This is a companion paper of a long work appeared in [C. Cremonini and P. Grassi, Pictures from super Chern-Simons theory, J. High Energy Phys. 03 (2020) 043] discussing the super-Chern-Simons theory on supermanifolds. Here, it is emphasized that the Batalin-Vilkovisky formalism is naturally formulated using integral forms for any supersymmetric and supergravity models and we show how to deal with $A_{\infty }$ algebras emerging from supermanifold structures.

We thoroughly analyze the number of independent zero modes and their zero points on the toroidal orbifold $T^2/{\mathbb{Z}}_N(N=2,3,4,6)$ with magnetic flux background, inspired by the Atiyah-Singer index theorem. We first show a complete list for the number $n_{\eta }$ of orbifold zero modes belonging to ${\mathbb{Z}}_N$ eigenvalue $\eta$. Since it turns out that $n_{\eta }$ quite complicatedly depends on the flux quanta $M$, the Scherk-Schwarz twist phase $({\alpha }_1,{\alpha }_2)$, and the ${\mathbb{Z}}_N$ eigenvalue $\eta$, it seems hard that $n_{\eta }$ can be universally explained in a simple formula. We, however, succeed in finding a single zero-mode counting formula $n_{\eta }=(M-V_{\eta })/N+1$, where $V_{\eta }$ denotes the sum of winding numbers at the fixed points on the orbifold $T^2/{\mathbb{Z}}_N$. The formula is shown to hold for any pattern.

We show that a suitable background field can bring a non-BPS topological soliton into its Bogomol’nyi-Prasad-Sommerfield (BPS), self-dual, counterpart. As an example we consider Skyrmions in the minimal Skyrme model. We prove the triviality of the corresponding moduli space. This means that the resulting self-dual Skyrmion does statically interact with the background field. We also show that the originally self-dual Skyrmions (e.g., solutions of the BPS Skyrme model) can preserve the self-duality after a coupling with a background field. In this case, BPS Skyrmions can be effortless moved with respect to the background.

In this work, we revisit the duality between a self-dual nongauge invariant theory and a topological massive theory in $3+1$ dimensions. The self-dual Lagrangian is composed by a vector field and an antisymmetric field tensor whereas the topological massive Lagrangian is built using a $B\wedge F$ term. Though the Lagrangians are quite different, they yield to equations of motion that are connected by a simple dual mapping among the fields. We discuss this duality by analyzing the degrees of freedom in both theories and comparing their propagating modes at the classical level. Moreover, we employ the master action method to obtain a fundamental Lagrangian that interpolates between these two theories and makes evident the role of the topological $B\wedge F$ term in the duality relation. By coupling these theories with matter fields, we show that the duality holds provided a Thirring-like term is included. In addition, we use the master action in order to probe the duality upon the quantized fields. We carried out a functional integration of the fields and compared the resulting effective Lagrangians.

Gravastars have been considered as a serious alternative to black holes in the past couple of decades. Stable models of gravastar have been constructed in many of the alternate gravity models besides standard general relativity (GR). The Randall-Sundrum (RS) braneworld model has been a popular alternative to GR, especially in the cosmological and astrophysical context. Here, we consider a gravastar model in RS brane gravity. The mathematical solutions in different regions have been obtained with calculation of matching conditions. Various important physical parameters for the shell have been calculated and plotted to note their variation with radial distance. We also calculate and plot the surface redshift to provide a very cursory check on the stability of the gravastar within the purview of RS brane gravity.

We consider a model of Bose-Einstein condensate of weakly interacting off-shell gravitons in the regime that is far from the quantum critical point. Working in static spherically symmetric setup, recent study has demonstrated that the effective spacetime geometry of this condensate is a gravastar. In this paper we make three generalizations: introducing a composite of two sets of off-shell gravitons with different wavelength to enable richer geometries for the interior and exterior spacetimes, working in $f(\mathcal{R})$ gravity, and extending the calculations to higher dimensions. We find that the effective spacetime geometry is again a gravastar, but now with a metric which strongly depends on the modified gravity function $f(\mathcal{R})$. This implies that the interior of the gravastar can be de Sitter or anti–de Sitter and the exterior can be Schwarzschild, Schwarzschild–de Sitter, or Schwarzschild–anti–de Sitter, with a condition that the cosmological constant for the exterior must be smaller than the one for the interior. These geometries are determined by the function $f(\mathcal{R})$, in contrast to previous works where they were selected by hand. We also presented a new possible value for the size of the gravastar provided a certain inequality is satisfied. This restriction can be seen manifested in the behavior of the interior graviton wavelength as a function of spacetime dimension.

Black holes are the simplest objects in the Universe. They correspond to extreme deformations of spacetime geometry and can exist even devoid of matter. In general relativity, (electro)vacuum black holes are uniquely determined by their mass, charge, and angular momentum. This feature follows from a uniqueness theorem, which can be evaded if one considers higher dimensions or matter fields coupled to gravity. Here we find that Einsteinian cubic gravity, a well-motivated modification of Einstein gravity that includes third-order curvature corrections in accordance with low-energy effective theory expectations, admits black hole solutions with charge greater than mass, when minimally coupled to a Maxwell field. Moreover, we find that, in this regime, there can be two asymptotically flat black holes with the same charge and mass, posing the first example of vacuum black hole nonuniqueness in four dimensions that is free from pathologies. Examination of these black hole’s thermodynamics reveals that when two branches coexist only the larger black hole is thermodynamically stable, while the smaller branch has negative specific heat. Einsteinian cubic gravity unveils two further surprising features. The charged black holes do not possess an inner horizon, in contrast with the usual Reissner-Nordström spacetime, thus avoiding the need to resort to strong cosmic censorship to uphold determinism. In addition to black holes, there exists a one-parameter family of naked singularity spacetimes sharing the same mass and charge as the former, but not continuously connected with them. These naked singularities exist in the under-extremal regime, being present even in pure (uncharged) Einsteinian cubic gravity.

In this brief report, we investigate the existence of four-dimensional static spherically symmetric black holes (BHs) in the Einstein-complex-scalar-Gauss-Bonnet gravity with an arbitrary potential $V(\varphi )$ and a coupling $f(\varphi )$ between the scalar field $\varphi$ and the Gauss-Bonnet (GB) term. We find that static regular BH solutions with complex scalar hairs do not exist. This conclusion does not depend on the coupling between the GB term and the scalar field nor on the scalar potential $V(\varphi )$ and the presence of a cosmological constant $\mathrm{\Lambda }$ (which can be either positive or negative), as long as the scalar field remains complex and is regular across the horizon.

Upcoming cosmic microwave background (CMB) data can be used to explore harmonic 3-point functions that involve the $B$-mode component of the CMB polarization signal. We focus on bispectra describing the non-Gaussian correlation of the $B$-mode field and the CMB temperature anisotropies ($T$) and/or $E$-mode polarization, i.e., $⟨TTB⟩$, $⟨EEB⟩$, and $⟨TEB⟩$. Such bispectra probe violations of the tensor consistency relation: the model-independent behavior of cosmological correlation functions that involve a large-wavelength tensor mode (gravitational wave). An observed violation of the tensor consistency relation would exclude a large number of inflation models. We describe a generalization of the Komatsu-Spergel-Wandelt (KSW) bispectrum estimator that allows statistical inference on this type of primordial non-Gaussianity with data of the CMB temperature and polarization anisotropies. The generalized estimator shares its statistical properties with the existing KSW estimator and retains the favorable numerical scaling with angular resolution. In this paper, we derive the estimator and present a set of Fisher forecasts. We show how the forecasts scale with various experimental parameters such as minimum and maximum multipole moments, relevant for, e.g., the upcoming ground-based Simons Observatory experiment and proposed LiteBIRD satellite experiment. We comment on possible contaminants due to secondary cosmological and astrophysical sources.

A redshift tomography of the Pantheon type Ia supernovae (SnIa) data focusing on the best fit value of the absolute magnitude $M$ and/or Hubble constant $H_0$ in the context of $\mathrm{\Lambda }\mathrm{CDM}$ indicates a local variation ($z\lesssim 0.2$) at $2\sigma$ level, with respect to the best fit of the full dataset. If this variation is not due to a statistical fluctuation, it can be interpreted as a locally higher value of $H_0$ by about 2%, corresponding to a local matter underdensity $\delta {\rho }_0/{\rho }_0\simeq -0.10\pm 0.04$. It can also be interpreted as a time variation of Newton’s constant which implies an evolving Chandrasekhar mass and thus an evolving absolute luminosity $L$ and absolute magnitude $M$ of low $z$ SnIa. The local void scenario would predict a degree of anisotropy in the best fit value of $H_0$ since it is unlikely that we are located at the center of a local spherical underdensity. Using a hemisphere comparison method, we find an anisotropy level that is consistent with simulated isotropic Pantheon-like datasets. We show however, that the anisotropic sky distribution of the Pantheon SnIa data induces a preferred range of directions even in simulated Pantheon data obtained in the context of isotropic $\mathrm{\Lambda }\mathrm{CDM}$. We thus construct a more isotropically distributed subset of the Pantheon SnIa and show that the preferred range of directions disappears. Using this more isotropically distributed subset we again find no evidence for statistically significant anisotropy using either the hemisphere comparison method or the dipole fit method. In the context of the modified gravity scenario, we allow for an evolving normalized Newton’s constant consistent with general relativity (GR) at early and late times $\mu (z)=G_{\mathrm{eff}}(z,g_a)/G_{\mathrm{N}}=1+g_a{z}^2/(1+z{)}^2-g_a{z}^4/(1+z{)}^4$ and fit for the parameter $g_a$ assuming $L\sim G_{\mathrm{eff}}^b$. For $b=-3/2$ indicated by some previous studies we find $g_a=-0.47\pm 0.36$ which is more than $1.5\sigma$ away from the GR value of $g_a=0$. This weak hint for weaker gravity at low $z$ coming from SnIa is consistent with similar evidence from growth and weak lensing cosmological data.

It is of interest to understand whether or not one can construct a classical field theory description of early cosmology which would be free of initial singularity and stable throughout the whole evolution. One of the known possibilities is genesis within the Horndeski theory, which is thought to be an alternative to or a possible completion of the inflationary scenario. In this model, the strong coupling energy scale tends to zero in the asymptotic past, $t\to -\infty$, making the model potentially intractable. We point out that despite the latter property, the classical setup may be trustworthy since the energy scale of the classical evolution (the inverse of its timescale) also vanishes as $t\to -\infty$. In the framework of a concrete model belonging to the Horndeski class, we show that the strong coupling energy scale of the cubic interactions vastly exceeds the classical energy scale in a certain range of parameters, indicating that the classical description is possible.

The strong discrepancy between local and early-time (inverse distance ladder) estimates of the Hubble constant $H_0$ could be pointing towards new physics beyond the concordance $\mathrm{\Lambda }\mathrm{CDM}$ model. Several attempts to address this tension through new physics rely on extended cosmological models, featuring extra free parameters beyond the six $\mathrm{\Lambda }\mathrm{CDM}$ parameters. However, marginalizing over additional parameters has the effect of broadening the uncertainties on the inferred parameters (including $H_0$), and it is often the case that within these models the $H_0$ tension is addressed due to larger uncertainties rather than a genuine shift in the central value of $H_0$. In this paper I consider an alternative viewpoint: what happens if a physical theory is able to fix the extra parameters to a specific set of nonstandard values? In this case, the degrees of freedom of the model are reduced with respect to the standard case where the extra parameters are free to vary. Focusing on the dark energy equation of state $w$ and the effective number of relativistic species $N_{\mathrm{eff}}$, I find that physical theories able to fix $w\approx -1.3$ or $N_{\mathrm{eff}}\approx 3.95$ would lead to an estimate of $H_0$ from cosmic microwave background, baryon acoustic oscillation, and type Ia supernovae data in perfect agreement with the local distance ladder estimate, without broadening the uncertainty on the former. These two nonstandard models are, from a model-selection perspective, strongly disfavored with respect to the baseline $\mathrm{\Lambda }\mathrm{CDM}$ model. However, models that predict $N_{\mathrm{eff}}\approx 3.45$ would be able to bring the tension down to $1.5\sigma$ while only being weakly disfavored with respect to $\mathrm{\Lambda }\mathrm{CDM}$, whereas models that predict $w\approx -1.1$ would be able to bring the tension down to $2\sigma$ (at the cost of the preference for $\mathrm{\Lambda }\mathrm{CDM}$ being definite). Finally, I estimate dimensionless multipliers relating variations in $H_0$ to variations in $w$ and $N_{\mathrm{eff}}$, which can be used to swiftly repeat the analysis of this paper in light of future more precise local distance ladder estimates of $H_0$, should the tension persist. As a caveat, these results were obtained from the 2015 Planck data release, but these findings would be qualitatively largely unaffected were I to use more recent data.

Based on the Kompaneets approximation, we develop a robust methodology to calculate spectral redistribution via inelastic neutrino-nucleon scattering in the context of core-collapse supernova simulations. The resulting equations conserve lepton number to machine precision and scale linearly, not quadratically, with number of energy groups. The formalism also provides an elegant means to derive the rate of energy transfer to matter which, as it must, automatically goes to zero when the neutrino radiation field is in thermal equilibrium. Furthermore, we derive the next higher order in $ϵ/m{c}^2$ correction to the neutrino Kompaneets equation. Unlike other Kompaneets schema, ours also generalizes to the case of anisotropic angular distributions, while retaining the conservative form that is a hallmark of the classical Kompaneets equation. Our formalism enables immediate incorporation into supernova codes that follow the spectral angular moments of the neutrino radiation fields.

The discovery of gravitational waves from binary black hole mergers has renewed interest in primordial black holes forming a part of the dark matter density of our Universe. Various tests have been proposed to test this hypothesis. One of the cleanest tests is the lensing of fast radio bursts. In this situation, the presence of a compact object near the line of sight produces two images of the radio burst. If the images are sufficiently separated in time, this technique can constrain the presence of primordial black holes. One can also try to detect the lensed image of the minibursts within the main burst. We show that this technique can produce the leading constraints over a wide range in lens masses $\gtrsim 2M_{\odot }$ if the primordial black holes follow a single mass distribution. Even if the primordial black holes have an extended mass distribution, the constraints that can be derived from lensing of fast radio bursts will be the most constraining over wide ranges of the parameter space. We show that this technique can probe exotic compact boson stars and fermion stars made up of beyond the Standard Model particles. This search strategy is competitive and can provide the leading constraints on parts of the particle physics parameter space when compared with gravitational wave observations.

Several sources of noise limit the sensitivity of current gravitational wave detectors. Currently, dominant noise sources include quantum noise and thermal Brownian noise, but future detectors will also be limited by other thermal noise channels. In this paper, we study a thermal noise source which is caused by spatial charge carrier density variations in semiconductor materials. We provide an analytical model for the understanding of charge carrier fluctuations under the presence of screening effects and show that charge carrier noise will not be a limiting noise source for third-generation gravitational wave detectors.

The analytic asymptotic expressions for the Casimir free energy and entropy for two parallel graphene sheets possessing nonzero energy gap $\mathrm{\Delta }$ and chemical potential $\mu$ are derived at arbitrarily low temperature. Graphene is described in the framework of thermal quantum field theory in the Matsubara formulation by means of the polarization tensor in ($2+1$)-dimensional space-time. Different asymptotic expressions are found under the conditions $\mathrm{\Delta }>2\mu$, $\mathrm{\Delta }=2\mu$, and $\mathrm{\Delta }<2\mu$ taking into account both the implicit temperature dependence due to a summation over the Matsubara frequencies and the explicit one caused by a dependence of the polarization tensor on temperature as a parameter. It is shown that for both $\mathrm{\Delta }>2\mu$ and $\mathrm{\Delta }<2\mu$ the Casimir entropy satisfies the third law of thermodynamics (the Nernst heat theorem), whereas for $\mathrm{\Delta }=2\mu$ this fundamental requirement is violated. The physical meaning of the discovered anomaly is considered in the context of thermodynamic properties of the Casimir effect between metallic and dielectric bodies.

We study the behavior of a universal combination of susceptibility and correlation length in the Ising model in two and three dimensions, in presence of both magnetic and thermal perturbations, in the neighborhood of the critical point. In three dimensions we address the problem using a parametric representation of the equation of state. In two dimensions we make use of the exact integrability of the model along the thermal and the magnetic axes. Our results can be used as a sort of “reference frame” to chart the critical region of the model. While our results can be applied in principle to any possible realization of the Ising universality class, we address in particular, as specific examples, three instances of Ising behavior in finite temperature QCD related in various ways to the deconfinement transition. In particular, in the last of these examples, we study the critical ending point in the finite density, finite temperature phase diagram of QCD. In this finite density framework, due to the well-known sign problem, Monte Carlo simulations are not possible and thus a direct comparison of experimental results with quantum field theory & statistical mechanics predictions like the one we discuss in this paper may be important. Moreover in this example it is particularly difficult to disentangle “magnetic-like” from “thermal-like” observables and thus an explicit charting of the neighborhood of the critical point can be particularly useful.

We identify a property of renormalizable SU(N)/U(1) gauge theories, intrinsic conformality (iCF), which underlies the scale invariance of physical observables and leads to a remarkably efficient method to solve the conventional renormalization scale ambiguity at every order in perturbative QCD (pQCD): the ${\mathrm{PMC}}_{\infty }$. This new method reflects the underlying conformal properties displayed by pQCD at next-to-next-to-leading order, eliminates the scheme dependence of pQCD predictions, and is consistent with the general properties of the principle of maximum conformality (PMC). We introduce a new method to identify conformal and $\beta$-terms which can be applied from either a numerical or an analytical calculations. We illustrate the ${\mathrm{PMC}}_{\infty }$ for the thrust and C-parameter distributions in $e^{+}{e}^{-}$ annihilation and then show how to apply this new method to general observables in QCD. We point out how the implementation of the ${\mathrm{PMC}}_{\infty }$ can significantly improve the precision of pQCD predictions; its implementation in a multiloop analysis also simplifies the calculation of higher order corrections in a general renormalizable gauge theory.

The finite volume effect on the QCD phase diagram is investigated via the two-flavor Polyakov-loop-modified Nambu-Jona-Lasinio model in the presence of the chiral chemical potential within the mean-field approximation. Our calculations concentrate on the quark condensate, chiral number density and its derivative, namely, QCD susceptibilities. We find the chiral number density decreases as the system size gets smaller. It is also confirmed that the volume of the strongly interacting matter has an influence on the phase diagram, in particular on the crossover region and the location of a chiral transition line. Therefore, the critical end point (CEP) also shifts with system size. On this basis it follows that study of the finite volume effect as well as the chiral chemical potential dedicated to the chiral phase transition and probing the location of the CEP.

In this work, we present an analysis of the sensitivity to the active-sterile neutrino mixing with the Indian Scintillator Matrix for Reactor Anti-Neutrino (ISMRAN) experimental setup at very short baseline. The 3 $(\text{active})+1$ (sterile) neutrino oscillation model is considered to study the sensitivity of the active-sterile neutrino in the mass splitting and mixing angle plane. In this article, we have considered the measurement of electron antineutrino induced events employing a single detector which can be placed either at a single position or moved between a near and far positions from the given reactor core. Results extracted in the later case are independent of the theoretical prediction of the reactor anti-neutrino spectrum and detector related systematic uncertainties. Our analysis shows that the results obtained from the measurement carried out at combination of the near and far detector positions are improved significantly at higher $\mathrm{\Delta }{m}_{41}^2$ compared to the ones obtained with the measurement at a single detector position only. It is found that the best possible combination of near and far detector positions from a $100{\mathrm{MW}}_{\mathrm{th}}$ power DHRUVA research reactor core are 7 m and 9 m, respectively, for which ISMRAN setup can exclude in the range $1.4{\mathrm{eV}}^2\le \mathrm{\Delta }{m}_{41}^2\le 4.0{\mathrm{eV}}^2$ of reactor antineutrino anomaly region along with the present best-fit point of active-sterile neutrino oscillation parameters. At those combinations of detector positions, the ISMRAN setup can observe the active sterile neutrino oscillation with a 95% confidence level provided that ${\sin }^{2}2{\theta }_{14}\ge 0.09$ at $\mathrm{\Delta }{m}_{41}^2=1{\mathrm{eV}}^2$ for an exposure of 1 ton-yr. The active-sterile neutrino mixing sensitivity can be improved by about 22% at the same exposure by placing the detector at near and far distances of 15 m and 17 m, respectively, from the compact proto-type fast breeder reactor (PFBR) facility which has a higher thermal power of $1250{\mathrm{MW}}_{\mathrm{th}}$.