In this work, we investigate the 4d path integral for Euclidean quantum gravity on a hypercubic lattice, as given by the spinfoam model by Engle, Pereira, Rovelli, Livine, Freidel and Krasnov. To tackle the problem, we restrict to a set of quantum geometries that reflects the large amount of lattice symmetries. In particular, the sum over intertwiners is restricted to quantum cuboids, i.e. coherent intertwiners which describe a cuboidal geometry in the large-$j$ limit. Using asymptotic expressions for the vertex amplitude, we find several interesting properties of the state sum. First of all, the value of coupling constants in the amplitude functions determines whether geometric or nongeometric configurations dominate the path integral. Secondly, there is a critical value of the coupling constant $\alpha$, which separates two phases. In both phases, the diffeomorphism symmetry appears to be broken. In one, the dominant contribution comes from highly irregular, in the other from highly regular configurations, both describing flat Euclidean space with small quantum fluctuations around them, viewed in different coordinate systems. On the critical point diffeomorphism symmetry is nearly restored, however. Thirdly, we use the state sum to compute the physical norm of kinematical states, i.e. their norm in the physical Hilbert space. We find that states which describe boundary geometry with high torsion have an exponentially suppressed physical norm. We argue that this allows one to exclude them from the state sum in calculations.

We revisit noninteracting string partition functions in Rindler space by summing over fields in the spectrum. In field theory, the total partition function splits in a natural way into a piece that does not contain surface terms and a piece consisting of solely the so-called edge states. For open strings, we illustrate that surface contributions to the higher-spin fields correspond to open strings piercing the Rindler origin, unifying the higher-spin surface contributions in string language. For closed strings, we demonstrate that the string partition function is not quite the same as the sum over the partition functions of the fields in the spectrum: an infinite overcounting is present for the latter. Next we study the partition functions obtained by excluding the surface terms. Using recent results of He et al. [J. High Energy Phys. 05 (2015) 106], this construction, first done by Emparan [arXiv:hep-th/9412003], can be put on much firmer ground. We generalize to type II and heterotic superstrings and demonstrate modular invariance. All of these exhibit an IR divergence that can be interpreted as a maximal acceleration close to the black hole horizon. Ultimately, since these partition functions are only part of the full story, divergences here should not be viewed as a failure of string theory: maximal acceleration is a feature of a faulty treatment of the higher-spin fields in the string spectrum. We comment on the relevance of this to Solodukhin’s recent proposal [Phys. Rev. D 91, 084028 (2015)]. A possible link with the firewall paradox is apparent.

Bekenstein and Mayo have revealed an interesting property of evaporating ($3+1$)-dimensional Schwarzschild black holes: their entropy emission rates ${\dot{S}}_{\mathrm{Sch}}$ are related to their energy emission rates $P$ by the simple relation ${\dot{S}}_{\mathrm{Sch}}=C_{\mathrm{Sch}}\times (P/\hslash {)}^{1/2}$, where $C_{\mathrm{Sch}}$ is a numerically computed dimensionless coefficient. Remembering that ($1+1$)-dimensional perfect black-body emitters are characterized by the same functional relation, ${\dot{S}}^{1+1}=C^{1+1}\times (P/\hslash {)}^{1/2}$ [with $C^{1+1}=(\pi /3{)}^{1/2}$], Bekenstein and Mayo have concluded that, in their entropy emission properties, ($3+1$)-dimensional Schwarzschild black holes behave effectively as ($1+1$)-dimensional entropy emitters. Later studies have shown that this intriguing property is actually a generic feature of all radiating ($D+1$)-dimensional Schwarzschild black holes. One naturally wonders whether all black holes behave as simple ($1+1$)-dimensional entropy emitters? In order to address this interesting question, we shall study in this paper the entropy emission properties of Reissner-Nordström black holes. We shall show, in particular, that the physical properties which characterize the neutral sector of the Hawking emission spectra of these black holes can be studied analytically in the near-extremal $T_{\mathrm{BH}}\to 0$ regime (here $T_{\mathrm{BH}}$ is the Bekenstein-Hawking temperature of the black hole). We find that the Hawking radiation spectra of massless neutral scalar fields and coupled electromagnetic-gravitational fields are characterized by the nontrivial entropy-energy relations ${\dot{S}}_{\mathrm{RN}}^{\text{Scalar}}=-C_{\mathrm{RN}}^{\text{Scalar}}\times (A{P}^3/{\hslash }^3{)}^{1/4}\ln (AP/\hslash )$ and ${\dot{S}}_{\mathrm{RN}}^{\mathrm{Elec}\text{−}\mathrm{Grav}}=-C_{\mathrm{RN}}^{\mathrm{Elec}\text{−}\mathrm{Grav}}\times (A^4{P}^9/{\hslash }^9{)}^{1/10}\ln (AP/\hslash )$ in the near-extremal $T_{\mathrm{BH}}\to 0$ limit (here $\{C_{\mathrm{RN}}^{\text{Scalar}},C_{\mathrm{RN}}^{\mathrm{Elec}\text{−}\mathrm{Grav}}\}$ are analytically calculated dimensionless coefficients and $A$ is the surface area of the Reissner-Nordström black hole). Our analytical results therefore indicate that not all black holes behave as simple ($1+1$)-dimensional entropy emitters.

The gravitational baryogensis may not generate a sufficient baryon asymmetry in the standard thermal history of the Universe when we take into account the gravitino problem. Hence, it has been suggested that anisotropy of the Universe can enhance the generation of the baryon asymmetry through the increase of the time change of the Ricci scalar curvature. We study the gravitational baryogenesis in the presence of anisotropy, which is produced at the end of an anisotropic inflation. Although we confirm that the generated baryon asymmetry is enhanced compared with the original isotropic cosmological model, taking into account the constraint on the anisotropy by the recent CMB observations, we find that it is still difficult to obtain the observed baryon asymmetry only through the gravitational baryogenesis without suffering from the gravitino problem.

We explore the possibility of explaining the recent $\sim 750\mathrm{GeV}$ excesses observed by ATLAS and CMS in the $\gamma \gamma$ spectrum in the context of a compelling theory of naturalness. The potential spin-zero resonance responsible for the excesses also requires the existence of new heavy charged states. We show that both such features are naturally realized in a see-saw composite Higgs model for electroweak symmetry breaking, where the new pseudo-Goldstone bosons are expected to be comparatively heavier than the Standard Model Higgs, and the new fermions have masses in the TeV range. If confirmed, the existence of this new resonance could be the first stone in the construction of a new theory of naturalness.

We explore a $Z^{\prime }$ boson coupled only with the Standard Model (SM) fermions ($Z^{\prime }f\overline{f}$) in the framework of minimal flavor violation. We study its effects on the processes with lepton flavor violation ${\ell }_j\to {\ell }_i{\ell }_k{\overline{\ell }}_l$, ${\ell }_j\to {\ell }_i\gamma$, ${\mu }^{-}N\to e^{-}N$, quark flavor-changing neutral currents $b\to s\ell \overline{\ell }$, neutral $B$ and $K$ meson mixing, and $e^{+}{e}^{-}\to f\overline{f}$ at the LEP experiment to constrain the parameter space of $Z^{\prime }$ mass and couplings. We find that among those relevant processes, $\mu \to e\gamma$, $\mu \to 3e$, $\mu \text{−}e$ conversion and $e^{+}{e}^{-}\to f\overline{f}$ can put more stringent bounds on $Z^{\prime }f\overline{f}$ couplings normalized by $Z^{\prime }$ mass. The implications for various processes are obtained, such as $B$ and $K$ mixing and $B/K\to M{\ell }_1{\overline{\ell }}_2$ decays. In addition, we also analyze $Z^{\prime }$ signatures at the LHC with $\sqrt{s}=8$ and 13 TeV.

Dark photons $\overline{\gamma }$ mediating long-range forces in a dark sector are predicted by various new physics scenarios, and are being intensively searched for in experiments. We extend a previous study of a new discovery process for dark photons proceeding via Higgs-boson production at the LHC. Thanks to the nondecoupling properties of the Higgs boson, $\mathrm{BR}(H\to \gamma \overline{\gamma })$ values up to a few percent are possible for a massless dark photon, even for heavy dark-sector scenarios. The corresponding signature consists (for a Higgs boson at rest) of a striking monochromatic photon with energy $E_{\gamma }=m_H/2$, and a similar amount of missing energy. We perform a model-independent analysis at the LHC of both the gluon-fusion and vector-boson fusion (VBF) Higgs production mechanisms at 14 TeV, including parton-shower effects, and updating our previous parton-level analysis at 8 TeV in the gluon-fusion channel by a more realistic background modeling. We find that a $5\sigma$ sensitivity can be reached in the gluon-fusion channel for $\mathrm{BR}(H\to \gamma \overline{\gamma })\simeq 0.1\%$ with an integrated luminosity of $L\simeq 300{\mathrm{fb}}^{-1}$. The corresponding VBF reach is instead restricted to 1%. Such decay rates can be naturally obtained in dark-photon scenarios arising from unbroken $U(1{)}_F$ models explaining the origin and hierarchy of the Yukawa couplings, strongly motivating the search for this exotic Higgs decay at the LHC.

The observed pattern of neutrino mixing angles is in good agreement with the hypothesis of neutrino anarchy, which posits that nature has chosen the entries of the leptonic mixing matrix at random. In this paper we investigate how stable this conclusion is under renormalization group (RG) effects. Working in the simplest type-I seesaw model and two variants of the inverse seesaw model we study how the statistical distributions of the neutrino mixing parameters evolve between the grand unification scale and the electroweak scale. Especially in the inverse seesaw case we find significant distortions: Mixing angles tend to be smaller after RG running, and the Dirac $CP$ phase tends to be closer to zero. The $p$-value describing the compatibility between the observed mixing angles and the anarchy hypothesis increases by 10%–20%. This illustrates that RG effects are highly relevant for quantitative studies of the anarchy scenario.

The combination of ${\nu }_{\mu }\text{−}{\nu }_{\tau }$ exchange together with $CP$ conjugation in the neutrino sector (known as ${\mathsf{CP}}^{\mu \tau }$ symmetry or $\mu \tau$ reflection) is known to predict the viable pattern ${\theta }_{23}=45°$, a maximal Dirac $CP$ phase, and trivial Majorana phases. We implement such a $CP$ symmetry as a new $CP$ symmetry in theories with $A_4$ flavor. The implementation in a complete renormalizable model leads to a new form for the neutrino mass matrix that leads to further predictions: a normal hierarchical spectrum with a lightest mass and $m_{\beta \beta }$ ($0\nu 2\beta$) of only few meV, and either ${\nu }_1$ or ${\nu }_2$ has opposite $CP$ parity. An approximate $L_{\mu }-L_{\tau }$ symmetry arises naturally and controls the flavor structure of the model. The light neutrino masses are generated by the extended seesaw mechanism with six right-handed neutrinos (RHNs). The requirement of negligible one-loop corrections to light neutrino masses, the validity of the extended seesaw approximation, and not too long-lived beyond-the-Standard-Model states to comply with big bang nucleosynthesis essentially restricts the parameters of the model to a small region: three relatively light right-handed neutrinos at the GeV scale, heavier neutrinos at the electroweak scale, and Yukawa couplings smaller than the electron Yukawa. Such small Yukawa couplings render these RHNs unobservable in terrestrial experiments.

We study the bosonic structure of $F$-term Nambu-Goto cosmic strings forming in a realistic SO(10) implementation, assuming standard hybrid inflation. We describe the supersymmetric grand unified theory, and its spontaneous symmetry breaking scheme in parallel with the inflationary process. We also write the explicit tensor formulation of its scalar sector, focusing on the subrepresentations singlet under the standard model, which is sufficient to describe the string structure. We then introduce an ansatz for Abelian cosmic strings, discussing in details the hypothesis, and write down the field equations and boundary conditions. Finally, after doing a perturbative study of the model, we present and discuss the results obtained with numerical solutions of the string structure.

In this article, we study a Galilean fluid with a conserved $U(1)$ current up to anomalies. We construct a relativistic system, which we call a null fluid and show that it is in one-to-one correspondence with a Galilean fluid living in one lower dimension. The correspondence is based on light cone reduction, which is known to reduce the Poincaré symmetry of a theory to Galilean in one lower dimension. We show that the proposed null fluid and the corresponding Galilean fluid have exactly same symmetries, thermodynamics, constitutive relations, and equilibrium partition to all orders in the derivative expansion. We also devise a mechanism to introduce $U(1)$ anomaly in even dimensional Galilean theories using light cone reduction, and study its effect on the constitutive relations of a Galilean fluid.

Self-accelerating backgrounds in massive gravity provide an arena to explore the Cauchy problem for derivatively coupled fields that obey complex constraints which reduce the phase space degrees of freedom. We present here an algorithm based on the Kronecker form of a matrix pencil that finds all hidden constraints, for example those associated with derivatives of the equations of motion, and characteristic curves for any $1+1$ dimensional system of linear partial differential equations. With the Regge-Wheeler-Zerilli decomposition of metric perturbations into angular momentum and parity states, this technique applies to fully $3+1$ dimensional perturbations of massive gravity around any spherically symmetric self-accelerating background. Five spin modes of the massive graviton propagate once the constraints are imposed: two spin-2 modes with luminal characteristics present in the massless theory as well as two spin-1 modes and one spin-0 mode. Although the new modes all possess the same—typically spacelike—characteristic curves, the spin-1 modes are parabolic while the spin-0 modes are hyperbolic. The joint system, which remains coupled by nonderivative terms, cannot be solved as a simple Cauchy problem from a single noncharacteristic surface. We also illustrate the generality of the algorithm with other cases where derivative constraints reduce the number of propagating degrees of freedom or order of the equations.

This paper presents measurements of $W^{\pm }Z$ production in $pp$ collisions at a center-of-mass energy of 8 TeV. The gauge bosons are reconstructed using their leptonic decay modes into electrons and muons. The data were collected in 2012 by the ATLAS experiment at the Large Hadron Collider and correspond to an integrated luminosity of $20.3{\mathrm{fb}}^{-1}$. The measured inclusive cross section in the detector fiducial region is ${\sigma }_{W^{\pm }Z\to {\ell }^{\prime }\nu \ell \ell }=35.1\pm 0.9(\mathrm{stat})\pm 0.8(\mathrm{sys})\pm 0.8(\mathrm{lumi})\mathrm{fb}$, for one leptonic decay channel. In comparison, the next-to-leading-order Standard Model expectation is $30.0\pm 2.1\mathrm{fb}$. Cross sections for $W^{+}Z$ and $W^{-}Z$ production and their ratio are presented as well as differential cross sections for several kinematic observables. Limits on anomalous triple gauge boson couplings are derived from the transverse mass spectrum of the $W^{\pm }Z$ system. From the analysis of events with a $W$ and a $Z$ boson associated with two or more forward jets an upper limit at 95% confidence level on the $W^{\pm }Z$ scattering cross section of 0.63 fb, for each leptonic decay channel, is established, while the Standard Model prediction at next-to-leading order is $0.13\pm 0.01\mathrm{fb}$. Limits on anomalous quartic gauge boson couplings are also extracted.

Recently, a lot of attention has been paid to the modifications of the power spectrum of primordial fluctuations caused by quantum cosmology effects. The origin of these modifications is corrections to the Mukhanov-Sasaki equations that govern the propagation of the primeval cosmological perturbations. The specific form of these corrections depends on a series of details of the quantization approach and of the prescription followed to implement it. Generally, the complexity of the theoretical quantum formulation is simplified in practice appealing to a semiclassical or effective approximation in order to perform concrete numerical computations. In this work, we introduce technical tools and design a procedure to deal with these quantum corrections beyond the most direct approximations employed so far in the literature. In particular, by introducing an interaction picture, we extract the quantum dynamics of the homogeneous geometry in absence of scalar field potential and inhomogeneities, dynamics that has been intensively studied and that can be integrated. The rest of our analysis focuses on the interaction evolution, putting forward methods to cope with it. The ultimate aim is to develop treatments that increase our ability to discriminate between the predictions of different quantization proposals for cosmological perturbations.

In a recent paper [Phys. Rev. D 92, 084012 (2015)], the author studied the classical ($1+1$)-dimensional Friedmann-Robertson-Walker (FRW) universe filled with a perfect fluid in the Hořava-Lifshitz (HL) theory of gravity. This theory is dynamical due to the anisotropic scaling of space and time. It also resembles the Jackiw-Teitelboim model, in which a dilatonic degree of freedom is necessary for dynamics. In this paper, I will take one step further in the understanding of ($1+1$)-dimensional HL cosmology by means of the quantization of the FRW universe filled with a perfect fluid with the equation of state (EoS) $p=w\rho$. The fluid will be introduced in the model via Schutz formalism and Dirac’s algorithm will be used for quantization. It will be shown that the Schrödinger equation for the wave function of the universe has the following properties: for $w=1$ (radiation fluid), the characteristic potential will be exponential, resembling Liouville quantum mechanics; for $w\ne 1$, a characteristic inverse square potential appears in addition to a regular polynomial that depends on the EoS. Explicit solutions for a few cases of interest will be found and the expectation value of the scale factor will be calculated. As in usual quantum cosmology, it will be shown that the quantum theory smooths out the big-bang singularity, but the classical behavior of the universe is recovered in the low-energy limit.

J-factors (or D-factors) describe the distribution of dark matter in an astrophysical system and determine the strength of the signal provided by annihilating (or decaying) dark matter respectively. We provide simple analytic formulas to calculate the J-factors for spherical cusps obeying the empirical relationship between enclosed mass, velocity dispersion and half-light radius. We extend the calculation to the spherical Navarro-Frenk-White model, and demonstrate that our new formulas give accurate results in comparison to more elaborate Jeans models driven by Markov chain Monte Carlo methods. Of the known ultrafaint dwarf spheroidals, we show that Ursa Major II, Reticulum II, Tucana II and Horologium I have the largest J-factors and so provide the most promising candidates for indirect dark matter detection experiments. Amongst the classical dwarfs, Draco, Sculptor and Ursa Minor have the highest J-factors. We show that the behavior of the J-factor as a function of integration angle can be inferred for general dark halo models with inner slope $\gamma$ and outer slope $\beta$. The central and asymptotic behavior of the J-factor curves are derived as a function of the dark halo properties. Finally, we show that models obeying the empirical relation on enclosed mass and velocity dispersion have J-factors that are most robust at the integration angle equal to the projected half-light radius of the dwarf spheroidal (dSph) divided by heliocentric distance. For most of our results, we give the extension to the D-factor which is appropriate for the decaying dark matter picture.

We explore the possibility of computing fermionic correlators on the lattice by combining a domain decomposition with a multilevel integration scheme. The quark propagator is expanded in series of terms with a well-defined hierarchical structure. The higher the order of a term, the (exponentially) smaller its magnitude, the less local is its dependence on the gauge field. Once inserted in a Wick contraction, the gauge-field dependence of the terms in the resulting series can be factorized so that it is suitable for multilevel Monte Carlo integration. We test the strategy in quenched QCD by computing the disconnected correlator of two flavor-diagonal pseudoscalar densities, and a nucleon two-point function. In either case we observe a significant exponential increase of the signal-to-noise ratio.

According to the Particle Data Group, the measurements of $\mathcal{B}(W^{+}\to {\tau }^{+}{\nu }_{\tau })$ and $\mathcal{B}(W^{+}\to {\ell }^{+}{\nu }_{\ell })$ ($\ell =e$, $\mu$) disagree with one another at the $2.3\sigma$ level. In this paper, we search for a new-physics (NP) explanation of this $W\to \tau \nu$ puzzle. We consider two NP scenarios: (i) the $W$ mixes with a $W^{\prime }$ boson that couples preferentially to the third generation, (ii) ${\tau }_{L,R}$ and ${\nu }_{\tau L}$ mix with isospin-triplet leptons. Unfortunately, once other experimental constraints are taken into account, neither scenario can explain the above experimental result. Our conclusion is that the $W\to \tau \nu$ puzzle is almost certainly just a statistical fluctuation.

We find new spontaneously generated fuzzy extra dimensions emerging from a certain deformation of $N=4$ supersymmetric Yang-Mills theory with cubic soft supersymmetry breaking and mass deformation terms. First, we determine a particular four-dimensional fuzzy vacuum that may be expressed in terms of a direct sum of product of two fuzzy spheres, and denote it in short as $S_F^{2\text{Int}}\times S_F^{2\text{Int}}$. The direct sum structure of the vacuum is clearly revealed by a suitable splitting of the scalar fields in the model in a manner that generalizes our approach in [Phys. Rev. D 92, 025022 (2015)]. Fluctuations around this vacuum have the structure of gauge fields over $S_F^{2\text{Int}}\times S_F^{2\text{Int}}$, and this enables us to conjecture the spontaneous broken model as an effective $U(n)$ $(n<\mathcal{N})$ gauge theory on the product manifold $M^4\times S_F^{2\text{Int}}\times S_F^{2\text{Int}}$. We support this interpretation by examining the $U(4)$ theory and determining all of the $SU(2)\times SU(2)$ equivariant fields in the model, characterizing its low energy degrees of freedom. Monopole sectors with winding numbers $(\pm 1,0),(0,\pm 1),(\pm 1,\pm 1)$ are accessed from $S_F^{2\text{Int}}\times S_F^{2\text{Int}}$ after suitable projections, and subsequently equivariant fields in these sectors are obtained. We indicate how Abelian Higgs type models with vortex solutions emerge after dimensionally reducing over the fuzzy monopole sectors as well. A family of fuzzy vacua is determined by giving a systematic treatment for the splitting of the scalar fields, and it is made manifest that suitable projections of these vacuum solutions yield all higher winding number fuzzy monopole sectors. We observe that the vacuum configuration $S_F^{2\text{Int}}\times S_F^{2\text{Int}}$ identifies with the bosonic part of the product of two fuzzy superspheres with $OSP(2,2)\times OSP(2,2)$ supersymmetry and elaborate on this unexpected and intriguing feature.

We investigate the linear response of an $O(N)$ scalar quantum field theory subject to external perturbations using the symmetry-improved two-particle irreducible effective action (SI-2PIEA) formalism [A. Pilaftsis and D. Teresi, Nucl. Phys. B874, 594 (2013)]. Despite satisfactory equilibrium behavior, we find a number of unphysical effects at the linear response level. Goldstone boson field fluctuations are overdetermined, with the only consistent solution being to set the fluctuations and their driving sources to zero, except for momentum modes where the Higgs and Goldstone self-energies obey a particular relationship. Also Higgs field fluctuations propagate masslessly, despite the Higgs propagator having the correct mass. These pathologies are independent of any truncation of the effective action and still exist even if we relax the overdetermining Ward identities, so long as the constraint is formulated $O(N)$ covariantly. We discuss possible reasons for the apparent incompatibility of the constraints and linear response approximation and possible ways forward.