We construct a fully covariant theory of massive gravity which does not require the introduction of an external reference metric, and overcomes the usual problems of massive gravity theories (fatal ghosts instabilities, acausality and/or van Dam-Veltman-Zakharov discontinuity). The equations of motion of the theory are nonlocal but respect causality. The starting point is the quadratic action proposed in the context of the degravitation idea. We show that it is possible to extend it to a fully nonlinear covariant theory. This theory describes the 5 degrees of freedom of a massive graviton plus a scalar ghost. However, contrary to generic nonlinear extensions of Fierz-Pauli massive gravity, the ghost has the same mass $m$ as the massive graviton, independently of the background, and smoothly goes into a nonradiative degree of freedom for $m\to 0$. As a consequence, for $m\sim H_0$ the vacuum instability induced by the ghost is irrelevant even over cosmological time scales. We finally show that an extension of the model degravitates a vacuum energy density of order $M_{\mathrm{Pl}}^4$ down to a value of order $M_{\mathrm{Pl}}^2{m}^2$, which for $m=\mathcal{O}(H_0)$ is of order of the observed value of the vacuum energy density.

In A. Henderson, A. Laddha, and C. Tomlin, preceding article, [Phys. Rev. D 88, 044028 (2013)], we initiated an approach towards quantizing the Hamiltonian constraint in loop quantum gravity by requiring that it generates an anomaly-free representation of constraint algebra of -shell. We investigated this issue in the case of a toy model of a ($2+1$)-dimensional $\mathrm{U}(1{)}^3$ gauge theory, which can be thought of as a weak coupling limit of Euclidean three-dimensional gravity. However, in paper I, we only focused on the most nontrivial part of the constraint algebra that involves the commutator of two Hamiltonian constraints. In this paper we continue with our analysis and obtain a representation of full constraint algebra in a loop quantized framework. We show that there is a representation of the diffeomorphism group with respect to which the Hamiltonian constraint quantized in paper I is diffeomorphism covariant. Our work can be thought of as a potential first step towards resolving some longstanding issues with the Hamiltonian constraint in canonical loop quantum gravity.

We analyze the issue of anomaly-free representations of the constraint algebra in loop quantum gravity (LQG) in the context of a diffeomorphism-invariant $\mathrm{U}(1{)}^3$ theory in three spacetime dimensions. We construct a Hamiltonian constraint operator whose commutator matches with a quantization of the classical Poisson bracket involving structure functions. Our quantization scheme is based on a geometric interpretation of the Hamiltonian constraint as a generator of phase space-dependent diffeomorphisms. The resulting Hamiltonian constraint at finite triangulation has a conceptual similarity with the $\overline{\mu }$ scheme in loop quantum cosmology and highly intricate action on the spin-network states of the theory. We construct a subspace of non-normalizable states (distributions) on which the continuum Hamiltonian constraint is defined which leads to an anomaly-free representation of the Poisson bracket of two Hamiltonian constraints in loop quantized framework. Our work, along with the work done in [C. Tomlin and M. Varadarajan, Phys. Rev. D 87, 044039 (2013)], suggests a new approach to the construction of anomaly-free quantum dynamics in Euclidean LQG.

Intrigued by the holographic principle, Padmanabhan recently proposed a novel idea, saying that our cosmic space is emergent as cosmic time progresses. In particular, the expansion rate of the Universe is related to the difference between the surface degrees of freedom on the holographic horizon and the bulk degrees of freedom inside. In this note, we generalize this interesting paradigm to brane world, scalar-tensor gravity, and f(R) theory, respectively, and find that in the cosmological setting the Friedmann equations can be successfully derived.

I examine two cosmological scenarios in which the thermodynamic arrow of time points in opposite directions in the asymptotic past and future. The first scenario, suggested by Aguirre and Gratton, assumes that the two asymptotic regions are separated by a de Sitter-like bounce, with low-entropy boundary conditions imposed at the bounce. Such boundary conditions naturally arise from quantum cosmology with Hartle-Hawking wave function of the universe. The bounce hypersurface breaks de Sitter invariance and represents the beginning of the universe in this model. The second scenario, proposed by Carroll and Chen, assumes some generic initial conditions on an infinite spacelike Cauchy surface. They argue that the resulting spacetime will be nonsingular, apart from black holes that could be formed as the initial data is evolved, and will exhibit eternal inflation in both time directions. Here I show, assuming the null convergence condition, that the Cauchy surface in a nonsingular (apart from black holes) universe with two asymptotically inflating regions must necessarily be compact. I also argue that the size of the universe at the bounce between the two asymptotic regions cannot much exceed the de Sitter horizon. The spacetime structure is then very similar to that in the Aguirre-Gratton scenario and does require special boundary conditions at the bounce. If cosmological singularities are allowed, then an infinite Cauchy surface with “random” initial data will generally produce inflating regions in both time directions. These regions, however, will be surrounded by singularities and will have singularities in their past or future.

KAGRA is a cryogenic interferometric gravitational-wave detector being constructed at the underground site of Kamioka mine in Gifu prefecture, Japan. We performed an optimization of the interferomter design, to achieve the best sensitivity and a stable operation, with boundary conditions of classical noises and under various practical constraints, such as the size of the tunnel or the mirror cooling capacity. Length and alignment sensing schemes for the robust control of the interferometer are developed. In this paper, we describe the detailed design of the KAGRA interferometer as well as the reasoning behind design choices.

Recent observations indicating the existence of a monochromatic $\gamma$-ray line with energy $\sim 130\mathrm{GeV}$ in the Fermi-LAT data have attracted great interest due to the possibility that the line feature stems from the annihilation of dark matter particles. Many studies examining the robustness of the putative line signal have concentrated on its spectral attributes. Here, we study the morphological features of the $\gamma$-ray line photons, which can be used to differentiate a putative dark matter signal from astrophysical backgrounds or instrumental artifacts. Photons stemming from dark matter annihilation will produce events tracing a specific morphology, with a statistical clustering that can be calculated based on models of the dark matter density profile in the inner Galaxy. We apply the density based spatial clustering of applications with noise clustering algorithm to Fermi $\gamma$-ray data, and show that we can rule out the possibility that 1 (2, 4) or fewer pointlike sources produce the observed morphology for the line photons at a 99%(95%, 90%) confidence level. Our study strongly disfavors the main astrophysical background envisioned to produce a line feature at energies above 100 GeV: cold pulsar winds. It is highly unlikely that four or more such objects have exactly the same monochromatic cosmic-ray energy needed to produce a $\gamma$-ray line, to within instrumental energy resolution. Furthermore, we show that the larger photon statistics expected with Air Cherenkov Telescopes such as H.E.S.S.-II will allow for extraordinarily stringent morphological tests of the origin of the “line photons.”

Being stimulated by the recent BESIII observation of a charged charmoniumlike structure $Z_c(3900)$, in this work we study the distributions of the $J/\psi {\pi }^{\pm }$ and ${\pi }^{+}{\pi }^{-}$ invariant mass spectra of the $Y(4260)\to {\pi }^{+}{\pi }^{-}J/\psi$ decay by the initial-single-pion-emission mechanism, where the interference effects of the initial-single-pion-emission mechanism with two other decay modes are also taken into account. The obtained $d\Gamma (Y(4260)\to {\pi }^{+}{\pi }^{-}J/\psi )/d{m}_{J/\psi {\pi }^{\pm }}$ and $d\Gamma (Y(4260)\to {\pi }^{+}{\pi }^{-}J/\psi )/d{m}_{{\pi }^{+}{\pi }^{-}}$ marvelously agree with the BESIII data to reproduce the $Z_c(3900)$ structure.

Mass formulas for the vector mesons written in terms of the gluon condensate, i.e., the trace anomaly in quantum chromodynamics (QCD), are derived on the basis of finite energy QCD sum rules. We utilize sum rules with $s^n$ and $s^{n+1/2}$ weights, which relate the energy-weighted spectral sums to the vacuum expectation values of certain commutation relations. After evaluating the commutation relations, the sum rules with $s^n$ weights are reduced to the familiar ones obtained from the operator product expansion (OPE). On the other hand, the sum rules with $s^{n+1/2}$ weights cannot be derived from OPE. They give new relations between the spectral sums and QCD vacuum fluctuations. To derive a simple mass formula, we adopt the $\mathrm{\text{pole}}+\mathrm{\text{continuum ansatz}}$ for the spectral function, and we solve coupled equations given by the sum rules with $s^{0,1}$ weights and the new sum rule with $s^{1/2}$ weight. Application of our approach to the axial-vector meson is also discussed.

We study the phase diagram of non-Abelian pure gauge theories in the presence of a topological $\theta$ term. The dependence of the deconfinement temperature on $\theta$ is determined on the lattice both by analytic continuation and by reweighting, obtaining consistent results. The general structure of the diagram is discussed on the basis of large-$N$ considerations and of the possible analogies and dualities existing with the phase diagram of QCD in the presence of an imaginary baryon chemical potential.

We present an improved light-cone sum rule analysis of the decay form factors of $D$ and $D_s$ into $\eta$ and ${\eta }^{\prime }$ and argue that these decays offer a very promising possibility to determine the leading Fock-state gluonic contribution of the ${\eta }^{\prime }$ at future experimental facilities such as FAIR or Super-KEKB. We also give the corresponding branching ratios for $B$ decays.

We investigate the one-gluon-exchange ($\alpha {\alpha }_s$) corrections to the real photon structure functions $W_{TT}$, $W_{LT}$, $W_{TT}^a$ and $W_{TT}^{\tau }$ in the massive parton model. We employ a technique based on the Cutkosky rules and the reduction of Feynman integrals to master integrals. We show that a positivity constraint, which is derived from the Cauchy-Schwarz inequality, is satisfied among the unpolarized and polarized structure functions $W_{TT}$, $W_{TT}^a$ and $W_{TT}^{\tau }$ calculated up to the next-to-leading order in QCD.

The branching fractions of $D_s^{\pm }$ meson decays serve to normalize many measurements of processes involving charm quarks. Using $586{\mathrm{pb}}^{-1}$ of $e^{+}{e}^{-}$ collisions recorded at a center of mass energy of 4.17 GeV, we determine absolute branching fractions for 13 $D_s^{\pm }$ decays in 16 reconstructed final states with a double tag technique. In particular we make a precise measurement of the branching fraction $\mathcal{B}(D_s\to K^{-}{K}^{+}{\pi }^{+})=(5.55\pm 0.14\pm 0.13)\%$, where the uncertainties are statistical and systematic, respectively. We find a significantly reduced value of $\mathcal{B}(D_s\to {\pi }^{+}{\pi }^0{\eta }^{\prime })$ compared to the world average, and our results bring the inclusively and exclusively measured values of $\mathcal{B}(D_s\to {\eta }^{\prime }X)$ into agreement. We also search for $CP$-violating asymmetries in $D_s$ decays and measure the cross section of $e^{+}{e}^{-}\to D_s^{*}{D}_s$ at $E_{\mathrm{cm}}=4.17\mathrm{GeV}$.

Stable vacua obtained from isotropic tori compactification might not be fully stable provided the existence of runaway directions in the Kähler directions of anisotropy. By implementing a genetic algorithm we report the existence of explicit flux configurations leading to stable de Sitter and anti–de Sitter vacua, consisting of Type IIB compactifications on a six-dimensional anisotropic torus threaded with standard and $S$-dual invariant nongeometric fluxes in the presence of orientifold 3-planes. In all de Sitter vacua the masses of the complex structure moduli are heavier than the Hubble scale suggesting that the axio-dilaton and Kähler moduli are natural candidates for small-field inflation. In this way, we also report new solutions on isotropic and semi-isotropic tori compactifications. Finally, we observe that, since all our solutions are obtained in the absence of solitonic objects, they are good candidates to be lifted to stable solutions in extended supersymmetric theories.

In the first part of the paper we study solitonic properties of the Calabi-Yau vacua of the string theory. We observe that the Calabi-Yau threefolds of the string theory may be thought of as Neveu-Schwarz–Neveu-Schwarz (NS-NS) objects whose masses are proportional to $1/g_s^2$. In the second part, which is the main part of this paper, we propose, based on the viewpoint that our three-dimensional space is a stack of Bogomol’nyi-Prasad-Sommerfield (BPS) D3-branes located at the conifold singularity of the Calabi-Yau threefold, a new mechanism to address the cosmological constant problem in the framework of the conventional compactifications, where the $n$-form fluxes including NS-NS three-form are all turned off. In this mechanism the four-dimensional cosmological constant $\lambda$ appears as two types, NS-NS type and R-R type, of vacuum energies on the brane plus supersymmetry breaking term, which constitute a brane action density ${\widehat{I}}_{\mathrm{brane}}$, and sum of these three terms of ${\widehat{I}}_{\mathrm{brane}}$ are forced to vanish by field equations so that $\lambda$ adjusts itself to zero as a result. Also in this mechanism the $d=4$ supersymmetry is broken in the brane region, while still maintaining $\lambda =0$. The supersymmetry breaking occurs as a result of the gauge symmetry breaking of the R-R four-form arising at the quantum level. The substance of the supersymmetry breaking term is a vacuum energy density (of the brane region) arising from the quantum excitations with components along the transverse directions to the D3-brane. We generalize the above mechanism to the case of the flux compactifications where the fluxes are all turned on to stabilize the moduli. In the generalized theory $\lambda$ appears as ${\widehat{I}}_{\mathrm{brane}}$ plus the scalar potential ${\mathcal{V}}_{\mathrm{scalar}}$ for the moduli, in contrast to the case of the ordinary flux compactifications where $\lambda$ is simply given by ${\mathcal{V}}_{\mathrm{scalar}}$. Also in this theory any nonzero ${\mathcal{V}}_{\mathrm{scalar}}$ arising from perturbative or nonperturbative corrections is gauged away by the gauge arbitrariness of ${\widehat{I}}_{\mathrm{brane}}$ and the condition $\lambda =0$. So $\lambda$ is again expressed only as a brane action density as before, or it simply vanishes by the cancellation between ${\widehat{I}}_{\mathrm{brane}}$ and ${\mathcal{V}}_{\mathrm{scalar}}$.

We consider a singleton deformation of the ${\mathrm{AdS}}_4$ higher-spin theory dual to the three-dimensional $O(N)$ vector model. The singleton couples to the higher-spin multiplet only through a marginal boundary interaction. We argue that the effect of such a deformation is to shift $N\to N+1$ in both sides of the holographic correspondence and we show how the gap equations of the three-dimensional $O(N)$ vector model arise from the higher-spin theory. The singleton deformation breaks higher-spin symmetry and gives rise to the well-known $1/N$ anomalous dimensions of the boundary theory.

Elliptic Calabi-Yau fibrations with Mordell-Weil group of rank two are constructed. Such geometries are the basis for F-theory compactifications with two Abelian gauge groups in addition to non-Abelian gauge symmetry. We present the elliptic fiber both as a ${\mathrm{Bl}}^2{\mathbb{P}}^2[3]$ fibration and in the birationally equivalent Weierstraß form. The spectrum of charged singlets and their Yukawa interactions are worked out in generality. This framework can be combined with the toric construction of tops to implement additional non-Abelian gauge groups. We utilize the classification of tops to construct $SU(5)\times U(1)\times U(1)$ gauge symmetries systematically and study the resulting geometries, presenting the defining equations, the matter curves and their charges, the Yukawa couplings and explaining the process in detail for an example. Brane recombination relates these geometries to a ${\mathrm{Bl}}^1{\mathbb{P}}^2[3]$ fibration with a corresponding class of $SU(5)\times U(1)$ models. We also present the $SU(5)$ tops based on the elliptic fiber ${\mathrm{Bl}}^1{\mathbb{P}}_{[1,1,2]}[4]$, corresponding to another class of $SU(5)\times U(1)$ models.

We calculate higher-spin Brower–Polchinski–Strassler–Tan (BPST) vertex operators for an open bosonic string and express these operators in terms of a Kummer function of the second kind. We derive an infinite number of recurrence relations among BPST vertex operators of different string states. These recurrence relations among BPST vertex operators lead to the recurrence relations among Regge string scattering amplitudes discovered recently.

Under the framework of the viscous chromohydrodynamics, the gluon self-energy is derived for the quark-gluon plasma with shear viscosity. The viscous chromoelectric permittivity and chromomagnetic permeability are evaluated from the gluon self-energy, through which the chromorefraction index is investigated. The numerical analysis indicates that the chromorefractive index becomes negative in some frequency range. The starting point for that frequency range is around the chromoelectric permittivity pole, and the chromomagnetic permeability pole determines the endpoint. As $\eta /s$ increases, the frequency range for the negative refraction becomes wider.

We consider the structure and physical properties of specific classes of neutron, quark, and “exotic” stars in Eddington-inspired Born-Infeld (EiBI) gravity. The latter reduces to standard general relativity in vacuum, but presents a different behavior of the gravitational field in the presence of matter. The equilibrium equations for a spherically symmetric configuration (mass continuity and Tolman-Oppenheimer-Volkoff) are derived, and their solutions are obtained numerically for different equations of state of neutron and quark matter. More specifically, stellar models, described by the stiff fluid, radiationlike, polytropic and the bag model quark equations of state are explicitly constructed in both general relativity and EiBI gravity, thus allowing a comparison between the predictions of these two gravitational models. As a general result it turns out that for all the considered equations of state, EiBI gravity stars are more massive than their general relativistic counterparts. Furthermore, an exact solution of the spherically symmetric field equations in EiBI gravity, describing an exotic star, with decreasing pressure but increasing energy density, is also obtained. As a possible astrophysical application of the obtained results we suggest that stellar mass black holes, with masses in the range of $3.8M_{\odot }$ and $6M_{\odot }$, respectively, could be in fact EiBI neutron or quark stars.