators have only Gaussian correlations between operators inserted near future/past infinity. The latter result may be interpreted as an analogue of the Coleman-Mandula theorem for QFTs on de Sitter spacetime.Comment: 20 pp; accepted to JHEP; latest version: expanded introduction, additional reference

The Habitability of our Evolving Galaxy

The notion of a Galactic Habitable Zone (GHZ), or regions of the Milky Way galaxy that preferentially maintain the conditions to sustain complex life, has recently gained attention due to the detection of numerous exoplanets and advances made in understanding habitability on the Earth and other environments. We discuss what a habitable environment means on large spatial and temporal scales, which necessarily requires an approximated definition of habitability to make an assessment of the astrophysical conditions that may sustain complex life. We discuss a few key exoplanet findings that directly relate to estimating the distribution of Earth-size planets in the Milky Way. With a broad notion of habitability defined and major observable properties of the Milky Way described, we compare selected literature on the GHZ and postulate why the models yield differing predictions of the most habitable regions at the present day, which include: (1) the majority of the galactic disk; (2) an annular ring between 7-9 kpc, and (3) the galactic outskirts. We briefly discuss the habitability of other galaxies as influenced by these studies. We note that the dangers to biospheres in the Galaxy taken into account in these studies may be incomplete and we discuss the possible role of Gamma-Ray Bursts and other dangers to life in the Milky Way. We speculate how changing astrophysical properties may affect the GHZ over time, including before the Earth formed, and describe how new observations and other related research may fit into the bigger picture of the habitability of the Galaxy.Comment: Chapter in Habitability of the Universe Before Earth, R. Gordon and A. Sharov (Eds.), Elsevie

Mutual information between thermo-field doubles and disconnected holographic boundaries

We use mutual information as a measure of the entanglement between 'physical' and thermo-field double degrees of freedom in field theories at finite temperature. We compute this "thermo-mutual information" in simple toy models: a quantum mechanics two-site spin chain, a two dimensional massless fermion, and a two dimensional holographic system. In holographic systems, the thermo-mutual information is related to minimal surfaces connecting the two disconnected boundaries of an eternal black hole. We derive a number of salient features of this thermo-mutual information, including that it is UV finite, positive definite and bounded from above by the standard mutual information for the thermal ensemble. We relate the construction of the reduced density matrices used to define the thermo-mutual information to the Schwinger-Keldysh formalism, ensuring that all our objects are well defined in Euclidean and Lorentzian signature.Comment: 31 pp., 8 figures. v.2: Expanded discussion. To appear in JHE

Modular Frobenius manifolds and their invariant flows

The space of Frobenius manifolds has a natural involutive symmetry on it: there exists a map $I$ which send a Frobenius manifold to another Frobenius manifold. Also, from a Frobenius manifold one may construct a so-called almost dual Frobenius manifold which satisfies almost all of the axioms of a Frobenius manifold. The action of $I$ on the almost dual manifolds is studied, and the action of $I$ on objects such as periods, twisted periods and flows is studied. A distinguished class of Frobenius manifolds sit at the fixed point of this involutive symmetry, and this is made manifest in certain modular properties of the various structures. In particular, up to a simple reciprocal transformation, for this class of modular Frobenius manifolds, the flows are invariant under the action of $I\,.

Specifications for modelling fuel cell and combustion-based residential cogeneration device within whole-building simulation programs

This document contains the specifications for a series of residential cogeneration device models developed within IEA/ECBCS Annex 42. The devices covered are: solid oxide and polymer exchange membrane fuel cells (SOFC and PEM), and internal combustion and Stirling engine units (ICE and SE). These models have been developed for use within whole-building simulation programs and one or more of the models described herein have been integrated into the following simulation packages: ESP-r, EnergyPlus, TRNSYS and IDA-ICE. The models have been designed to predict the energy performance of cogeneration devices when integrated into a residential building (dwelling). The models account for thermal performance (dynamic thermal performance in the case of the combustion engine models), electrochemical and combustion reactions where appropriate, along with electrical power output. All of the devices are modelled at levels of detail appropriate for whole-building simulation tools

The IR stability of de Sitter QFT: results at all orders

We show that the Hartle-Hawking vacuum for theories of interacting massive scalars in de Sitter space is both perturbatively well-defined and stable in the IR. Correlation functions in this state may be computed on the Euclidean section and Wick-rotated to Lorentz-signature. The results are manifestly de Sitter-invariant and contain only the familiar UV singularities. More importantly, the connected parts of all Lorentz-signature correlators decay at large separations of their arguments. Our results apply to all cases in which the free Euclidean vacuum is well defined, including scalars with masses belonging to both the complementary and principal series of $SO(D,1)$. This suggests that interacting QFTs in de Sitter -- including higher spin fields -- are perturbatively IR-stable at least when i) the Euclidean vacuum of the zero-coupling theory exists and ii) corresponding Lorentz-signature zero-coupling correlators decay at large separations. This work has significant overlap with a paper by Stefan Hollands, which is being released simultaneously.Comment: 30 pp., 4 figures. Small typos fixed, refs adde