We investigate both the theoretical and computational aspects of using wavelet bases to perform an exact decomposition of a local field theory by spatial resolution. The decomposition admits natural volume and resolution truncations. We demonstrate that flow equation methods can be used to eliminate short-distance degrees of freedom in truncated theories. The method is tested on a free scalar field in one dimension, where the spatial derivatives couple the degrees of freedom on different scales, although the method is applicable to more complex field theories. The flow equation method is shown to decouple both distance and energy scales in this example. The response to changing the volume and resolution cutoffs and the mass is discussed.

Differential and double-differential cross sections for the production of top quark pairs in proton-proton collisions at 13 TeV are measured as a function of jet multiplicity and of kinematic variables of the top quarks and the top quark-antiquark system. This analysis is based on data collected by the CMS experiment at the LHC corresponding to an integrated luminosity of $2.3{\mathrm{fb}}^{-1}$. The measurements are performed in the $\mathrm{lepton}+\text{jets}$ decay channels with a single muon or electron in the final state. The differential cross sections are presented at particle level, within a phase space close to the experimental acceptance, and at parton level in the full phase space. The results are compared to several standard model predictions.

The ultraviolet completion of a large $N$ QCD model requires introducing new degrees of freedom at certain scale so that the UV behavior may become asymptotically conformal with no Landau poles and no UV divergences of Wilson loops. These UV degrees of freedom are represented by certain antibranes arranged on the blown-up sphere of a warped resolved conifold in a way that they are separated from the other set of branes that control the IR behavior of the theory. This separation of the branes and the antibranes creates instability in the theory. Further complications arise from the curvature of the ambient space. We show that, despite these analytical hurdles, stability may still be achieved by switching on appropriate world-volume fluxes on the branes. The UV degrees of freedom, on the other hand, modify the RG flow in the model. We discuss this in details by evaluating the flow from IR confining to UV conformal. Finally we lay down a calculational scheme to study bulk viscosity which, in turn, would signal the inherent nonconformality in this model.

This paper proves that if eternal neutral black holes satisfy some general conditions and matter fields only appear in the outside of the Killing horizon, the strong energy condition is a sufficient condition to insure that the vacuum Schwarzschild black hole has the fastest action growth of the same total energy. This result is consistent with the bound of computational complexity growth rate and gives strong evidence for the holographic complexity-action conjecture.

In 2009, Bañados, Silk, and West (BSW) pointed out the possibility of having an unbounded limit of center-of-mass collision energy for test particles in the field of an extremal Kerr black hole, if one of them has fine-tuned parameters and the collision point is approaching the horizon. The possibility of this “BSW effect” attracted much attention: it was generalized to arbitrary (“dirty”) rotating black holes and an analogy was found for collisions of charged particles in the field of nonrotating charged black holes. Our work considers the unification of these two mechanisms, which have so far been studied only separately. Exploring the enlarged parameter space, we find kinematic restrictions that may prevent the fine-tuned particles from reaching the limiting collision point. These restrictions are first presented in a general form, which can be used with an arbitrary black-hole model, and then visualized for the Kerr-Newman solution by plotting the “admissible region” in the parameter space of critical particles, reproducing some known results and obtaining a number of new ones. For example, we find that (marginally) bounded critical particles with enormous values of angular momentum can, curiously enough, approach the degenerate horizon, if the charge of the black hole is very small. Such “mega-BSW” behavior is excluded in the case of a vacuum black hole, or a black hole with large charge. It may be interesting in connection with the small “Wald charge” induced on rotating black holes in external magnetic fields.

Spontaneous collapse models are phenomological theories formulated to address major difficulties in macroscopic quantum mechanics. We place significant bounds on the parameters of the leading collapse models, the continuous spontaneous localization (CSL) model, and the Diosi-Penrose (DP) model, by using LISA Pathfinder’s measurement, at a record accuracy, of the relative acceleration noise between two free-falling macroscopic test masses. In particular, we bound the CSL collapse rate to be at most $(2.96\pm 0.12)\times {10}^{-8}{\mathrm{s}}^{-1}$. This competitive bound explores a new frequency regime, 0.7 to 20 mHz, and overlaps with the lower bound ${10}^{-8\pm 2}{\mathrm{s}}^{-1}$ proposed by Adler in order for the CSL collapse noise to be substantial enough to explain the phenomenology of quantum measurement. Moreover, we bound the regularization cutoff scale used in the DP model to prevent divergences to be at least $40.1\pm 0.5\mathrm{fm}$, which is larger than the size of any nucleus. Thus, we rule out the DP model if the cutoff is the size of a fundamental particle.

We introduce a double power series method for finding approximate analytical solutions for systems of differential equations commonly found in cosmological perturbation theory. The method was set out, in a noncosmological context, by Feshchenko, Shkil’ and Nikolenko (FSN) in 1966, and is applicable to cases where perturbations are on subhorizon scales. The FSN method is essentially an extension of the well known Wentzel–Kramers–Brillouin (WKB) method for finding approximate analytical solutions for ordinary differential equations. The FSN method we use is applicable well beyond perturbation theory to solve systems of ordinary differential equations, linear in the derivatives, that also depend on a small parameter, which here we take to be related to the inverse wave–number. We use the FSN method to find new approximate oscillating solutions in linear order cosmological perturbation theory for a flat radiation–matter universe. Together with this model’s well-known growing and decaying Mészáros solutions, these oscillating modes provide a complete set of subhorizon approximations for the metric potential, radiation and matter perturbations. Comparison with numerical solutions of the perturbation equations shows that our approximations can be made accurate to within a typical error of 1%, or better. We also set out a heuristic method for error estimation. A Mathematica notebook which implements the double power series method is made available online.

We perform an exhaustive scan of the allowed resonant production regime for sterile neutrino dark matter in order to improve constraints for dark matter structures which arise from the nonthermal sterile neutrino energy spectra. Small-scale structure constraints are particularly sensitive to large lepton asymmetries/small mixing angles which result in relatively warmer sterile neutrino momentum distributions. We revisit Milky Way galaxy subhalo count constraints and combine them with recent searches for x-ray emission from sterile neutrino decays. Together, they rule out models outside the mass range $7.0\mathrm{keV}\le m_{{\nu }_s}\le 36\mathrm{keV}$ and lepton asymmetries smaller than $15\times {10}^{-6}$ per unit entropy density at 95% confidence interval or greater. We also find that, while a portion of the parameter space remains unconstrained, the combination of subhalo counts and x-ray data indicates the candidate 3.55 keV x-ray line signal potentially originating from a 7.1 keV sterile neutrino decay to be disfavored at 93% confidence interval.

In this work, we investigate the prospects of future $e^{+}{e}^{-}$ colliders in testing a Higgs triplet model with a scalar triplet and a scalar singlet under $SU(2)$. The parameters of the model are fixed so that the lightest $CP$-even state corresponds to the Higgs particle observed at the LHC at around 125 GeV. This study investigates if the second heaviest $CP$-even, the heaviest $CP$-odd and the singly charged states can be observed at existing and future colliders by computing their accessible production and decay channels. In general, the LHC is not well equipped to produce a Higgs boson which is not mainly doubletlike, so we turn our focus to lepton colliders. We find distinctive features of this model in cases where the second heaviest $CP$-even Higgs is tripletlike, singletlike or a mixture. These features could distinguish the model from other scenarios at future $e^{+}{e}^{-}$ colliders.

The quasiprobabilistic Wigner distributions are the quantum mechanical analog of the classical phase-space distributions. We investigate quark Wigner distributions for a quark state dressed with a gluon, which can be thought of as a simple composite and relativistic spin-$1/2$ state with a gluonic degree of freedom. We calculate various polarization configurations, namely, unpolarized, longitudinally polarized, and transversely polarized quark, and the target state using light-front wave functions in this model. At the leading twist, one can define 16 quark Wigner distributions; however, we obtain only 8 independent nonzero Wigner distributions in our model. We compare our results with other model calculations for the proton.

We report the first measurement of the longitudinal double-spin asymmetry $A_{LL}$ for midrapidity dijet production in polarized $pp$ collisions at a center-of-mass energy of $\sqrt{s}=200\mathrm{GeV}$. The dijet cross section was measured and is shown to be consistent with next-to-leading order (NLO) perturbative QCD predictions. $A_{LL}$ results are presented for two distinct topologies, defined by the jet pseudorapidities, and are compared to predictions from several recent NLO global analyses. The measured asymmetries, the first such correlation measurements, support those analyses that find positive gluon polarization at the level of roughly 0.2 over the region of Bjorken-$x>0.05$.

We start from a static, spherically symmetric space-time in the presence of an electrostatic field and construct the mini-superspace Lagrangian that reproduces the well known Reissner-Nordström solution. We identify the classical integrals of motion that are to be mapped to quantum observables and which are associated with the mass and charge. Their eigenvalue equations are used as supplementary conditions to the Wheeler-DeWitt equation and a link is provided between the existence of an horizon and to whether the spectrum of the observables is fully discrete or not. For each case we provide an orthonormal basis of states as emerges through the process of canonical quantization.

In this paper we will revisit the large $N$ solution of the $\mathbb{C}{P}^N$ sigma model on a finite interval of length $L$. We will find a family of boundary conditions for which the large $N$ saddle point can be found analytically. For a certain choice of the boundary conditions the theory has only one phase for all values of $L$. Also, we will provide an example when there are two phases: for large $L$ there is a standard phase with an unbroken $U(1)$ gauge symmetry and for small $L$ there is a Higgs phase with a broken gauge symmetry.

An invertible field transformation is such that the old field variables correspond one-to-one to the new variables. As such, one may think that two systems that are related by an invertible transformation are physically equivalent. However, if the transformation depends on field derivatives, the equivalence between the two systems is nontrivial due to the appearance of higher derivative terms in the equations of motion. To address this problem, we prove the following theorem on the relation between an invertible transformation and Euler-Lagrange equations: If the field transformation is invertible, then any solution of the original set of Euler-Lagrange equations is mapped to a solution of the new set of Euler-Lagrange equations, and vice versa. We also present applications of the theorem to scalar-tensor theories.

We investigate black holes formed by static perfect fluid with $p=-\rho /3$. These represent the black holes in $S_3$ and $H_3$ spatial geometries. There are three classes of black-hole solutions, two $S_3$ types and one $H_3$ type. The interesting solution is the $S_3$ type one, which possesses two singularities. One is at the north pole behind the horizon, and the other is naked at the south pole. The observers, however, are free from falling to the naked singularity. There are also nonstatic cosmological solutions in $S_3$ and $H_3$ and a singular static solution in $H_3$.

The Poincaré gauge gravity (PGG) with the underlying vector fields of tetrads and spin-connections is perhaps the best theory candidate for gravitation to be unified with the other three elementary forces of nature. There is a clear analogy between the local frame in PGG and the local internal symmetry space in the Standard Model. As a result, the spin-connection fields, gauging the local frame Lorentz symmetry group $SO(1,3{)}_{\mathrm{LF}}$, appear in PGG much as photons and gluons appear in SM. We propose that such an analogy may follow from their common emergent nature allowing us to derive PGG in the same way as conventional gauge theories. In essence, we start with an arbitrary theory of some vector and fermion fields which possesses only global spacetime symmetries, such as Lorentz and translational invariance, in flat Minkowski space. The two vector field multiplets involved are proposed to belong, respectively, to the adjoint ($A_{\mu }^{ij}$) and vector ($e_{\mu }^i$) representations of the starting global Lorentz symmetry. We show that if these prototype vector fields are covariantly constrained, $A_{\mu }^{ij}{A}_{ij}^{\mu }=\pm M_A^2$ and $e_{\mu }^i{e}_i^{\mu }=\pm M_e^2$, thus causing a spontaneous violation of the accompanying global symmetries ($M_{A,e}$ are their proposed violation scales), then the only possible theory compatible with these length-preserving constraints is turned out to be the gauge invariant PGG, while the corresponding massless (pseudo)Goldstone modes are naturally collected in the emergent gauge fields of tetrads and spin-connections. In a minimal theory case being linear in a curvature we unavoidably come to the Einstein-Cartan theory. The extended theories with propagating spin-connection and tetrad modes are also considered and their possible unification with the Standard Model is briefly discussed.

We investigate the viability of submillimeter-wavelength oscillating deviations from the Newtonian potential at both the theoretical and the experimental/observational level. At the theoretical level, such deviations are generic predictions in a wide range of extensions of general relativity (GR) including $f(R)$ theories, massive Brans-Dicke (BD) scalar-tensor theories, compactified extra dimension models, and nonlocal extensions of GR. However, the range of parameters associated with such oscillating deviations is usually connected with instabilities present at the perturbative level. An important exception emerges in nonlocal gravity theories where oscillating deviations from Newtonian potential occur naturally on submillimeter scales without any instabilities. As an example of a model with unstable Newtonian oscillations, we review an $f(R)$ expansion around general relativity of the form $f(R)=R+\frac{1}{6m^2}{R}^2$ with $m^2<0$, pointing out possible stabilization mechanisms. As an example of a model with stable Newtonian oscillations, we discuss nonlocal gravity theories. If such oscillations are realized in nature on submillimeter scales, a signature is expected in torsion balance experiments testing the validity of Newton’s law. We search for such a signature in the torsion balance data of the Washington experiment [D. J. Kapner, T. S. Cook, E. G. Adelberger, J. H. Gundlach, B. R. Heckel, C. D. Hoyle, and H. E. Swanson, Phys. Rev. Lett. 98, 021101 (2007).] (combined torque residuals of experiments I, II, and III), testing Newton’s law at submillimeter scales. We show that an oscillating residual ansatz with spatial wavelength $\lambda \simeq 0.1\mathrm{mm}$ provides a better fit to the data compared to the residual Newtonian constant ansatz by $\mathrm{\Delta }{\chi }^2=-15$. Similar improved fits however, also occur in about 10% of the Monte Carlo realization of Newtonian data on similar or larger scales. Thus, the significance level of this improved fit is at a level of not more than $2\sigma$. The energy scale corresponding to this best-fit wavelength is identical to the dark energy length scale, ${\lambda }_{de}\equiv \sqrt{4}\hslash c/{\rho }_{de}\approx 0.1\mathrm{mm}$.

We propose that stellar-mass binary black holes like GW150914 will become a tool to explore the local Universe within $\sim 100\mathrm{Mpc}$ in the era of the Laser Interferometer Space Antenna (LISA). High calibration accuracy and annual motion of LISA could enable us to localize up to $\approx 60$ binaries more accurately than the error volume of $\approx 100{\mathrm{Mpc}}^3$ without electromagnetic counterparts under moderately optimistic assumptions. This accuracy will give us a fair chance to determine the host object solely by gravitational waves. By combining the luminosity distance extracted from gravitational waves with the cosmological redshift determined from the host, the local value of the Hubble parameter will be determined up to a few % without relying on the empirically constructed distance ladder. Gravitational-wave cosmography would pave the way for resolution of the disputed Hubble tension, where the local and global measurements disagree in the value of the Hubble parameter at $3.4\sigma$ level, which amounts to $\approx 9\%$.