We propose a new type of moduli stabilization scenario where the supersymmetric and supersymmetry-breaking minima are degenerate at the leading level. The inclusion of the loop corrections originating from the matter fields resolves this degeneracy of vacua. Light axions are predicted in one of our models.

We show that the dimension of spacetime becomes complex-valued when its short-scale geometry is invariant under a discrete scaling symmetry. This characteristic can generically arise in quantum gravities, for instance, in those based on combinatorial or multifractal structures or as the partial breaking of continuous dilation symmetry in any conformal-invariant theory. With its infinite scale hierarchy, discrete scale invariance overlaps with the traditional separation between ultraviolet and infrared physics and it can leave an all-range observable imprint, such as a pattern of log oscillations and sharp features in the cosmic microwave background primordial power spectrum.

Recent study has shown that a nonsingular oscillating potential—a feature of infinite derivative gravity theories—matches current experimental data better than the standard General Relativity potential. In this work, we show that this nonsingular oscillating potential can be given by a wider class of theories which allows the defocusing of null rays and therefore geodesic completeness. We consolidate the conditions whereby null geodesic congruences may be made past complete, via the Raychaudhuri equation, with the requirement of a nonsingular Newtonian potential in an infinite derivative gravity theory. In doing so, we examine a class of Newtonian potentials characterized by an additional degree of freedom in the scalar propagator, which returns the familiar potential of General Relativity at large distances.

We provide an elegant way of solving analytically the third post-Newtonian (3PN) accurate Kepler equation, associated with the 3PN-accurate generalized quasi-Keplerian parametrization for compact binaries in eccentric orbits. An additional analytic solution is presented to check the correctness of our compact solution and we perform comparisons between our PN-accurate analytic solution and a very accurate numerical solution of the PN-accurate Kepler equation. We adapt our approach to compute crucial 3PN-accurate inputs that will be required to compute analytically both the time and frequency domain ready-to-use amplitude-corrected PN-accurate search templates for compact binaries in inspiralling eccentric orbits.

We study an effective quantum description of the static gravitational potential for spherically symmetric systems up to the first post-Newtonian order. We start by obtaining a Lagrangian for the gravitational potential coupled to a static matter source from the weak field expansion of the Einstein-Hilbert action. By analyzing a few classical solutions of the resulting field equation, we show that our construction leads to the expected post-Newtonian expressions. Next, we show that one can reproduce the classical Newtonian results very accurately by employing a coherent quantum state, and modifications to include the first post-Newtonian corrections are considered. Our findings establish a connection between the corpuscular model of black holes and post-Newtonian gravity, and set the stage for further investigations of these quantum models.

Making use of the SNIa data set, Nesseris and Perivolaropoulos [Phys. Rev. D 73, 103511 (2006)] have found the gravitation constant to evolve in accordance with scalar-tensor gravity. On the other hand, Majerotto et al. [arXiv:astro-ph/0410543] and Guo et al. [Phys. Rev. D 76, 023508 (2007)] have found a definite signature of dark energy–dark matter coupling in Einstein tensor gravity background. However, the results of the above works are quite contradictory, so we cannot be sure which of these results should be accepted because both models use different background gravitation. We construct a more inclusive model with scalar-background space-time and scalar-matter couplings. Making use of SNIa(Union) and baryon acoustic oscillation data sets, we made likelihood analyses; the results show that the background gravitation has the tensor characteristics within a confidence level of 68% and the scalar-matter coupling has a rather large positive value $\delta =\pm 1.01$. As Guo et al. showed, however, inclusion of the cosmic microwave background (CMB) data set in the likelihood analysis significantly reduces the allowed region of the coupling compared to the case without CMB data. Therefore, the value of scalar-matter coupling in this paper could have been estimated too large and the inclusion of CMB data in the next work is expected to yield a more realistic result.

Recent analysis of the rotation curves of a large sample of galaxies with very diverse stellar properties reveals a relation between the radial acceleration purely due to the baryonic matter and the one inferred directly from the observed rotation curves. Assuming the dark matter (DM) exists, this acceleration relation is tantamount to an acceleration relation between DM and baryons. This leads us to a universal maximum acceleration for all halos. Using the latter in DM profiles that predict inner cores implies that the central surface density ${\mu }_{\mathrm{DM}}={\rho }_s{r}_s$ must be a universal constant, as suggested by previous studies of selected galaxies, revealing a strong correlation between the density ${\rho }_s$ and scale $r_s$ parameters in each profile. We then explore the consequences of the constancy of ${\mu }_{\mathrm{DM}}$ in the context of the ultralight scalar field dark matter model (SFDM). We find that for this model ${\mu }_{\mathrm{DM}}=648M_{\odot }{\mathrm{pc}}^{-2}$ and that the so-called WaveDM soliton profile should be a universal feature of the DM halos. Comparing with the data from the Milky Way and Andromeda satellites, we find that they are all consistent with a boson mass of the scalar field particle of the order of ${10}^{-21}\mathrm{eV}/c^2$, which puts the SFDM model in agreement with recent cosmological constraints.

We analyze the scattering of fermions, Higgs and electroweak gauge bosons in order to obtain the partial-wave unitarity bounds on dimension-six effective operators, including those involving fermions. We also quantify whether, at the LHC energies, the dimension-six operators lead to unitarity violation after taking into account the presently available constraints on their Wilson coefficients. Our results show that for most dimension-six operators relevant for the LHC physics there is no unitarity violation at the LHC energies, and consequently there is no need for the introduction of form factors in the experimental and phenomenological analyses, making them model independent. We also identify two operators for which unitarity violation is still an issue at the LHC Run II.

We present results for the interaction of two kaons at maximal isospin. The calculation is based on $N_f=2+1+1$ flavor gauge configurations generated by the European Twisted Mass Collaboration with pion masses ranging from about 230 MeV to 450 MeV at three values of the lattice spacing. The elastic scattering length $a_0^{I=1}$ is calculated at several values of the bare strange and light quark masses. We find $M_K{a}_0=-0.385(16{)}_{\mathrm{stat}}(\genfrac{}{}{0ex}{}{+0}{-12}{)}_{m_s}(\genfrac{}{}{0ex}{}{+0}{-5}{)}_{Z_P}(4{)}_{r_f}$ as the result of a combined extrapolation to the continuum and to the physical point, where the first error is statistical, and the three following are systematical. This translates to $a_0=-0.154(6{)}_{\mathrm{stat}}{(}_{-5}^{+0}{)}_{m_s}{(}_{-2}^{+0}{)}_{Z_P}(2{)}_{r_f}\mathrm{fm}$.

We study the axial $U(1)$ symmetry at a finite temperature in two-flavor lattice QCD. Employing the Möbius domain-wall fermions, we generate gauge configurations slightly above the critical temperature $T_c$ with different lattice sizes $L=2–4\mathrm{fm}$. Our action allows frequent topology tunneling while keeping good chiral symmetry close enough to that of overlap fermions. This allows us to recover full chiral symmetry by an overlap/domain-wall reweighting. Above the phase transition, a strong suppression of the low-lying modes is observed in both overlap and domain-wall Dirac spectra. We, however, find a sizable violation of the Ginsparg-Wilson relation in the Möbius domain-wall Dirac eigenmodes, which dominates the signals of the axial $U(1)$ symmetry breaking near the chiral limit. We also find that the use of the overlap fermion only in the valence sector is dangerous since it suffers from the artifacts due to partial quenching. Reweighting the Möbius domain-wall fermion determinant to that of the overlap fermion, we observe the axial U(1) breaking to vanish in the chiral limit, which is stable against the changes of the lattice volume and lattice spacing.

It is known since the 1980s that the instanton-induced ’t Hooft effective Lagrangian not only can solve the so-called $U(1)a$ problem, by making the ${\eta }^{\prime }$ meson heavy etc., but it can also lead to chiral symmetry breaking. In the 1990s it was demonstrated that, taken to higher orders, this Lagrangian correctly reproduces effective forces in a large set of hadronic channels, mesonic and baryonic ones. Recent progress in understanding gauge topology at finite temperatures is related with the so-called instanton-dyons, the constituents of the instantons. Some of them, called $L$-dyons, possess the antiperiodic fermionic zero modes, and thus form a new version of the ’t Hooft effective Lagrangian. This paper is our first study of a wide set of hadronic correlation function. We found that, at the lowest temperatures at which this approach is expected to be applicable, those may be well compatible with what is known about them based on phenomenological and lattice studies, provided $L$ and $M$ type dyons are strongly correlated.

It has been revealed from the path-integral formulation of the hadronic tensor that there are connected sea and disconnected sea partons. The former is responsible for the Gottfried sum rule violation primarily and evolves the same way as the valence. Therefore, the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution equations can be extended to accommodate them separately. We discuss its consequences and implications vis-á-vis lattice calculations.

We study the perturbative unitarity of the Lee-Wick models, formulated as nonanalytically Wick rotated Euclidean theories. The complex energy plane is divided into disconnected regions and the values of a loop integral in the various regions are related to one another by a nonanalytic procedure. We show that the one-loop diagrams satisfy the expected, unitary cutting equations in each region: only the physical d.o.f. propagate through the cuts. The goal can be achieved by working in suitable subsets of each region and proving that the cutting equations can be analytically continued as a whole. We make explicit calculations in the cases of the bubble and triangle diagrams and address the generality of our approach. We also show that the same higher-derivative models violate unitarity if they are formulated directly in Minkowski spacetime.

We numerically investigated how nonlinear dynamics depends on the dimensionality and on the higher-order curvature corrections in the form of Gauss-Bonnet (GB) terms. We especially monitored the processes of appearances of a singularity (or black hole) in two models: (i) a perturbed wormhole throat in spherically symmetric space-time, and (ii) colliding scalar pulses in plane-symmetric space-time. We used a dual-null formulation for evolving the field equations, which enables us to locate the trapping horizons directly, and also enables us to follow close to the large-curvature region due to its causal integrating scheme. We observed that the fate of a perturbed wormhole is either a black hole or an expanding throat depending on the total energy of the structure, and its threshold depends on the coupling constant of the GB terms (${\alpha }_{\mathrm{GB}}$). We also observed that a collision of large scalar pulses will produce a large-curvature region, of which the magnitude also depends on ${\alpha }_{\mathrm{GB}}$. For both models, the normal corrections (${\alpha }_{\mathrm{GB}}>0$) work for avoiding the appearance of singularity, although it is inevitable. We also found that in the critical situation for forming a black hole, the existence of the trapped region in the Einstein-GB gravity does not directly indicate the formation of a black hole.

We propose an optomechanics experiment that can search for signatures of a fundamentally classical theory of gravity and in particular of the many-body Schrödinger-Newton (SN) equation, which governs the evolution of a crystal under a self-gravitational field. The SN equation predicts that the dynamics of a macroscopic mechanical oscillator’s center-of-mass wave function differ from the predictions of standard quantum mechanics [H. Yang, H. Miao, D.-S. Lee, B. Helou, and Y. Chen, Phys. Rev. Lett. 110, 170401 (2013)]. This difference is largest for low-frequency oscillators, and for materials, such as tungsten or osmium, with small quantum fluctuations of the constituent atoms around their lattice equilibrium sites. Light probes the motion of these oscillators and is eventually measured in order to extract valuable information on the pendulum’s dynamics. Due to the nonlinearity contained in the SN equation, we analyze the fluctuations of measurement results differently than standard quantum mechanics. We revisit how to model a thermal bath, and the wave-function collapse postulate, resulting in two prescriptions for analyzing the quantum measurement of the light. We demonstrate that both predict features, in the outgoing light’s phase fluctuations’ spectrum, which are separate from classical thermal fluctuations and quantum shot noise, and which can be clearly resolved with state of the art technology.

We consider a model with two real scalar fields which admits phantom domain wall solutions. We investigate the structure and evolution of these phantom domain walls in an expanding homogeneous and isotropic universe. In particular, we show that the increase of the tension of the domain walls with cosmic time, associated to the evolution of the phantom scalar field, is responsible for an additional damping term in their equations of motion. We describe the macroscopic dynamics of phantom domain walls, showing that extended phantom defects whose tension varies on a cosmological time scale cannot be the dark energy.

To explain the small neutrino masses, heavy Majorana neutrinos are introduced in the left-right twin Higgs model. The heavy neutrinos—together with the charged scalars and the heavy gauge bosons—may contribute large mixings between the neutrinos and the charged leptons, which may induce some distinct lepton-flavor-violating processes. We check ${\overline{\ell }}_i{\ell }_j$ ($i,j=e,\mu ,\tau ,i\ne j$) production in $\gamma \gamma$ collisions in the left-right twin Higgs model, and find that the production rates may be large in some specific parameter space. In optimal cases, it is even possible to detect them with reasonable kinematical cuts. We also show that these collisions can effectively constrain the model parameters—such as the Higgs vacuum expectation value, the right-handed neutrino mass, etc.—and may serve as a sensitive probe of this new physics model.

We extract constraints on the parameter space of the Manohar and Wise model by comparing the cross sections for dijet, top-pair, dijet-pair, $t\overline{t}t\overline{t}$ and $b\overline{b}b\overline{b}$ productions at the LHC with the strongest available experimental limits from ATLAS or CMS at 8 or 13 TeV. Overall we find mass limits around 1 TeV in the most sensitive regions of parameter space, and lower elsewhere. This is at odds with generic limits for color octet scalars often quoted in the literature where much larger production cross sections are assumed. The constraints that can be placed on coupling constants are typically weaker than those from existing theoretical considerations, with the exception of the parameter ${\eta }_D$.

We perform a pilot study of the perturbative renormalization of a supersymmetric gauge theory with matter fields on the lattice. As a specific example, we consider supersymmetric $\mathcal{N}=1$ QCD (SQCD). We study the self-energies of all particles which appear in this theory, as well as the renormalization of the coupling constant. To this end we compute, perturbatively to one-loop, the relevant two-point and three-point Green’s functions using both dimensional and lattice regularizations. Our lattice formulation involves the Wilson discretization for the gluino and quark fields; for gluons we employ the Wilson gauge action; for scalar fields (squarks) we use naïve discretization. The gauge group that we consider is $SU(N_c)$, while the number of colors, $N_c$, the number of flavors, $N_f$, and the gauge parameter, $\alpha$, are left unspecified. We obtain analytic expressions for the renormalization factors of the coupling constant ($Z_g$) and of the quark ($Z_{\psi }$), gluon ($Z_u$), gluino ($Z_{\lambda }$), squark ($Z_{A_{\pm }}$), and ghost ($Z_c$) fields on the lattice. We also compute the critical values of the gluino, quark and squark masses. Finally, we address the mixing which occurs among squark degrees of freedom beyond tree level: we calculate the corresponding mixing matrix which is necessary in order to disentangle the components of the squark field via an additional finite renormalization.