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The vacuum entanglement entropy of a general conformal field theory (CFT) in $d=5$ spacetime dimensions contains a universal term, $F(A)$, which has a complicated and non-local dependence on the geometric details of the region $A$ and the theory. Analogously to the previously known $d=3$ case, we prove that for CFTs in $d=5$ which are holographically dual to Einstein gravity, $F(A)$ is equal to a four-dimensional version of the ``Willmore energy'' associated to a doubled and closed version of the Ryu-Takayanagi (RT) surface of $A$ embedded in $\mathbb{R}^5$. This generalized Willmore energy is shown to arise from a conformal-invariant codimension-two functional obtained by evaluating six-dimensional Conformal Gravity on the conically-singular orbifold of the replica trick. The new functional involves an integral over the doubled RT surface of a linear combination of three quartic terms in extrinsic curvatures and is free from ultraviolet divergences by construction. We verify explicitly the validity of our new formula for various entangling regions and argue that, as opposed to the $d=3$ case, $F(A)$ is not globally minimized by a round ball $A=\mathbb{B}^4$. Rather, $F(A)$ can take arbitrarily positive and negative values as a function of $A$. Hence, we conclude that the round ball is not a global minimizer of $F(A)$ for general five-dimensional CFTs., Comment: 48 pages, 5 figures

Factor analysis is a way to characterize the relationships between many (observable) variables in terms of a smaller number of unobservable random variables which are called factors. However, the application of factor models and its success can be subjective or difficult to gauge, since infinitely many factor models that produce the same correlation matrix can be fit given sample data. Thus, there is a need to operationalize a criterion that measures how meaningful or "interpretable" a factor model is in order to select the best among many factor models. While there are already techniques that aim to measure and enhance interpretability, new indices, as well as rotation methods via mathematical optimization based on them, are proposed to measure interpretability. The proposed methods directly incorporate semantics with the help of natural language processing and are generalized to incorporate any "prior information". Moreover, the indices allow for complete or partial specification of relationships at a pairwise level. Aside from these, two other main benefits of the proposed methods are that they do not require the estimation of factor scores, which avoids the factor score indeterminacy problem, and that no additional explanatory variables are necessary. The implementation of the proposed methods is written in Python 3 and is made available together with several helper functions through the package interpretablefa on the Python Package Index. The methods' application is demonstrated here using data on the Experiences in Close Relationships Scale, obtained from the Open-Source Psychometrics Project.

We study a class of binary treatment choice problems with partial identification, through the lens of robust (multiple prior) Bayesian analysis. We use a convenient set of prior distributions to derive ex-ante and ex-post robust Bayes decision rules, both for decision makers who can randomize and for decision makers who cannot. Our main messages are as follows: First, ex-ante and ex-post robust Bayes decision rules do not tend to agree in general, whether or not randomized rules are allowed. Second, randomized treatment assignment for some data realizations can be optimal in both ex-ante and, perhaps more surprisingly, ex-post problems. Therefore, it is usually with loss of generality to exclude randomized rules from consideration, even when regret is evaluated ex-post. We apply our results to a stylized problem where a policy maker uses experimental data to choose whether to implement a new policy in a population of interest, but is concerned about the external validity of the experiment at hand (Stoye, 2012); and to the aggregation of data generated by multiple randomized control trials in different sites to make a policy choice in a population for which no experimental data are available (Manski, 2020; Ishihara and Kitagawa, 2021).

We present a decision-theoretic justification for viewing the question of how to best choose where to experiment in order to optimize external validity as a k-median (clustering) problem, a popular problem in computer science and operations research. We present conditions under which minimizing the worst-case, welfare-based regret among all nonrandom schemes that select k sites to experiment is approximately equal - and sometimes exactly equal - to finding the k most central vectors of baseline site-level covariates. The k-median problem can be formulated as a linear integer program. Two empirical applications illustrate the theoretical and computational benefits of the suggested procedure.

We study the (anti-)self-duality conditions under which the electric and magnetic parts of the conserved charges of the dyonic Kerr-Newman-NUT-AdS solution become equivalent. Within a holographic framework, the stress tensor and the boundary Cotton tensor are computed from the electric/magnetic content of the Weyl tensor. The holographic stress tensor/Cotton tensor duality is recovered along the (anti-)self-dual curve in parameter space. We show that the latter not only implies a duality relation for the mass but also for the angular momentum. The partition function is computed to first order in the saddle-point approximation and a BPS bound is obtained. The ground state of the theory is enlarged to all the (anti-)self-dual configurations when the $SO(4)$ and $U(1)$ Pontryagin densities are introduced. We demonstrate this at the level of the action and variations thereof., Comment: v1: 18 pages; v2: References added. Accepted for publication in PRD

We consider impulse response inference in a locally misspecified vector autoregression (VAR) model. The conventional local projection (LP) confidence interval has correct coverage even when the misspecification is so large that it can be detected with probability approaching 1. This result follows from a "double robustness" property analogous to that of popular partially linear regression estimators. In contrast, the conventional VAR confidence interval with short-to-moderate lag length can severely undercover, even for misspecification that is small, economically plausible, and difficult to detect statistically. There is no free lunch: the VAR confidence interval has robust coverage only if the lag length is so large that the interval is as wide as the LP interval.

We present a formalism for new $U(1)$ interactions involving weak hypercharge, baryon, and lepton numbers, and a possible axial symmetry generator $F_A$ in the presence of a second Brout-Englert-Higgs doublet. The resulting $U$ boson, after mixing with the $Z$, interpolates between a generalised dark photon, a dark $Z$, and an axially coupled gauge boson. We especially focus on the axial couplings originating from $F_A$ or from mixing with the $Z$, determined by the scalar sector via parameters like $\tan\beta$ and the v.e.v. of an extra dark singlet. We explore the distinctive features of axially coupled interactions, especially in the ultrarelativistic limit, where the $U$ boson behaves much as an axion-like particle, with enhanced interactions to quarks and leptons. This enhancement is particularly relevant for future muon beam dump experiments, since the muon mass considerably increases the effective coupling, proportional to $2m_\mu/m_U$, compared to analogous experiments with electrons. We also analyse the shape of the expected beam dump exclusion or discovery regions, influenced by $U$ boson interactions and the experiment geometry. Different situations are considered, limited in particular by cases for which the $U$ decays before reaching the detector, or has too small couplings to produce detectable events. We also compare to vectorially coupled bosons and axion-like pseudoscalars, highlighting the importance of understanding the parameter space for future experiment design and optimisation.

Strongly supercooled first order phase transitions (FOPTs) can produce primordial black hole (PBH) dark matter (DM) along with observable gravitational waves (GWs) from bubble collisions. Such FOPTs may also produce coherent magnetic fields generated by bubble collisions and by turbulence in the primordial plasma. Here we find that the requirement for PBH DM can produce large primordial magnetic fields which subsequently yield intergalactic magnetic fields in the present universe (with magnitude $\lesssim 20$ pG across coherence length scales of $\simeq 0.001$-$0.01$ Mpc, assuming maximally helical magnetic fields) that easily exceed lower bounds from blazar observations. We follow a largely model independent approach and highlight the possibility of producing DM and observable multi-messenger magnetic fields and GW signals visible in next generation experiments., Comment: 8 pages, 3 figures

We apply classical statistical decision theory to a large class of treatment choice problems with partial identification, revealing important theoretical and practical challenges but also interesting research opportunities. The challenges are: In a general class of problems with Gaussian likelihood, all decision rules are admissible; it is maximin-welfare optimal to ignore all data; and, for severe enough partial identification, there are infinitely many minimax-regret optimal decision rules, all of which sometimes randomize the policy recommendation. The opportunities are: We introduce a profiled regret criterion that can reveal important differences between rules and render some of them inadmissible; and we uniquely characterize the minimax-regret optimal rule that least frequently randomizes. We apply our results to aggregation of experimental estimates for policy adoption, to extrapolation of Local Average Treatment Effects, and to policy making in the presence of omitted variable bias.

We study the renormalization of a particular sector of Horndeski theory. In particular, we focus on the nonminimal coupling of a scalar field to the Gauss-Bonnet term and its kinetic coupling to the Einstein tensor. Adopting a power expansion on the scalar function that couples the Gauss-Bonnet term, we find specific conditions on their coefficients such that the action and charges are finite. To accomplish the latter, we add a finite set of intrinsic boundary terms. The contribution of the nonminimal coupling generates an effective scalar mass, allowing us to recover a modified Breitenlohner-Freedman bound. Furthermore, we compute the holographic 1-point functions and Ward identities associated with the scalar field and the metric. We constrain the parameter space of the theory by taking into account the preservation of scaling symmetry at the boundary., Comment: 35 pages. Comments and references added. Accepted for publication in JHEP

$\gamma$-ray emission of blazars infer the presence of large-scale magnetic fields in the intergalactic medium, but their origin remains a mystery. Using recent data from MAGIC, H.E.S.S. and $\textit{Fermi}$-LAT, we investigate whether the large-scale magnetic fields in the intergalactic medium could have been generated by a first-order electroweak phase transition in the two-Higgs-doublet model (2HDM). We study two representative scenarios where we vary the initial conditions of the magnetic field and the plasma, assuming either a primordial magnetic field with maximal magnetic helicity or a primordial magnetic field with negligible magnetic helicity in a plasma with kinetic helicity. By considering a primordial magnetic field with maximal helicity and applying the conservative constraints derived from MAGIC and $\textit{Fermi}$-LAT data, we demonstrate that a first-order electroweak phase transition within the 2HDM may account for the observed intergalactic magnetic fields in the case of the strongest transitions. We show that this parameter space also predicts strong gravitational wave signals in the reach of space-based detectors such as LISA, providing a striking multi-messenger signal of the 2HDM.

In three-dimensional pseudo-Riemannian manifolds, the Cotton tensor arises as the variation of the gravitational Chern-Simons action with respect to the metric. It is Weyl-covariant, symmetric, traceless and covariantly conserved. Performing a reduction of the Cotton tensor with respect to Carrollian diffeomorphisms in a suitable frame, one discloses four sets of Cotton Carrollian relatives, which are conformal and obey Carrollian conservation equations. Each set of Carrollian Cotton tensors is alternatively obtained as the variation of a distinct Carroll-Chern-Simons action with respect to the degenerate metric and the clock form of a strong Carroll structure. The four Carroll-Chern-Simons actions emerge in the Carrollian reduction of the original Chern-Simons ascendant. They inherit its anomalous behaviour under diffeomorphisms and Weyl transformations. The extremums of these Carrollian actions are commented and illustrated., Comment: v1: 1+21 pages, Latex, v2: JHEP version

Recently the ATLAS collaboration has reported the first results of searches for heavy scalar resonances decaying into a $Z$ boson and a lighter new scalar resonance, where the $Z$ boson decays leptonically and the lighter scalar decays into a top-quark pair, giving rise to $\ell^+ \ell^- t \bar{t}$ final states. This had previously been identified as a smoking-gun signature at the LHC for a first-order electroweak phase transition (FOEWPT) within the framework of two Higgs doublet models (2HDMs). In addition, ATLAS also presented new limits where the $Z$ boson decays into pairs of neutrinos and the lighter scalar resonance into bottom-quark pairs, giving rise to the $\nu \nu b \bar b$ final state. We analyze the impact of these new searches on the 2HDM parameter space, with emphasis on their capability to probe currently allowed 2HDM regions featuring a strong FOEWPT. We also study the complementarity of these new searches with other LHC probes that could target the FOEWPT region of the 2HDM. Remarkably, the ATLAS search in the $\ell^+ \ell^- t \bar{t}$ final state shows a local $2.85\,\sigma$ excess (for masses of about 650 GeV and 450 GeV for the heavy and light resonance) in the 2HDM parameter region that would yield a FOEWPT in the early universe, which could constitute the first experimental hint of baryogenesis at the electroweak scale. We analyze the implications of this excess, and discuss the detectability prospects for the associated gravitational wave signal from the FOEWPT. Furthermore, we project the sensitivity reach of the $\ell^+ \ell^- t \bar{t}$ signature for the upcoming runs of the LHC. Finally, we introduce the python package thdmTools, a state-of-art tool for the exploration of the 2HDM., Comment: 36 pages, 7 figures

We identify, in spacetimes satisfying the null convergence condition, a certain natural class of null hypersurfaces that admit null sections with constant surface gravity. Our work is meant to offer complementary results to previous work on null hypersurfaces of zero expansion arising from the study of Cauchy and black hole horizons in general relativity., Comment: 21 pages

We present a streamlined proof that any Einstein-AdS space is a solution of the Lu, Pang and Pope conformal gravity theory in six dimensions. The reduction of conformal gravity into Einstein theory manifestly shows that the action of the latter can be written as the Einstein-Hilbert term plus the Euler topological density and an additional contribution that depends on the Laplacian of the bulk Weyl tensor squared. The prescription for obtaining this form of the action by embedding the Einstein theory into a Weyl-invariant purely metric theory, was dubbed Conformal Renormalization and its resulting action was shown to be equivalent to the one obtained by holographic renormalization. As a non-trivial application of the method, we compute the Noether-Wald charges and thermodynamic quantities for topological black hole solutions with generic transverse section in Einstein-AdS$_6$ theory., Comment: 25 pages, version accepted in JHEP

We show that primordial black holes - in the observationally allowed mass window with $f_{\rm pbh}=1$ - formed from late nucleating patches in a first order phase transition imply upcoming gravitational wave interferometers will see a large stochastic background arising from the bubble collisions. As an example, we use a classically scale invariant $B-L$ model, in which the right handed neutrinos explain the neutrino masses and leptogenesis, and the dark matter consists of primordial black holes. The conclusion regarding the gravitational waves is, however, expected to hold model independently for black holes coming from such late nucleating patches., Comment: 38 pages, appendix added, accepted for publication in JHEP

We explore the consistent truncation of conserved charges in Quadratic Curvature Gravity (QCG) with anti-de Sitter asymptotics to the linear order in the Weyl tensor. The QCG action is given by the most general curvature-squared corrections to Einstein gravity, and it is suitably rendered finite by the addition of extrinsic counterterms (Kounterterms). The conserved charges derived from this action are, as a consequence, nonlinear in the spacetime Riemann tensor. A detailed analysis of the falloff of generic static solutions leads to a charge proportional to the electric part of the Weyl tensor, without loss of information on the energy of the system. The procedure followed provides firmer ground to the extension of the notion of Conformal Mass to higher-curvature gravity, as it appears as associated to a renormalized action. We observe that criticality condition in QCG poses an obstruction to the charge linearization, in contrast to previous results in Lovelock gravity, where degeneracy condition plays a key role., Comment: 38 pages, no figures; in v2, one reference added

Observations of debris disks have significantly improved over the past decades, both in terms of sensitivity and spatial resolution. At near-infrared wavelengths, new observing strategies and post-processing algorithms allow us to drastically improve the final images, revealing faint structures in the disks. These structures inform us about the properties and spatial distribution of the small dust particles. We present new $H$-band observations of the disk around HD 129590, which display an intriguing arc-like structure in total intensity but not in polarimetry, and propose an explanation for the origin of this arc. Assuming geometric parameters for the birth ring of planetesimals, our model provides the positions of millions of particles of different sizes to compute scattered light images. We demonstrate that if the grain size distribution is truncated or strongly peaks at a size larger than the radiation pressure blow-out size we are able to produce an arc quite similar to the observed one. If the birth ring is radially narrow, given that particles of a given size have similar eccentricities, they will have their apocenters at the same distance from the star. Since this is where the particles will spend most of their time, this results in a "apocenter pile-up" that can look like a ring. Due to more efficient forward scattering this arc only appears in total intensity observations and remains undetected in polarimetric data. This scenario requires sharp variations either in the grain size distribution or for the scattering efficiencies $Q_\mathrm{sca}$. Alternative possibilities such as a wavy size distribution and a size-dependent phase function are interesting candidates to strengthen the apocenter pile-up. We also discuss why such arcs are not commonly detected in other systems, which can mainly be explained by the fact that most parent belts are usually broad., Comment: Accepted for publication in A&A, abstract shortened

Prompt engineering is an increasingly important skill set needed to converse effectively with large language models (LLMs), such as ChatGPT. Prompts are instructions given to an LLM to enforce rules, automate processes, and ensure specific qualities (and quantities) of generated output. Prompts are also a form of programming that can customize the outputs and interactions with an LLM. This paper describes a catalog of prompt engineering techniques presented in pattern form that have been applied to solve common problems when conversing with LLMs. Prompt patterns are a knowledge transfer method analogous to software patterns since they provide reusable solutions to common problems faced in a particular context, i.e., output generation and interaction when working with LLMs. This paper provides the following contributions to research on prompt engineering that apply LLMs to automate software development tasks. First, it provides a framework for documenting patterns for structuring prompts to solve a range of problems so that they can be adapted to different domains. Second, it presents a catalog of patterns that have been applied successfully to improve the outputs of LLM conversations. Third, it explains how prompts can be built from multiple patterns and illustrates prompt patterns that benefit from combination with other prompt patterns.

We study the classical problem of predicting an outcome variable, $Y$, using a linear combination of a $d$-dimensional covariate vector, $\mathbf{X}$. We are interested in linear predictors whose coefficients solve: % \begin{align*} \inf_{\boldsymbol{\beta} \in \mathbb{R}^d} \left( \mathbb{E}_{\mathbb{P}_n} \left[ \left(Y-\mathbf{X}^{\top}\beta \right)^r \right] \right)^{1/r} +\delta \, \rho\left(\boldsymbol{\beta}\right), \end{align*} where $\delta>0$ is a regularization parameter, $\rho:\mathbb{R}^d\to \mathbb{R}_+$ is a convex penalty function, $\mathbb{P}_n$ is the empirical distribution of the data, and $r\geq 1$. We present three sets of new results. First, we provide conditions under which linear predictors based on these estimators % solve a \emph{distributionally robust optimization} problem: they minimize the worst-case prediction error over distributions that are close to each other in a type of \emph{max-sliced Wasserstein metric}. Second, we provide a detailed finite-sample and asymptotic analysis of the statistical properties of the balls of distributions over which the worst-case prediction error is analyzed. Third, we use the distributionally robust optimality and our statistical analysis to present i) an oracle recommendation for the choice of regularization parameter, $\delta$, that guarantees good out-of-sample prediction error; and ii) a test-statistic to rank the out-of-sample performance of two different linear estimators. None of our results rely on sparsity assumptions about the true data generating process; thus, they broaden the scope of use of the square-root lasso and related estimators in prediction problems.