We describe the application of a novel approach for the reduction of scattering amplitudes, based on multivariate polynomial division, which we have recently presented. This technique yields the complete integrand decomposition for arbitrary amplitudes, regardless of the number of loops. It allows for the determination of the residue at any multiparticle cut, whose knowledge is a mandatory prerequisite for applying the integrand-reduction procedure. By using the division modulo Gröbner basis, we can derive a simple integrand recurrence relation that generates the multiparticle pole decomposition for integrands of arbitrary multiloop amplitudes. We apply the new reduction algorithm to the two-loop planar and nonplanar diagrams contributing to the five-point scattering amplitudes in $\mathcal{N}=4$ super Yang-Mills and $\mathcal{N}=8$ supergravity in four dimensions, whose numerator functions contain up to rank-two terms in the integration momenta. We determine all polynomial residues parametrizing the cuts of the corresponding topologies and subtopologies. We obtain the integral basis for the decomposition of each diagram from the polynomial form of the residues. Our approach is well suited for a seminumerical implementation, and its general mathematical properties provide an effective algorithm for the generalization of the integrand-reduction method to all orders in perturbation theory.

It has been proposed that the supermassive black hole candidates at the centers of galaxies might be wormholes formed in the early Universe and connecting our Universe with other sister universes. The analysis of the profile of the relativistic $\mathrm{K}\alpha$ iron line is currently the only available approach to probe the spacetime geometry around these objects. In this paper, we compute the expected $\mathrm{K}\alpha$ iron line in some wormhole spacetimes and we compare the results with the line produced around Kerr black holes. The line produced in accretion disks around nonrotating or very slow-rotating wormholes is relatively similar to the one expected around Kerr black holes with mid or high value of spin parameter and current observations are still marginally compatible with the possibility that the supermassive black hole candidates in galactic nuclei are these objects. For wormholes with spin parameter $a_{*}\gtrsim 0.02$, the associated $\mathrm{K}\alpha$ iron line is instead quite different from the one produced around Kerr black holes, and their existence may already be excluded.

It has been recently suggested that, as a gravitational Aharonov-Bohm effect due to a gravitomagnetic potential, possible effects of Chern-Simons gravity on a quantum interferometer are dependent on the latitude and direction of the interferometer on Earth in orbital motion around the Sun. Continuing work initiated in an earlier publication [H. Okawara, K. Yamada, and H. Asada, Phys. Rev. Lett. 109, 231101 (2012)], we perform numerical calculations of time variation in the induced phase shifts for nonequatorial cases. We show that the maximum phase shift at any latitude might occur at 6, 0 (and 12), and 18 hours (in local time) of each day, when the normal vector to the interferometer is vertical, eastbound, and northbound, respectively. If two identical interferometers were located at different latitudes, the difference between two phase shifts measured at the same local time would be $O(\sin \delta \phi )$ for a small latitude difference $\delta \phi$. It might thus become maximally $\sim 20\%$ for $\delta \phi \sim 10°$, for instance.

Ernst’s solution-generating technique is adapted to Einstein-Maxwell theory conformally (and minimally) coupled to a scalar field. This integrable system enjoys an SU(2,1) symmetry which enables one to move, by Kinnersley transformations, through the axisymmetric and stationary solution space, building an infinite tower of physically inequivalent solutions. As a specific application, metrics associated to scalar hairy black holes—such as the ones discovered by Bocharova, Bronnikov, Melnikov, and Bekenstein—are embedded in the external magnetic field of the Melvin universe.

Tantalizing cosmological and terrestrial evidence suggests the number of light neutrinos may be greater than 3, motivating a careful reexamination of cosmological bounds on extra light species. Big bang nucleosynthesis constrains the number of relativistic neutrino species present during nucleosynthesis, $N_{\mathrm{eff}}^{\mathrm{BBN}}$, while measurements of the cosmic microwave background (CMB) angular power spectrum constrain the effective energy density in relativistic neutrinos at the time of matter-radiation equality, $N_{\mathrm{eff}}^{\mathrm{CMB}}$. There are a number of scenarios where new sterile neutrino species may have different contributions to $\Delta N_{\mathrm{eff}}^{\mathrm{BBN}}$ and $\Delta N_{\mathrm{eff}}^{\mathrm{CMB}}$, for masses that may be relevant to reconciling cosmological constraints with various terrestrial claims of neutrino oscillations. We consider a scenario with two sterile neutrinos and explore whether partial thermalization of the sterile states can ease the tension between cosmological constraints on $N_{\mathrm{eff}}^{\mathrm{BBN}}$ and terrestrial data. We then investigate the effect of a nonzero neutrino mass on their contribution to the radiation abundance, finding reductions in $\Delta N_{\mathrm{eff}}^{\mathrm{CMB}}$ of more than 5% for neutrinos with masses above 0.5 eV. While the effects we investigate here could play a role, we nevertheless find that two additional light sterile neutrinos species cannot fit all the data at the 95% confidence level.

Recent measurements like the $t\overline{t}\gamma$ production by CDF as well as the $\mathrm{Br}(B\to X_s\gamma )$ and $A_{CP}(B\to X_s\gamma )$ are used to constrain the magnetic and electric dipole moments of the top quark. The $B\to X_s\gamma$ measurements by themselves define an allowed parameter region that sets up stringent constraints on both dipole moments, actually, significantly more stringent than previously reported. The measurement by CDF has a $\sim 37\%$ error that is too large to set any competitive bounds, for which a much lower 5% error would be required at least. On the other hand, because of the LHC’s higher energy (apart from its higher luminosity) the same measurement performed there could indeed further constrain the allowed parameter region given by the $B\to X_s\gamma$ measurement.

General limits on exotic heavy quarks $T$, $B$, and $X$ with masses above 300 GeV are presented for arbitrary branching fractions of $T\to W^{+}b$, $T\to Zt$, $T\to Ht$, $B\to W^{-}t$, $B\to Zb$, $B\to Hb$, and $X\to W^{+}t$. The results are based on a CMS search in final states with three isolated leptons ($e$ or $\mu$) or two isolated leptons with the same electric charge. Exotic heavy quark pair production through the strong interaction is considered. In the context of vectorlike quark models, $T$ quarks with a mass $m_T<480\mathrm{GeV}$ and $m_T<550\mathrm{GeV}$ are excluded for weak isospin singlets and doublets, respectively, and $B$ quarks with a mass $m_B<480\mathrm{GeV}$ are excluded for singlets, all at a 95% confidence level. Mass limits at the 95% confidence level for $T$ and $B$ singlets, $(T,B)$ doublets, and $(X,T)$ doublets are presented as a function of the corresponding heavy quark masses. For equal mass $m_T=m_B$ and $m_X=m_T$, vectorlike quarks are excluded at the 95% confidence level with masses below 550 GeV for $T$ and $B$ singlets, 640 GeV for a $(T,B)$ doublet, and 640 GeV for a $(X,T)$ doublet.

We develop the representation of interacting bulk gauge fields and charged scalar matter in anti–de Sitter in terms of nonlocal observables in the dual conformal field theory (CFT). We work in the holographic gauge in the bulk, $A_z=0$. The correct statement of micro-causality in the holographic gauge is somewhat subtle, so we first discuss it from the bulk point of view. We then show that in the $1/N$ expansion, CFT correlators can be lifted to obtain bulk correlation functions that satisfy microcausality. This requires adding an infinite tower of higher-dimension multitrace operators to the CFT definition of a bulk observable. For conserved currents, the Ward identities in the CFT prevent the construction of truly local bulk operators (i.e., operators that commute at spacelike separation with everything); however, the resulting nonlocal commutators are exactly those required by the bulk Gauss constraint. In contrast, a CFT which only has nonconserved currents can be lifted to a bulk theory which is truly local. Although our explicit calculations are for gauge theory, similar statements should hold for gravity.

We compare two competing conjectures of the color confinement in QCD, the monopole condensation and the Abelian dominance, and show that it is the monopole condensation that is responsible for the confinement. To demonstrate this we present a new gauge-invariant integral expression of the one-loop QCD effective action which has no infrared divergence. With this we show that, just as the Gliozzi-Scherk-Olive projection restores the supersymmetry and modular invariance in NSR string theory, the color reflection invariance (“the C projection”) assures the gauge invariance and the stability of the monopole condensation. This establishes the monopole dominance in QCD. In doing so we point out critical defects in the calculation of the Savvidy-Nielsen-Olesen effective action.

The canonical quantization of a charged particle in an intense laser background is developed and the associated two-point function calculated. It is shown how the causal propagator can be extracted. We provide an interpretation of this propagator in terms of degenerate quantum processes. The spectral properties of the propagator are derived, and we show how multipole structures emerge as a perturbative feature. We also calculate the associated multiple wave-function renormalizations to all orders in perturbation theory. Our calculations are for both circular and linearly polarized plane wave laser backgrounds.

It has been known for some time that 2-loop renormalization group equations of a dimensionless parameter can be solved in a closed form in terms of the Lambert $W$ function. We apply the method to a generic theory with a Gaussian fixed point to construct renormalization group invariant physical parameters such as a coupling constant and a physical squared mass. As a further application, we speculate a possible exact effective potential for the $O(N)$ linear sigma model in four dimensions.

A model that gives rise to vacuum bubbles is considered where the domain wall field interacts with another real scalar field, resulting in the formation of domain ribbons within the host domain wall. Ribbon-antiribbon annihilations produce elementary bosons whose mass inside the wall is different from the mass in vacuum. Two cases are considered, where the bosons get trapped either within the bubble wall or the bosons get trapped within the vacuum enclosed by the bubble. The bosonic (meta)stabilization effect on the bubble is examined in each case. It is found that when the bosons become trapped within the bubble wall, the stabilization mechanism lasts for only a limited amount of time, and then the bubble undergoes unchecked collapse. However, when the bosons become trapped within the bubble’s interior volume, the bubble can be long-lived, provided that it has a sufficiently thin wall.

A string-inspired effective theory of gravity, containing Gauss-Bonnet invariant interacting with a scalar field, is considered in view of obtaining cosmological dark energy solutions. A Lagrange multiplier is inserted into the action in order to achieve the cosmological reconstruction by selecting suitable forms of couplings and potentials. Several cosmological exact solutions (including dark energy of quintessence, phantom, or Little Rip type) are derived in the presence and in the absence of the Lagrange multiplier showing the difference in the two dynamical approaches. In the models that we consider, the Lagrange multiplier behaves as a sort of dust fluid that realizes the transitions between matter-dominated and dark energy epochs. The relation between Lagrange multipliers and Noether symmetries is discussed.

The complete form of the high-temperature expansion of the one-loop contribution to the free energy of a scalar field on a stationary gravitational background is derived. The explicit expressions for the divergent and finite parts of the high-temperature expansion in a three-dimensional space without boundaries are obtained. These formulas generalize the known one for the stationary spacetime. In particular, we confirm that for a massless conformal scalar field the leading correction to the Planck law proportional to the temperature squared turns out to be nonzero due to the nonstatic nature of the metric. The explicit expression for the so-called energy-time anomaly is found. The interrelation between this anomaly and the conformal (trace) anomaly is established. The natural simplest Lagrangian for the “Killing vector field” is given.

We improve the effective-one-body (EOB) description of nonspinning coalescing black-hole binaries by incorporating several recent analytical advances, notably: (i) logarithmic contributions to the conservative dynamics; (ii) resummed horizon-absorption contribution to the orbital angular momentum loss; and (iii) a specific radial component of the radiation-reaction force implied by consistency with the azimuthal one. We then complete this analytically improved EOB model by comparing it to accurate numerical-relativity (NR) simulations performed by the Caltech-Cornell-CITA group for mass ratios $q=(1,2,3,4,6)$. In particular, the comparison to NR data allows us to determine with high accuracy ($\sim {10}^{-4}$) the value of the main EOB radial potential: $A(u;\nu )$, where $u=GM/(R{c}^2)$ is the interbody gravitational potential and $\nu =q/(q+1{)}^2$ is the symmetric mass ratio. We introduce a new technique for extracting from NR data an intrinsic measure of the phase evolution [$Q_{\omega }(\omega )$ diagnostics]. Aligning the NR-completed EOB quadrupolar waveform and the NR one at low frequencies, we find that they keep agreeing (in phase and amplitude) within the NR uncertainties throughout the evolution for all mass ratios considered. We also find good agreement for several subdominant multipoles without having to introduce and tune any extra parameters.

The collision of two $D$-dimensional, ultra-relativistic particles—described in general relativity as Aichelburg-Sexl shock waves—is inelastic. In first-order perturbation theory, the fraction of the initial center-of-mass energy radiated away was recently shown to be $1/2-1/D$. Here, we extend the formalism to higher orders in perturbation theory, and derive a general expression to extract the inelasticity—valid nonperturbatively—based on the Bondi mass-loss formula. Then, to clarify why perturbation theory captures relevant physics of a strong-field process in this problem, we provide one variation of the problem where the perturbative framework breaks down: the collision of ultra-relativistic charged particles. The addition of charge, and the associated repulsive nature of the source, originates an extra radiation burst, which we argue to be an artifact of the perturbative framework, veiling the relevant physics.

We investigate properties of generalized time-dependent $q$-deformed coherent states for a noncommutative harmonic oscillator. The states are shown to satisfy a generalized version of Heisenberg’s uncertainty relations. For the initial value in time the states are demonstrated to be squeezed, i.e., the inequalities are saturated, whereas when time evolves the uncertainty product oscillates away from this value albeit still respecting the relations. For the canonical variables on a noncommutative space we verify explicitly that Ehrenfest’s theorem holds at all times. We conjecture that the model exhibits revival times to infinite order. Explicit sample computations for the fractional revival times and superrevival times are presented.

This analysis aims at exploring what can be said about the growth rate of magnetized inhomogeneities under two concurrent hypotheses: a phase of quasi—de Sitter dynamics driven by a single inflaton field and the simultaneous presence of a spectator field coupled to gravity and to the gauge sector. Instead of invoking ad hoc correlations between the various components, the system of scalar inhomogeneities is diagonalized in terms of two gauge-invariant quasinormal modes whose weighted sum gives the curvature perturbations on comoving orthogonal hypersurfaces. The predominance of the conventional adiabatic scalar mode implies that the growth rate of magnetized inhomogeneities must not exceed 2.2 in Hubble units if the conventional inflationary phase is to last about 70 e-folds and for a range of slow roll parameters between 0.1 and 0.001. Longer and shorter durations of the quasi—de Sitter stage lead, respectively, either to tighter or to looser bounds which are anyway more constraining than the standard backreaction demands imposed on the gauge sector. Since a critical growth rate of order 2 leads to a quasiflat magnetic energy spectrum, the upper bounds on the growth rate imply a lower bound on the magnetic spectral index. The advantages of the uniform curvature gauge are emphasized and specifically exploited throughout the treatment of the multicomponent system characterizing this class of problems.

We construct lists of supersymmetric models with extended gauge groups at intermediate steps, all of which are inspired by $SO(10)$ unification. We consider three different kinds of setups: (i) the model has exactly one additional intermediate scale with a left-right (LR) symmetric group; (ii) $SO(10)$ is broken to the LR group via an intermediate Pati-Salam scale; and (iii) the LR group is broken into $SU(3{)}_c\times SU(2{)}_L\times U(1{)}_R\times U(1{)}_{B-L}$, before breaking to the standard model (SM) group. We use sets of conditions, which we call the “sliding mechanism,” which yield unification with the extended gauge group(s) allowed at arbitrary intermediate energy scales. All models thus can have new gauge bosons within the reach of the LHC, in principle. We apply additional conditions, such as perturbative unification, renormalizability and anomaly cancellation and find that, despite these requirements, for the ansatz (i) with only one additional scale still around 50 different variants exist that can have a LR symmetry below 10 TeV. For the more complicated schemes (ii) and (iii) literally thousands of possible variants exist, and for scheme (ii) we have also found variants with very low Pati-Salam scales. We also discuss possible experimental tests of the models from measurements of supersymmetry masses. Assuming mSugra boundary conditions we calculate certain combinations of soft terms, called “invariants,” for the different classes of models. Values for all the invariants can be classified into a small number of sets, which contain information about the class of models and, in principle, the scale of beyond-minimal supersymmetric extension of the Standard Model physics, even in case the extended gauge group is broken at an energy beyond the reach of the LHC.

We take up again the study of the mass spectrum of the quark sector in a model with gauge symmetry $SU(3{)}_c\otimes SU(3{)}_L\otimes U(1{)}_X$ (331). In a special type II-like 3-3-1 model, we obtain specific zero-texture mass matrices for the quarks which predict four massless quarks $(u,c,d,s)$ and two massive quarks $(b,t)$ at the electroweak scale ($\sim \mathrm{GeV}$). By considering the mixing between the standard model quarks and new exotic quarks at large scales predicted by the model, we find that a third quark (associated to the charm quark) acquires a mass. The remaining light quarks $(u,d,s)$ get small masses ($\sim \mathrm{MeV}$) via radiative corrections.