We consider the possibility that the gauge hierarchy is a byproduct of the metastability of the electroweak vacuum, i.e., that whatever mechanism is responsible for the latter also sets the running Higgs mass to a value smaller than its natural value by many orders of magnitude. We find that the metastability of the electroweak vacuum, together with the requirement that such a nontrivial vacuum exists, requires the Higgs mass to be smaller than the instability scale by around 1 order of magnitude. While this bound is quite weak in the Standard Model (SM), as the instability scale is $\sim {10}^{11}\mathrm{GeV}$, simple and well-motivated extensions of the SM significantly tighten the bound by lowering the instability scale. We first consider the effect of right-handed neutrinos in the $\nu \mathrm{MSM}$ with approximate $B-\tilde{L}$ symmetry, which allows for masses of order TeV for the right-handed neutrinos and $\mathcal{O}(1)$ Yukawa couplings. We find that right-handed neutrinos cannot by themselves fully explain the gauge hierarchy, as the tightest upper bound compatible with current experimental constraints is $\sim {10}^8\mathrm{GeV}$. As we demonstrate on the example of the minimal SU(4)/Sp(4) composite Higgs model, this bound can be lowered significantly through the interplay of the neutrinos and a dimension-six operator. In this scenario, the bound can be brought down considerably, with the smallest value accessible by our perturbative treatment being of order $\simeq 10\mathrm{TeV}$, and consistently several orders of magnitude below its natural value. While this is insufficient to fully solve the gauge hierarchy problem, our results imply that, assuming the SM symmetry-breaking pattern, small running Higgs masses are a universal property of theories giving rise to metastability, suggesting a common origin of the two underlying fine-tunings and providing a strong constraint on any attempt to explain metastability.

We analyze the behavior of quarks coupled to a $SU(N_c)$ gauge theory in $1+1$ dimensions. In the limit of strong coupling, the model reduces to a Wess-Zumino-Novikov-Witten (WZNW) model. At nonzero density, excitations near the Fermi surface form a non-Fermi liquid. With $N_f$ flavors, the finite density of quarks reduce to a free $U(1)$ field, which governs fluctuations in baryon number, together with a WZNW $SU(N_f)$ nonlinear sigma model at level $N_c$, from the pion/kaon modes. We compute the singularity in the charge susceptibility at the Fermi surface and the attendant power-law correlations. We suggest that this is relevant to the quarkyonic regime of cold, dense QCD in ($3+1$) dimensions, in the limit that the Fermi surface is covered by many small patches, and the theory is effectively one dimensional. In this regime the dominant excitations near the Fermi surface are not baryons, but gapless bosonic modes.

The aim of this work is to study some possible local and global $U(1)$ axial condensates in the high-temperature chirally restored phase of QCD, by means of two nonperturbative analytical techniques: (i) by expressing the functional averages in terms of the spectral density of the Euclidean Dirac operator and (ii) by evaluating the functional integrals in the instanton-background approximation. In this way, besides proving that these condensates are indeed different from zero in the high-temperature regime, we shall also derive their asymptotic temperature dependence and compare it with that of the topological susceptibility.

We present analytical results for higher order corrections to the decay spectra of inclusive semileptonic heavy hadron weak decays, using the heavy quark expansion (HQE). We compute analytically the spectrum of the leptonic invariant mass for $B\to X_c\ell \overline{\nu }$ up to and including terms of order $1/m_Q^3$ within the HQE at next-to-leading order in ${\alpha }_s$. The full dependence of the differential rate on the mass of the final-state quark is taken into account. We discuss the implications of our results for the precision determination of the Cabbibo-Kobayashi-Maskawa matrix element $|V_{cb}|$.

Perturbative QCD is applied to investigate the near threshold heavy quarkonium photoproduction at large momentum transfer. We take into account the contributions from the leading three-quark Fock states of the nucleon. The dominant contribution comes from the three-quark Fock state with one unit quark orbital angular momentum (OAM) whereas that from zero-quark OAM is suppressed at the threshold. From our analysis, we also show that there is no direct connection between the near threshold heavy quarkonium photoproduction and the gluonic gravitational form factors without additional approximation. Based on the comparison between our result and recent GlueX data of $J/\psi$ photoproduction, we make predictions for ${\psi }^{\prime }$ and $\mathrm{\Upsilon }$ (1S,2S) states which can be tested in future experiments.

We report the results of the search for dark photons with mass around $1.5\mathrm{eV}/{\mathrm{c}}^2$ using a multilayer dielectric haloscope equipped with an affordable and commercially available photosensor. The multilayer stack, which enables the conversion of dark photons (DP) to Standard Model photons, is made of 23 bilayers of alternating ${\mathrm{SiO}}_2$ and ${\mathrm{Si}}_3{\mathrm{N}}_4$ thin films with linearly increasing thicknesses through the stack (a configuration known as a “chirped stack”). The thicknesses have been chosen according to an optimization algorithm in order to maximize the DP-photon conversion in the energy region where the photosensor sensitivity peaks. This prototype experiment, dubbed “MuDHI” (Multilayer Dielectric Haloscope Investigation) by the authors of this paper, has been designed, developed, and run at the Astroparticle Laboratory of New York University Abu Dhabi, which marks the first time a dark matter experiment has been operated in the Middle East. No significant signal excess is observed, and the method of maximum log likelihood is used to set exclusion limits at 90% confidence level on the kinetic mixing coupling constant between dark photons and ordinary photons.

For classical gravitational systems the lapse function and the shift vector are usually determined by imposing appropriate gauge-fixing conditions and then demanding their preservation with respect to the dynamics generated by a canonical Hamiltonian. Effective descriptions encoding quantum geometric effects motivated by loop quantum gravity for symmetry-reduced models are often captured by polymerization of connection (or related) variables in gauge-fixing conditions as well as constraints. Usually, one chooses the same form of polymerization in both cases. A pertinent question is if the dynamical stability of the effective gauge-fixing conditions under the effective dynamics generated by the polymerized canonical Hamiltonian is provided by the lapse function and the shift vector obtained from the polymerization of their classical counterparts. If this is the case, then we say that gauge fixing and polymerization commute. In this manuscript we investigate these issues and obtain consistency conditions for the commutativity of gauge fixing and polymerization. Our analysis shows that such a commutativity occurs in rather special situations and reveals pitfalls in making seemingly well-motivated choices which turn out to be inconsistent with the effective dynamics. We illustrate these findings via examples of symmetry-reduced models in the loop quantization of the Schwarzschild interior and Lemaître-Tolman-Bondi spacetimes and report the noncommutativity of gauge fixing and polymerization and inherent limitations of some choices made in the literature with a consistent effective dynamics.

We present a general method of computing corrections to the extremality bound and entropy of Kerr-Newman black holes due to an arbitrary perturbation using the Iyer-Wald formalism. In this method, corrections to the extremality bound are given by an integral over an effective stress tensor which, in particular cases of interest, reduces to the usual stress tensor. This clarifies the relation between extremality corrections and energy conditions. In particular, we show that a necessary condition to decrease the mass of an extremal black hole in a canonical ensemble, as required by the weak gravity conjecture, is that the perturbation violates the dominant energy condition. As an application of our method, we compute higher-derivative corrections to charged black holes in anti–de Sitter and Kerr black holes.

We discuss the computation of the quantum effective action of strongly interacting field theories using holographic duality and its use to determine quasiequilibrium parameters of first-order phase transitions relevant for gravitational wave production. A particularly simple holographic model is introduced, containing only the metric and a free massive scalar field. Despite the simplicity, the model contains a rich phase diagram, including first-order phase transitions at nonzero temperature, due to various multitrace deformations. We obtain the leading terms in the effective action from homogeneous black brane solutions in the gravity dual and linearized perturbations around them. We then employ the effective action to construct bubble and domain wall solutions in the field theory side and study their properties. In particular, we show how the scaling of the effective action with the effective number of degrees of freedom of the quantum field theory determines the corresponding scaling of gravitational wave parameters.

Considering a doubly holographic model, we study the evolution of holographic subregion complexity corresponding to deformations of the bath state by a relevant scalar operator, which corresponds to a renormalization group flow from the anti–de Sitter-Schwarzschild to the Kasner universe in the bulk. The subregion complexity shows a discontinuous jump at Page time at a fixed perturbation, where the discontinuity depends solely on the system’s parameters. We show that the amount of discontinuity decreases with the perturbation as well as with the scaling dimension of the relevant scalar operator.

We provide the first holographic evidence for the existence of a nonsupersymmetric conformal manifold arising from exactly marginal but supersymmetry-breaking deformations of a superconformal three-dimensional field theory. In particular, we construct a 2-parameter nonsupersymmetric deformation of a supersymmetric AdS nongeometric background in type IIB string theory. We prove that the nonsupersymmetric backgrounds are perturbatively stable and also do not suffer from various nonperturbative instabilities. Finally, we argue that diffeomorphism symmetry protects our solutions against higher-derivative string corrections.

While the phase structure of the $U(1)\times U(1)$-symmetric Higgs theory is still under debate, a version of this theory with an additional Chern-Simons term was recently shown to undergo a second-order phase transition [Vira Shyta et al., Phys. Rev. Lett. 127, 045701 (2021)]. This theory is dual to a topological field theory of massless fermions featuring two gauge fields. Here we elaborate on several aspects of this duality, focusing on the critical current correlators and on the nature of the critical point as reflected by the bosonization duality. The current correlators associated with the $U(1)\times U(1)$ symmetry and the topological current are shown to coincide up to a universal prefactor, which we find to be the same for both $U(1)$ and $U(1)\times U(1)$ topological Higgs theories. The established duality offers in addition another way to substantiate the claim about the existence of a critical point in the bosonic Chern-Simons $U(1)\times U(1)$ Higgs model: a Schwinger-Dyson analysis of the fermionic dual model shows that no dynamical mass generation occurs. The same cannot be said for the theory without the Chern-Simons term in the action.

The renormalization properties of two local gauge invariant composite operators $(O,R_{\mu }^a)$ corresponding, respectively, to the gauge invariant description of the Higgs particle and of the massive gauge vector boson, are analyzed to all orders in perturbation theory by means of the algebraic renormalization in the $SU(2)$ Higgs model, with a single scalar in the fundamental representation, when quantized in the Landau gauge in Euclidean space-time. The present analysis generalizes earlier results presented in the case of the $U(1)$ Higgs model. A powerful global Ward identity, related to an exact custodial symmetry, is derived for the first time, with deep consequences at the quantum level. In particular, the gauge invariant vector operators $R_{\mu }^a$ turn out to be the conserved Noether currents of the above-mentioned custodial symmetry. As such, these composite operators do not renormalize, as expressed by the fact that the renormalization $Z$-factors of the corresponding external sources, needed to define the operators $R_{\mu }^a$ at the quantum level, do not receive any quantum corrections. Using this Ward identity, one can also prove that the longitudinal component of the two-point correlation function $⟨R_{\mu }^a(p)R_{\nu }^b(-p)⟩$ exhibits only a tree level nonvanishing contribution which, moreover, is momentum independent, thus it is not associated to any physical propagating mode. Finally, we point out that the renowned nonrenormalization theorem for the ghost-antighost-vector boson vertex in Landau gauge remains true to all orders, also in the presence of the Higgs field.

We complete the set of spin-projector operators for fields up to rank 3 by providing all operators connecting sectors with the same spin and parity. In this way, we can broaden the search for unitary and nontachyonic particle propagation in quadratic Lagrangians with interfield mixing. We use the properties of projector algebra to reanalyze known theories and shed light on new, healthy ones. We do so with full control over the gauge constraints by determining the form of the saturated propagator in an appropriate frame of reference.

We study late-time behaviors of massive scalar fields in general static and spherically symmetric extremal black hole spacetimes in arbitrary dimensions. We show the existence of conserved quantities on the extremal black hole horizons for specific mass squared and multipole modes of the scalar fields. Those quantities on the horizon are called the Aretakis constants and are constructed from the higher-order derivatives of the fields. Focusing on the region near the horizon at late times, where it is well approximated by the near-horizon geometry, we show that the leading behaviors of the fields are described by power-law tails. The late-time power-law tails lead to the Atetakis instability: blowups of the transverse derivatives of the fields on the horizon. We further argue that the Aretakis constants and instability correspond to, respectively, constants and blowups of components of covariant derivatives of the fields at the late time in the parallelly propagated null geodesic frame along the horizon. We finally discuss the relation between the Aretakis constants and ladder operators constructed from the approximate spacetime conformal symmetry near the extremal black hole horizons.

The propagation of gravitational waves (GWs) at cosmological distances offers a new way to test the gravitational interaction at the largest scales. Many modified theories of gravity, usually introduced to explain the observed acceleration of the Universe, can be probed in an alternative and complementary manner with respect to standard electromagnetic (EM) observations. In this paper we consider a homogeneous and isotropic cosmology with extra spatial dimensions at large scales, which represents a simple phenomenological prototype for extradimensional modified gravity cosmological models. By assuming that gravity propagates through the higher-dimensional spacetime, while photons are constrained to the usual four dimensions of general relativity, we derive from first principles the relation between the luminosity distance measured by GW detectors and the one inferred by EM observations. We then use this relation to constrain the number of cosmological extra dimensions with the binary neutron star event GW170817 and the binary black hole merger GW190521. We further provide forecasts for the Laser Interferometer Space Antenna (LISA) by simulating multimessenger observations of massive black hole binary (MBHB) mergers. This paper extends and updates previous analyses which crucially neglected an additional redshift dependency in the GW-EM luminosity distance relation which affects results obtained from multimessenger GW events at high redshift, in particular constraints expected from LISA MBHBs.

In this paper we pursue the study of linear perturbations around a Schwarzschild black hole in a generalized Einstein-Cartan theory of gravity, called torsion bigravity. This theory contains both massless and massive spin-2 excitations. Here we consider non spherically symmetric perturbations with generic multipolarity $L\ge 1$. We extend the conclusion of linear stability, previously obtained for $L=0$ [Phys. Rev. D 104, 024032], to the generic $L\ge 1$ case. We prove that the mass $\kappa$ of the massive spin-2 excitation must be large enough, namely $\kappa r_h>\sqrt{1+\eta }$, to avoid the presence of singularities in the perturbation equations. The perturbation equations are shown to have a triangular structure, where massive spin-2 excitations satisfy decoupled equations, while the Einstein-like massless spin-2 ones satisfy inhomogeneous equations sourced by the massive spin-2 sector. We study quasibound states, and exhibit some explicit complex quasibound frequencies. We briefly discuss the issue of superradiance instabilities.

We investigate the properties of high-density compact objects in a vector-type theory, inspired by Einstein’s 1919 theory of elementary particles, in which Einstein assumed that elementary particles are held together by gravitational as well as electromagnetic-type forces. From a modern perspective, Einstein’s theory can be interpreted as a vector-type model, with the gravitational action constructed as a linear combination of the Ricci scalar, of the trace of the matter energy-momentum tensor, and of a massive self-interacting vector-type field. To obtain the properties of stellar models we consider the field equations for a static, spherically symmetric system, and we investigate numerically their solutions for different equations of state of quark and neutron matter, by assuming that the self-interaction potential of the vector field either vanishes or is quadratic in the vector field potential. We consider quark stars described by the MIT bag model equation of state, and in the color-flavor-locked phase, as well as compact stars consisting of a Bose-Einstein condensate of neutron matter, with neutrons forming Cooper pairs. Constant density stars, representing a generalization of the interior Schwarzschild solution of general relativity, are also analyzed. As an example of stars described by equations of state obtained by using effective nuclear interactions of the Skyrme type we consider the Douchin-Haensel (SLy) equation of state. The numerical solutions are explicitly obtained in both standard general relativity and the Einstein dark energy model, and an in-depth comparison between the astrophysical predictions of these two theories is performed. As a general conclusion of our study we find that for all the considered equations of state a much larger variety of stellar structures can be obtained in the Einstein dark energy model, including classes of stars that are more massive than their general relativistic counterparts. As a concrete application of our results we suggest that compact objects with masses of the order of $2.5M_{\odot }$, associated, for example, with the GW190814 gravitational-wave event, could be in fact quark or neutron stars, described by the Einstein dark energy model.

Scalar-tensor theories with first-derivative self-interactions, known as $k$-essence, may provide interesting phenomenology on cosmological scales. On smaller scales, however, initial value evolutions (which are crucial for predicting the behavior of astrophysical systems, such as binaries of compact objects) may run into instabilities related to the Cauchy problem becoming potentially ill-posed. Moreover, on local scales, the dynamics may enter in the nonlinear regime, which may lie beyond the range of validity of the infrared theory. Completions of $k$-essence in the ultraviolet, when they are known to exist, mitigate these problems, as they both render Cauchy evolutions well-posed at all times and allow for checking the relation between nonlinearities and the low-energy theory’s range of validity. Here, we explore these issues explicitly by considering an ultraviolet completion to $k$-essence and performing vacuum $1+1$ dynamical evolutions within it. The results are compared to those obtained with the low-energy theory and with the low-energy theory suitably deformed with a phenomenological “fixing the equations” approach. We confirm that the ultraviolet completion does not incur in any breakdown of the Cauchy problem’s well-posedness, and we find that evolutions agree with the results of the low-energy theory when the system is within the regime of validity of the latter. However, we also find that the nonlinear behavior of $k$-essence lies (for the most part) outside this regime.

We analyze the evolution of a homogenous and pressureless ball of dust (or “star”) in ghost-free massive gravity on de Sitter spacetime. We find that gravitational collapse does not take place for all parameters of the massive gravity theory. For parameters where it does occur, we find the expression for the location of the apparent horizon where it crosses the surface of the star, indicating the location of the apparent horizon of the vacuum solution at that moment. We determine the Ricci curvature at the boundary of the star and extract the finite correction to the curvature of the apparent horizon due to the graviton mass. Finally, we argue that our collapsing solutions cannot be matched to a static, spherically symmetric vacuum solution at the star’s surface, providing further evidence that physical black hole solutions in massive gravity are likely time-dependent.