We develop an innovative technique for studying inhomogeneous phases with a spontaneous broken symmetry. The method relies on the knowledge of the exact form of the free energy in the homogeneous phase and on a specific gradient expansion of the order parameter. We apply this method to quark matter at vanishing temperature and large chemical potential, which is expected to be relevant for astrophysical considerations. The method is remarkably reliable and fast as compared to performing the full numerical diagonalization of the quark Hamiltonian in momentum space and is designed to improve the standard Ginzburg-Landau expansion close to the phase transition points. For definiteness, we focus on inhomogeneous chiral symmetry breaking, accurately reproducing known results for one-dimensional and two-dimensional modulations and examining novel crystalline structures, as well. Consistently with previous results, we find that the energetically favored modulation is the so-called one-dimensional real-kink crystal. We propose a qualitative description of the pairing mechanism to motivate this result.

Ultralight axions have sparked attention because their tiny mass $m\sim {10}^{-22}\mathrm{eV}$, which leads to a kiloparsec-scale de Broglie wavelength comparable to the size of a dwarf galaxy, could alleviate the so-called small-scale crisis of massive cold dark matter (CDM) candidates. However, recent analyses of the Lyman-$\alpha$ forest power spectrum set a tight lower bound on their mass of $m\gtrsim {10}^{-21}\mathrm{eV}$ which makes them much less relevant from an astrophysical point of view. An important caveat to these numerical studies is that they do not take into account self-interactions among ultralight axions. Furthermore, for axions which acquired a mass through nonperturbative effects, this self-interaction is attractive and, therefore, could counteract the quantum “pressure” induced by the strong delocalization of the particles. In this work, we show that even a tiny attractive interaction among ultralight axions can have a significant impact on the stability of cosmic structures at low redshift. After a brief review of known results about solitons in the absence of gravity, we discuss the stability of filamentary and pancakelike solutions when quantum pressure, attractive interactions and gravity are present. The analysis based on 1 degree of freedom, namely the breathing mode, reveals that pancakes are stable, while filaments are unstable if the mass per unit length is larger than a critical value. However, we show that pancakes are unstable against transverse perturbations. We expect this to be true for halos and filaments as well. Instabilities driven by the breathing mode will not be seen in the low column density Lyman-$\alpha$ forest unless the axion decay constant is extremely small, $f\lesssim {10}^{13}\mathrm{GeV}$. Notwithstanding, axion solitonic cores could leave a detectable signature in the Lyman-$\alpha$ forest if the normalization of the unknown axion core—filament mass relation is $\sim 100$ larger than it is for spherical halos. We hope our work motivates future numerical studies of the impact of axion self-interactions on cosmic structure formation.

Light new particles can be emitted in decays of excited nuclear states. Experiments analyzing such transitions and incorporating high-resolution detectors can be sensitive to new MeV-scale physics at a level competitive with upcoming collider and other fixed target experiments, provided sufficient luminosity. We demonstrate this in the case of the ${}^8\mathrm{Be}$ system, showing that searches targeting the reported anomaly in ${}^8\mathrm{Be}$ nuclear transitions can also be sensitive to currently unexplored regions of the canonical dark photon parameter space with $1\mathrm{MeV}\lesssim m_{A^{\prime }}\lesssim 18\mathrm{MeV}$ and ${ϵ}^2\gtrsim {10}^{-7}$. These experiments could be performed on a short time scale, at low cost, and directly probe both the hadronic and leptonic couplings of light hidden particles.

In recent work [J. Feldbrugge et al. Phys. Rev. D 95, 103508 (2017). and J. Feldbrugge et al. Phys. Rev. Lett. 119, 171301 (2017).], we introduced Picard-Lefschetz theory as a tool for defining the Lorentzian path integral for quantum gravity in a systematic semiclassical expansion. This formulation avoids several pitfalls occurring in the Euclidean approach. Our method provides, in particular, a more precise formulation of the Hartle-Hawking no boundary proposal, as a sum over real Lorentzian four-geometries interpolating between an initial three-geometry of zero size, i.e., a point, and a final three-geometry. With this definition, we calculated the no boundary amplitude for a closed universe with a cosmological constant, assuming cosmological symmetry for the background and including linear perturbations. We found the opposite semiclassical exponent to that obtained by Hartle and Hawking for the creation of a de Sitter spacetime “from nothing.” Furthermore, we found the linearized perturbations to be governed by an inverse Gaussian distribution, meaning they are unsuppressed and out of control. Recently, Diaz Dorronsoro et al. [Phys. Rev. D 96, 043505 (2017)] followed our methods but attempted to rescue the no boundary proposal by integrating the lapse over a different, intrinsically complex contour. Here, we show that, in addition to the desired Hartle-Hawking saddle point contribution, their contour yields extra, nonperturbative corrections which again render the perturbations unsuppressed. We prove there is no choice of complex contour for the lapse which avoids this problem. We extend our discussion to include backreaction in the leading semiclassical approximation, fully nonlinearly for the lowest tensor harmonic and to second order for all higher modes. Implications for quantum de Sitter spacetime and for cosmic inflation are briefly discussed.

We suggest an approach to perturbative calculations of large-scale clustering in the Universe that includes from the start the stream crossing (multiple velocities for mass elements at a single position) that is lost in traditional calculations. Starting from a functional integral over displacement, the perturbative series expansion is in deviations from (truncated) Zel’dovich evolution, with terms that can be computed exactly even for stream-crossed displacements. We evaluate the one-loop formulas for displacement and density power spectra numerically in 1D, finding dramatic improvement in agreement with N-body simulations compared to the Zel’dovich power spectrum (which is exact in 1D up to stream crossing). Beyond 1D, our approach could represent an improvement over previous expansions even aside from the inclusion of stream crossing, but we have not investigated this numerically. In the process we show how to achieve effective-theory-like regulation of small-scale fluctuations without free parameters.

We study the effects of long-lived massive particles, which decayed during the big-bang nucleosynthesis (BBN) epoch, on the primordial abundance of light elements. Compared to previous studies, (i) the reaction rates of standard BBN reactions are updated, (ii) the most recent observational data on the light element abundance and cosmological parameters are used, (iii) the effects of the interconversion of energetic nucleons at the time of inelastic scattering with background nuclei are considered, and (iv) the effects of the hadronic shower induced by energetic high-energy antinucleons are included. We compare the theoretical predictions on the primordial abundance of light elements with the latest observational constraints, and we derive upper bounds on the relic abundance of the decaying particle as a function of its lifetime. We also apply our analysis to an unstable gravitino, the superpartner of a graviton in supersymmetric theories, and obtain constraints on the reheating temperature after inflation.

We argue how to identify the supersymmetric quiver quantum mechanics description of BPS states, which arise in string theory in brane systems representing knots. This leads to a surprising relation between knots and quivers: to a given knot, we associate a quiver, so that various types of knot invariants are expressed in terms of characteristics of a moduli space of representations of the corresponding quiver. This statement can be regarded as a novel type of categorification of knot invariants, and among its various consequences we find that Labastida-Mariño-Ooguri-Vafa (LMOV) invariants of a knot can be expressed in terms of motivic Donaldson-Thomas invariants of the corresponding quiver; this proves integrality of LMOV invariants (once the corresponding quiver is identified), conjectured originally based on string theory and M-theory arguments.

Calculating the abundance of thermally produced dark matter particles has become a standard procedure, with sophisticated methods guaranteeing a precision that matches the percent-level accuracy in the observational determination of the dark matter density. Here, we point out that one of the main assumptions in the commonly adopted formalism, namely local thermal equilibrium during the freeze-out of annihilating dark matter particles, does not have to be satisfied in general. We present two methods for how to deal with such situations, in which the kinetic decoupling of dark matter happens so early that it interferes with the chemical decoupling process: (i) an approximate treatment in terms of a coupled system of differential equations for the leading momentum moments of the dark matter distribution, and (ii) a full numerical solution of the Boltzmann equation in phase space. For illustration, we apply these methods to the case of scalar singlet dark matter. We explicitly show that even in this simple model the prediction for the dark matter abundance can be affected by up to 1 order of magnitude compared to the traditional treatment.

At second order in perturbation theory, the unstable $r$-mode of a rotating star includes growing differential rotation whose form and growth rate are determined by gravitational-radiation reaction. With no magnetic field, the angular velocity of a fluid element grows exponentially until the mode reaches its nonlinear saturation amplitude and remains nonzero after saturation. With a background magnetic field, the differential rotation winds up and amplifies the field, and previous work where large mode amplitudes were considered [L. Rezzolla, F. K. Lamb, and S. L. Shapiro, Astrophys. J. 531, L139 (2000).], suggests that the amplification may damp out the instability. A background magnetic field, however, turns the saturated time-independent perturbations corresponding to adding differential rotation into perturbations whose characteristic frequencies are of order the Alfvén frequency. As found in previous studies, we argue that magnetic-field growth is sharply limited by the saturation amplitude of an unstable mode. In contrast to previous work, however, we show that if the amplitude is small, i.e., $\lesssim {10}^{-4}$, then the limit on the magnetic-field growth is stringent enough to prevent the loss of energy to the magnetic field from damping or significantly altering an unstable $r$-mode in nascent neutron stars with normal interiors and in cold stars whose interiors are type II superconductors. We show this result first for a toy model, and we then obtain an analogous upper limit on magnetic-field growth using a more realistic model of a rotating neutron star. Our analysis depends on the assumption that there are no marginally unstable perturbations, and this may not hold when differential rotation leads to a magnetorotational instability.

We report on the measurement of the all-particle cosmic ray energy spectrum with the High Altitude Water Cherenkov (HAWC) Observatory in the energy range 10 to 500 TeV. HAWC is a ground-based air-shower array deployed on the slopes of Volcan Sierra Negra in the state of Puebla, Mexico, and is sensitive to gamma rays and cosmic rays at TeV energies. The data used in this work were taken over 234 days between June 2016 and February 2017. The primary cosmic-ray energy is determined with a maximum likelihood approach using the particle density as a function of distance to the shower core. Introducing quality cuts to isolate events with shower cores landing on the array, the reconstructed energy distribution is unfolded iteratively. The measured all-particle spectrum is consistent with a broken power law with an index of $-2.49\pm 0.01$ prior to a break at $(45.7\pm 0.1)\mathrm{TeV}$, followed by an index of $-2.71\pm 0.01$. The spectrum also represents a single measurement that spans the energy range between direct detection and ground-based experiments. As a verification of the detector response, the energy scale and angular resolution are validated by observation of the cosmic ray Moon shadow’s dependence on energy.

Single crystals have high atomic electric fields as much as $10^{11}\mathrm{V}/\mathrm{m}$, which correspond to magnetic fields of $\sim {10}^3\mathrm{T}$. These fields can be utilized to convert x-rays into axionlike particles (ALPs) coherently similar to x-ray diffraction. In this paper, we perform the first theoretical calculation of the Laue-case conversion in crystals based on the Darwin dynamical theory of x-ray diffraction. The calculation shows that the Laue-case conversion has longer interaction length than the Bragg case, and that ALPs in the keV range can be resonantly converted by tuning an incident angle of x-rays. ALPs with mass up to $\mathcal{O}(10\mathrm{keV})$ can be searched by light-shining-through-a-wall (LSW) experiments at synchrotron x-ray facilities.

We present a new technique for extracting decay and transition rates into final states with any number of hadrons. The approach is only sensitive to total rates, in which all out-states with a given set of QCD quantum numbers are included. For processes involving photons or leptons, differential rates with respect to the nonhadronic kinematics may also be extracted. Our method involves constructing a finite-volume Euclidean four-point function, with a corresponding spectral function that measures the decay and transition rates in the infinite-volume limit. This requires solving the inverse problem of extracting the spectral function from the correlator and also necessitates a smoothing procedure so that a well-defined infinite-volume limit exists. Both of these steps are accomplished by the Backus-Gilbert method, and, as we show with a numerical example, reasonable precision can be expected in cases with multiple open decay channels. Potential applications include nucleon structure functions and the onset of the deep-inelastic scattering regime, as well as semileptonic $D$ and $B$ decay rates.

Topological defects (kinks) in a relativistic ${\varphi }^4$ scalar field theory in $D=(1+1)$ are studied using the matrix product state tensor network. The one kink state is approximated as a matrix product state and the kink mass is calculated. The approach used is quite general and can be applied to a variety of theories and tensor networks. Additionally, the contribution of kink-antikink excitations to the ground state is examined and a general method to estimate the scalar mass from equal time ground state observables is provided. The scalar and kink mass are compared at strong coupling and behave as expected from universality arguments. This suggests that the matrix product state can adequately capture the physics of defect-antidefect excitations and thus provides a promising technique to study challenging nonequilibrium physics such as the Kibble-Zurek mechanism of defect formation.

Tests on $B-L$ symmetry breaking models are important probes to search for new physics. One proposed model with $\mathrm{\Delta }(B-L)=2$ involves the oscillations of a neutron to an antineutron. In this paper, a new limit on this process is derived for the data acquired from all three operational phases of the Sudbury Neutrino Observatory experiment. The search concentrated on oscillations occurring within the deuteron, and 23 events were observed against a background expectation of 30.5 events. These translated to a lower limit on the nuclear lifetime of $1.48\times {10}^{31}\mathrm{yr}$ at 90% C.L. when no restriction was placed on the signal likelihood space (unbounded). Alternatively, a lower limit on the nuclear lifetime was found to be $1.18\times {10}^{31}\mathrm{yr}$ at 90% C.L. when the signal was forced into a positive likelihood space (bounded). Values for the free oscillation time derived from various models are also provided in this article. This is the first search for neutron-antineutron oscillation with the deuteron as a target.

We present results from large-scale numerical simulations of a first order thermal phase transition in the early Universe, in order to explore the shape of the acoustic gravitational wave and the velocity power spectra. We compare the results with the predictions of the recently proposed sound shell model. For the gravitational wave power spectrum, we find that the predicted $k^{-3}$ behavior, where $k$ is the wave number, emerges clearly for detonations. The power spectra from deflagrations show similar features, but exhibit a steeper high-$k$ decay and an extra feature not accounted for in the model. There are two independent length scales: the mean bubble separation and the thickness of the sound shell around the expanding bubble of the low temperature phase. It is the sound shell thickness which sets the position of the peak of the power spectrum. The low wave number behavior of the velocity power spectrum is consistent with a causal $k^3$, except for the thinnest sound shell, where it is steeper. We present parameters for a simple broken power law fit to the gravitational wave power spectrum for wall speeds well away from the speed of sound where this form can be usefully applied. We examine the prospects for the detection, showing that a LISA-like mission has the sensitivity to detect a gravitational wave signal from sound waves with an RMS fluid velocity of about $0.05c$, produced from bubbles with a mean separation of about ${10}^{-2}$ of the Hubble radius. The shape of the gravitational wave power spectrum depends on the bubble wall speed, and it may be possible to estimate the wall speed, and constrain other phase transition parameters, with an accurate measurement of a stochastic gravitational wave background.

We study the thermal diffusivity $D_T$ in models of metals without quasiparticle excitations (“strange metals”). The many-body quantum chaos and transport properties of such metals can be efficiently described by a holographic representation in a gravitational theory in an emergent curved spacetime with an additional spatial dimension. We find that at generic infrared fixed points $D_T$ is always related to parameters characterizing many-body quantum chaos: the butterfly velocity $v_B$ and Lyapunov time ${\tau }_L$ through $D_T\sim v_B^2{\tau }_L$. The relationship holds independently of the charge density, periodic potential strength, or magnetic field at the fixed point. The generality of this result follows from the observation that the thermal conductivity of strange metals depends only on the metric near the horizon of a black hole in the emergent spacetime and is otherwise insensitive to the profile of any matter fields.

I present the effective potential at three-loop order for a general renormalizable theory, using the $\overline{\mathrm{MS}}$ renormalization scheme and Landau gauge fixing. As applications and illustrative points of reference, the results are specialized to the supersymmetric Wess-Zumino model and to the standard model. In each case, renormalization group scale invariance provides a consistency check. In the Wess-Zumino model, the required vanishing of the minimum vacuum energy yields an additional check. For the standard model, I carry out the resummation of Goldstone boson contributions, which provides yet more opportunities for nontrivial checks, and obtain the minimization condition for the Higgs vacuum expectation value at full three-loop order. An infrared divergence due to doubled photon propagators appears in the three-loop standard model effective potential, but it does not affect the minimization condition or physical observables and can be eliminated by resummation.

The Thirring model is a four-fermion theory with a current-current interaction and $U(2N)$ chiral symmetry. It is closely related to three-dimensional QED and other models used to describe properties of graphene. In addition, it serves as a toy model to study chiral symmetry breaking. In the limit of flavor number $N\to 1/2$ it is equivalent to the Gross-Neveu model, which shows a parity-breaking discrete phase transition. The model was already studied with different methods, including Dyson-Schwinger equations, functional renormalization group methods, and lattice simulations. Most studies agree that there is a phase transition from a symmetric phase to a spontaneously broken phase for a small number of fermion flavors, but no symmetry breaking for large $N$. But there is no consensus on the critical flavor number $N^{\mathrm{cr}}$ above which there is no phase transition anymore and on further details of the critical behavior. Values of $N$ found in the literature vary between 2 and 7. All earlier lattice studies were performed with staggered fermions. Thus it is questionable if in the continuum limit the lattice model recovers the internal symmetries of the continuum model. We present new results from lattice Monte Carlo simulations of the Thirring model with SLAC fermions which exactly implement all internal symmetries of the continuum model even at finite lattice spacing. If we reformulate the model in an irreducible representation of the Clifford algebra, we find, in contradiction to earlier results, that the behavior for even and odd flavor numbers is very different: for even flavor numbers, chiral and parity symmetry are always unbroken; for odd flavor numbers, parity symmetry is spontaneously broken below the critical flavor number $N_{\mathrm{ir}}^{\mathrm{cr}}=9$, while chiral symmetry is still unbroken.

Supermassive stars (SMSs) of mass $\gtrsim {10}^5{M}_{\odot }$ are candidates for seeds of supermassive black holes found in the center of many massive galaxies. We simulate the gravitational collapse of a rigidly rotating SMS core including nuclear burning effects in axisymmetric numerical relativity. We consider SMS cores composed of primordial metallicity and of helium in this paper. We find that for our chosen initial conditions, the nuclear burning does not play an important role. After the collapse, a torus surrounding a rotating black hole is formed and a fraction of the torus material is ejected by a hydrodynamical effect. We quantitatively study the relation between the properties of these objects and rotation. We find that if a SMS core is sufficiently rapidly rotating, the rest mass of the torus and outflow are approximately 6% and 1% of the initial rest mass, respectively. The typical average velocity and the total kinetic energy of the outflow are $0.2c$ and $10^{54-56}\mathrm{erg}$ where $c$ is the speed of light. Finally, we briefly discuss the possibility for observing the outflow, ringdown gravitational waves associated with the formation of black holes, and gravitational waves from the torus.

The question of what gravitational theory could supersede General Relativity has been central in theoretical physics for decades. Many disparate alternatives have been proposed motivated by cosmology, quantum gravity and phenomenological angles, and have been subjected to tests derived from cosmological, solar system and pulsar observations typically restricted to linearized regimes. Gravitational waves from compact binaries provide new opportunities to probe these theories in the strongly gravitating/highly dynamical regimes. To this end however, a reliable understanding of the dynamics in such a regime is required. Unfortunately, most of these theories fail to define well posed initial value problems, which prevents at face value from meeting such challenge. In this work, we introduce a consistent program able to remedy this situation. This program is inspired in the approach to “fixing” viscous relativistic hydrodynamics introduced by Israel and Stewart in the late 70’s. We illustrate how to implement this approach to control undesirable effects of higher order derivatives in gravity theories and argue how the modified system still captures the true dynamics of the putative underlying theories in $3+1$ dimensions. We sketch the implementation of this idea in a couple of effective theories of gravity, one in the context of Noncommutative Geometry, and one in the context of Chern-Simons modified General Relativity.