Lattice four-fermion models containing $N$ flavors of staggered fermions, which are invariant under $Z_2$ and $U(1)$ chiral symmetries, are known to suffer from sign problems when formulated using the auxiliary field approach. Although these problems have been ignored in previous studies, they can be severe. Here we show that the sign problems disappear when the models are formulated in the fermion bag approach, allowing us to solve them rigorously for the first time.

Mass spectrum of $0^{++}$ glueballs is produced using a dual supergravity theory we proposed for pure $\mathcal{N}=1$ $SU(N)$ gauge theory in four dimensions in the large $N$ limit in the IR. The glueball states are expressed in terms of Whittaker functions. The spectrum is discrete and a function whose roots give the masses is written. The ratios of the masses are independent of the parameters of the theory and comparison to recent nonsupersymmetric large $N$ lattice QCD data available for the lowest three states shows agreement to within 5%.

In this work, we consider the light front quantum electrodynamics in ($3+1$) dimensions and evaluate the photon polarization tensor at one loop for both zero and finite temperatures. In the first case, we apply the dimensional regularization method to extract the finite contribution and find the transverse structure for the amplitude in terms of the light front coordinates. The result agrees with one-loop covariant calculation. For the thermal corrections, we generalize the hard thermal loop approximation to the light front and calculate the dominant temperature contribution to the polarization tensor, consistent with the Ward identity. In both zero as well as finite temperature calculations, we use the oblique light front coordinates.

We analyze the spectrum of axions radiated from collapse of domain walls, which have received less attention in the literature. The evolution of topological defects related to the axion models is investigated by performing field-theoretic lattice simulations. We simulate the whole process of evolution of the defects, including the formation of global strings, the formation of domain walls, and the annihilation of the defects due to the tension of walls. The spectrum of radiated axions has a peak at the low frequency, which implies that axions produced by the collapse of domain walls are not highly relativistic. We revisit the relic abundance of cold dark matter axions and find that the contribution from the decay of defects can be comparable with the contribution from strings. This result leads to a more severe upper bound on the axion decay constant.

We explore the relationship between the quantum effective action and the ground state (and excited state) wave functions of a field theory. Applied to the Yang-Mills theory in $2+1$ dimensions, we find the leading terms of the effective action from the ground state wave function previously obtained in the Hamiltonian formalism by solving the Schrödinger equation.

I discuss theories that describe fully nonlinear physics, while being practically linear (PL), in that they require solving only linear differential equations. These theories may be interesting in themselves as manageable nonlinear theories. But, they can also be chosen to emulate genuinely nonlinear theories of special interest, for which they can serve as approximations. The idea can be applied to a large class of nonlinear theories, exemplified here with a PL analogs of scalar theories, and of Born-Infeld (BI) electrodynamics. The general class of such PL theories of electromagnetism are governed by a Lagrangian $\mathcal{L}=-(1/2)F_{\mu \nu }{Q}^{\mu \nu }+\tilde{\mathcal{S}}(Q_{\mu \nu })$, where $F_{\mu \nu }=A_{\nu ,\mu }-A_{\mu ,\nu }$, and $A_{\mu }$ couples to currents in the standard way, while $Q_{\mu \nu }=B_{\nu ,\mu }-B_{\mu ,\nu }$ is an auxiliary field that does not couple directly to currents. By picking a special form of $\tilde{\mathcal{S}}(Q_{\mu \nu })$, we can make such a theory similar in some regards to a given fully nonlinear theory, governed by the Lagrangian $-\tilde{\mathcal{U}}(F_{\mu \nu })$. For example, by similar we may imply that the theories are equivalent to second order in the expansion for weak fields, and that they are also equivalent for static configurations with one-dimensional symmetry (e.g., near point charges). A particularly felicitous choice, which implies the above similarities, is to take $\tilde{\mathcal{S}}$ as the Legendre transform of $\tilde{\mathcal{U}}$ in the variables $F_{\mu \nu }$. For the BI theory, this Legendre transform has the same form as the BI Lagrangian itself: $\tilde{\mathcal{S}}(Q_{\mu \nu },E_0^2)=\tilde{\mathcal{U}}(Q_{\mu \nu },-E_0^2)$ ($E_0$ is the limiting field of the BI theory). Various matter-of-principle questions remain to be answered regarding such theories. As a specific example, I discuss BI electrostatics in more detail. As an aside, for BI, I derive an exact expression for the short-distance force between two arbitrary point charges of the same sign, in any dimension.

We demonstrate that there appear finite-time future singularities in $f(T)$ gravity with $T$ being the torsion scalar. We reconstruct a model of $f(T)$ gravity with realizing the finite-time future singularities. In addition, it is explicitly shown that a power-law-type correction term $T^{\beta }$ ($\beta >1$) such as a $T^2$ term can remove the finite-time future singularities in $f(T)$ gravity. Moreover, we study $f(T)$ models with realizing inflation in the early universe, the $\Lambda \mathrm{CDM}$ model, little rip cosmology and pseudo-rip cosmology. It is demonstrated that the disintegration of bound structures for little rip and pseudo-rip cosmologies occurs in the same way as in gravity with corresponding dark energy fluid. We also discuss that the time-dependent matter instability in the star collapse can occur in $f(T)$ gravity. Furthermore, we explore thermodynamics in $f(T)$ gravity and illustrate that the second law of thermodynamics can be satisfied around the finite-time future singularities for the universe with the temperature inside the horizon being the same as that of the apparent horizon.

Starting from concrete AdS/CFT dual pairs, one can introduce ingredients which produce cosmological solutions, including metastable de Sitter and its decay to nonaccelerating Friedmann-Robertson-Walker. We present simple Friedmann-Robertson-Walker solutions sourced by magnetic flavor branes and analyze correlation functions and particle and brane dynamics. To obtain a holographic description, we exhibit a time-dependent warped metric on the solution and interpret the resulting redshifted region as a Lorentzian low energy effective field theory in one fewer dimension. At finite times, this theory has a finite cutoff, a propagating lower-dimensional graviton, and a finite covariant entropy bound, but at late times the lower-dimensional Planck mass and entropy go off to infinity in a way that is dominated by contributions from the low energy effective theory. This opens up the possibility of a precise dual at late times. We reproduce the time-dependent growth of the number of degrees of freedom in the system via a count of available microscopic states in the corresponding magnetic brane construction.

Recently a new picture has been developed for examining Wilson lines, and the corresponding anomalous dimensions which govern their renormalization properties. By making a particular coordinate transform, the calculation of the cusp anomalous dimension in QED or QCD can be related to the energy of a pair of static charges in Euclidean Anti-de Sitter space. This paper shows how the same picture can be used to describe Wilson lines in quantum gravity. We show how the relevant cusp anomalous dimension (which has recently been shown to be one-loop exact) can be obtained using the Newtonian limit of general relativity. We also show how both the QED and gravity cases emerge as special cases of a general formulation, and that a continuous parameter exists which interpolates between them. The results may be useful in examining the relations between gauge and gravity theories.

We elaborate on our proposal regarding a connection between global physics and local galactic dynamics via quantum gravity. This proposal calls for the concept of MONDian dark matter which behaves like cold dark matter at cluster and cosmological scales but emulates modified Newtonian dynamics (MOND) at the galactic scale. In the present paper, we first point out a surprising connection between the MONDian dark matter and an effective gravitational Born-Infeld theory. We then argue that these unconventional quanta of MONDian dark matter must obey infinite statistics, and the theory must be fundamentally nonlocal. Finally, we provide a possible top-down approach to our proposal from the matrix theory point of view.

A diffusion equation for a black hole is derived from the Bunster-Carlip equations. Its solution has the standard form of a Gaussian distribution. The second moment of the distribution determines the quantum of black hole area. The entropy of diffusion process is the same, apart from the logarithmic corrections, as the Bekenstein-Hawking entropy.

We study here circular timelike geodesics in the Janis-Newman-Winicour and Gamma metric spacetimes which contain a strong curvature naked singularity and reduce to the Schwarzschild metric for a specific value of one of the parameters. We show that for both the metrics the range of allowed parameters can be divided into three regimes where structure of the circular geodesics is qualitatively different. It follows that the properties of the accretion disks around such naked singularities can be significantly different from those of disks around black holes. This adds to previous studies showing that if naked singularities exist in nature, their observational signature would be significantly different from that of the black hole.

We present numerical relativity simulations of nine-orbit equal-mass binary neutron star covering the quasicircular late inspiral and merger. The extracted gravitational waveforms are analyzed for convergence and accuracy. Second-order convergence is observed up to contact, i.e. about 3–4 cycles to merger; error estimates can be made up to this point. The uncertainties on the phase and the amplitude are dominated by truncation errors and can be minimized to 0.13 rad and $\lesssim 1\%$, respectively, by using several simulations and extrapolating in resolution. In the latter case finite-radius extraction uncertainties become a source of error of the same order and have to be taken into account. The waveforms are tested against accuracy standards for data analysis. The uncertainties on the waveforms are such that accuracy standards are generically not met for signal-to-noise ratios relevant for detection, except for some best cases using extrapolation from several runs. A detailed analysis of the errors is thus imperative for the use of numerical relativity waveforms from binary neutron stars in quantitative studies. The waveforms are compared with the post-Newtonian Taylor T4 approximants both for point-particle and including the analytically known tidal corrections. The T4 approximants accumulate significant phase differences of 2 rad at contact and 4 rad at merger, underestimating the influence of finite-size effects. Tidal signatures in the waveforms are thus important at least during the last six orbits of the merger process.

We investigate the ambiguities in the Fock quantization of the scalar perturbations of a Friedmann-Lemaître-Robertson-Walker model with a massive scalar field as matter content. We consider the case of compact spatial sections (thus avoiding infrared divergences), with the topology of a three-sphere. After expanding the perturbations in series of eigenfunctions of the Laplace-Beltrami operator, the Hamiltonian of the system is written up to quadratic order in them. We fix the gauge of the local degrees of freedom in two different ways, reaching in both cases the same qualitative results. A canonical transformation, which includes the scaling of the matter-field perturbations by the scale factor of the geometry, is performed in order to arrive at a convenient formulation of the system. We then study the quantization of these perturbations in the classical background determined by the homogeneous variables. Based on previous work, we introduce a Fock representation for the perturbations in which: (a) the complex structure is invariant under the isometries of the spatial sections and (b) the field dynamics is implemented as a unitary operator. These two properties select not only a unique unitary equivalence class of representations, but also a preferred field description, picking up a canonical pair of field variables among all those that can be obtained by means of a time-dependent scaling of the matter field (completed into a linear canonical transformation). Finally, we present an equivalent quantization constructed in terms of gauge-invariant quantities. We prove that this quantization can be attained by a mode-by-mode time-dependent linear canonical transformation which admits a unitary implementation, so that it is also uniquely determined.

A shift of the baryon acoustic oscillation (BAO) scale to smaller values than predicted by linear theory was observed in simulations. In this paper, we try to provide an intuitive physical understanding of why this shift occurs, explaining in more pedagogical detail earlier perturbation theory calculations. We find that the shift is mainly due to the following physical effect. A measurement of the BAO scale is more sensitive to regions with long-wavelength overdensities than underdensities, because (due to nonlinear growth and bias) these overdense regions contain larger fluctuations and more tracers and hence contribute more to the total correlation function. In overdense regions the BAO scale shrinks because such regions locally behave as positively curved closed universes, and hence a smaller scale than predicted by linear theory is measured in the total correlation function. Other effects which also contribute to the shift are briefly discussed. We provide approximate analytic expressions for the nonlinear shift including a brief discussion of biased tracers and explain why reconstruction should entirely reverse the shift. Our expressions and findings are in agreement with simulation results, and confirm that nonlinear shifts should not be problematic for next-generation BAO measurements.

We reconsider the effect of electromagnetic radiation from superconducting strings on cosmic microwave background $\mu$ and $y$ distortions and derive present (COBE-FIRAS) and future (PIXIE) constraints on the string tension, ${\mu }_s$, and electric current, $I$. We show that absence of distortions of the cosmic microwave background in PIXIE will impose strong constraints on ${\mu }_s$ and $I$, leaving the possibility of light strings ($G{\mu }_s\lesssim {10}^{-18}$) or relatively weak currents ($I\lesssim 10\mathrm{TeV}$).

A stellar-mass compact object spiraling into a supermassive black hole, an extreme mass-ratio inspiral, is one of the targets for future space-based gravitational-wave detectors. Such inspirals offer a unique opportunity to learn about astrophysics and test general relativity in the strong field. Here we study whether scalar-tensor theories in asymptotically flat spacetimes can be further constrained with these inspirals. In the extreme mass-ratio limit, and assuming analyticity of the coupling functions entering the action, we show that all scalar-tensor theories universally reduce to massive or massless Brans-Dicke theory. We also show that in this limit, black holes do not emit dipolar radiation to all orders in post-Newtonian theory. For massless theories and quasicircular orbits, we calculate the scalar energy flux in the test-particle Teukolsky formalism to all orders in post-Newtonian theory and fit it to a high-order post-Newtonian expansion. We then derive the post-Newtonian corrections to the scalar-tensor modified, Fourier transform of the gravitational-wave response function and map it to the parametrized post-Einsteinian framework. With the Teukolsky flux at hand, we use the effective-one-body framework adapted to extreme mass-ratio inspirals to calculate the scalar-tensor modifications to the gravitational waveform. We find that such corrections are smaller than those induced in the early inspiral of comparable-mass binaries, leading to projected bounds on the Brans-Dicke coupling parameter that are worse than current Solar System ones. This is because Brans-Dicke theory modifies the weak field, leading to deviations in the energy flux that are largest at small velocities. For massive theories, superradiance can produce resonances in the scalar energy flux that can lead to quasicircular floating orbits outside the innermost stable circular orbit and that last until the supermassive black hole loses enough mass and spin-angular momentum. If such floating orbits occur in the frequency band of a LISA-like mission, they would lead to a large dephasing (typically $\sim {10}^6\mathrm{rads}$) that would prevent detection of such modified inspirals using general relativity templates. A detection that is consistent with general relativity would then rule out the presence of floating resonances at frequencies lower than the lowest inspiral frequency observed, allowing for the strongest constraints yet on massive scalar-tensor theories.

The ATLAS and CMS collaborations have recently shown data suggesting the presence of a Higgs boson in the vicinity of 125 GeV. We show that a two-Higgs-doublet model spectrum, with the pseudoscalar state being the lightest, could be responsible for the diphoton signal events. In this model, the other scalars are considerably heavier and are not excluded by the current LHC data. If this assumption is correct, future LHC data should show a strengthening of the $\gamma \gamma$ signal, while the signals in the $Z{Z}^{(*)}\to 4\ell$ and $W{W}^{(*)}\to 2\ell 2\nu$ channels should diminish and eventually disappear, due to the absence of diboson tree-level couplings of the $CP$-odd state. The heavier $CP$-even neutral scalars can now decay into channels involving the $CP$-odd light scalar which, together with their larger masses, allow them to avoid the existing bounds on Higgs searches. We suggest additional signals to confirm this scenario at the LHC, in the decay channels of the heavier scalars into $AA$ and $AZ$. Finally, this inverted two-Higgs-doublet spectrum is characteristic in models where fermion condensation leads to electroweak symmetry breaking. We show that in these theories it is possible to obtain the observed diphoton signal at or somewhat above the prediction for the standard model Higgs for the typical values of the parameters predicted.

We examined the neutrino sector in $E_6\times SU(2{)}_F$ supersymmetric grand unified theory with spontaneous $CP$ violation. At first glance, the discrete symmetry, which is introduced in order to solve the supersymmetric $CP$ problem, constrains the allowed operators too strongly for the neutrino sector to be consistent with the experimental data, i.e., the $\mu$ neutrino becomes massless as commented in the previous paper. We showed that this issue can be solved if some operators are taken into account. And we saw that such operators do not play an important role in studying quark and charged lepton sectors. The predictions on the neutrino masses and mixings are the same as the $E_6$ models, which are consistent with various experiments on the neutrino oscillations.

We derive direct representations of the scaling functions of the $3dO(4)$ model which are relevant for comparisons to other models, in particular, QCD. This is done in terms of expansions in the scaling variable $z=\overline{t}/h^{1/\Delta }$. The expansions around $z=0$ and the corresponding asymptotic ones for $z\to \pm \infty$ overlap such that no interpolation is needed. The expansion coefficients are determined numerically from the data of a previous high statistics simulation of the $O(4)$ model on a three-dimensional lattice of linear extension $L=120$. From the scaling function of the magnetization we calculate the leading asymptotic coefficients of the scaling function of the free energy density. As a result we obtain the universal amplitude ratio $A^{+}/A^{-}=1.84(4)$ for the specific heat. Comparing the scaling function of the energy density to the data we find the nonsingular part of the energy density ${ϵ}_{\mathrm{ns}}(T)$ with high precision and at the same time excellent scaling properties.