We calculate gauge theory one-loop amplitudes with the aid of the complex shift used in the Britto-Cachazo-Feng-Witten (BCFW) recursion relations of tree amplitudes. We apply the shift to the integrand and show that the contribution from the limit of infinite shift vanishes after integrating over the loop momentum, with a judicious choice of basis for polarization vectors. This enables us to write the one-loop amplitude in terms of on shell tree and lower-point one-loop amplitudes. Some of the tree amplitudes are forward amplitudes. We show that their potential singularities do not contribute and the BCFW recursion relations can be applied in such a way as to avoid these singularities altogether. We calculate in detail $n$-point one-loop amplitudes for $n=2$, 3, 4, and outline the generalization of our method to $n>4$.

The hybrid gauge transformation and its nontrivial phenomenological implications are investigated using the noncommutative gauge theory with the Seiberg-Witten map expanded scenario. Particularly, the $e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-}$ process is studied with a generalized noncommutative standard model (NCSM) including massive neutrinos and neutrino-photon interaction. In this model, the hybrid gauge transformation in the lepton sector is naturally introduced through the requirement of gauge invariance of the seesaw neutrino mass term. It is shown that in the NCSM without hybrid gauge transformation the noncommutative correction to the scattering amplitude of the $e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-}$ process appears only as a phase factor, predicting no new physical deviation in the cross section. However, when the hybrid feature is considered, the noncommutative effect appears in the single channel process. The cross section and angular distribution are analyzed in the laboratory frame including Earth’s rotation. It is proposed that pair production of muons in the upcoming TeV International Linear Collider (ILC) can provide an ideal opportunity for exploring not only the NC space-time, but also the mathematical structure of the corresponding gauge theory.

We discuss hairy black hole solutions with scalar hair of scaling dimension $\Delta$ and (small) electromagnetic coupling $q^2$, near extremality. Using trial functions, we show that hair forms below a critical temperature $T_c$ in the region of parameter space $(\Delta ,q^2)$ above a critical line $q_c^2(\Delta )$. For $\Delta >{\Delta }_0$, the critical coupling $q_c^2$ is determined by the ${\mathrm{AdS}}_2$ geometry of the horizon. For $\Delta <{\Delta }_0$, $q_c^2$ is below the value suggested by the near horizon geometry at extremality. We provide an analytic estimate of ${\Delta }_0$ (numerically, ${\Delta }_0\approx 0.64$). We also compute analytically the true critical line for the entire range of the scaling dimension. In particular for $q=0$, we obtain an instability down to the unitarity bound. We perform explicit analytic calculations of $T_c$, the condensate and the conductivity. We show that the energy gap in units of $T_c$ diverges as we approach the critical line ($T_c\to 0$).

We consider $\mathcal{N}=2$ SQCD with the $\mathrm{U}(N)$ gauge group and $N_f$ flavors ($N_f>N$) perturbed by an $\mathcal{N}=2$ breaking deformation–a small mass term $\mu$ for the adjoint matter. We study $r$-vacua, with the constraint $\frac{2}{3}{N}_f<r\le N$. At large values of the parameter $\xi \sim \mu m$ ($m$ is a typical value of the quark masses) $r$ quark flavors condense, by construction. The effective low-energy theory with the gauge group $\mathrm{U}(r)\times \mathrm{U}(1{)}^{N-r}$ is at weak coupling. Upon reducing $\xi$ the original theory undergoes a crossover transition from weak to strong coupling. As the original theory becomes strongly coupled, at low energies it is described by a weakly coupled infrared-free dual theory with the gauge group $\mathrm{U}(N_f-r)\times \mathrm{U}(1{)}^{N-N_f+r}$ and $N_f$ light dyon flavors. These dyons condense triggering formation of non-Abelian strings which still confine monopoles, rather than quarks, contrary to naive duality arguments. “Instead-of-confinement” mechanism for quarks and gauge bosons of the original theory takes place: screened quarks and gauge bosons of the original theory decay, on curves of the marginal stability (CMS), into confined monopole-antimonopole pairs that form stringy mesons. Next, we increase the deformation parameter $\mu$ thus decoupling the adjoint fields. Then our theory flows to $\mathcal{N}=1$ SQCD. The gauge group of the dual theory becomes $U(N_f-r)$. We show that the dual theory is weakly coupled if we are sufficiently close to the Argyres–Douglas point. The “instead-of-confinement” mechanism for quarks and gauge bosons survives in the limit of large $\mu$. It determines low-energy non-Abelian dynamics in the $r$-vacua of $\mathcal{N}=1$ SQCD.

We study scattering of polarized light by a rotating (Kerr) black hole of mass $M$ and angular momentum $J$. In order to keep trace of the polarization dependence of photon trajectories one can use the following dimensionless parameter: $\epsilon =\pm (\omega M{)}^{-1}$, where $\omega$ is the photon frequency and the sign $+$ ($-$) corresponds to the right (left) circular polarization. We assume that $|\epsilon |\ll 1$ and use the modified geometric optics approximation developed in [Phys. Rev. D 84, 044026 (2011)]; that is, we include the first order in $\epsilon$ polarization-dependent terms into the eikonal equation. These corrections modify late-time behavior of photons. We demonstrate that the photon moves along a null curve, which in the limit $\epsilon =0$ becomes a null geodesic. We focus on the scattering problem for polarized light. Namely, we consider the following problems: (i) How does the photon’s bending angle depend on its polarization? (ii) How does the position of the image of a pointlike source depend on its polarization? (iii) How does the arrival time of photons depend on their polarization? We perform the numerical calculations that illustrate these effects for an extremely rotating black hole and discuss their possible applications.

It is a known fact that the Kerr-Schild type solutions in general relativity satisfy both exact and linearized Einstein field equations. We show that this property remains valid also for a special class of the Kerr-Schild metrics in arbitrary dimensions in generic quadratic curvature theory. In addition to the anti-de Sitter (AdS) wave (or Siklos) metric which represents plane waves in an AdS background, we present here a new exact solution, in this class, to the quadratic gravity in $D$ dimensions which represents a spherical wave in an AdS background. The solution is a special case of the Kundt metrics belonging to spacetimes with constant curvature invariants.

We show by explicit computations that the product of all the horizon areas is independent of the mass, regardless of the topology of the horizons. The universal character of this relation holds for all known five-dimensional asymptotically flat black rings, and for black strings. This gives further evidence for the crucial role that the thermodynamic properties at each horizon play in understanding the entropy at the microscopic level. To this end we propose a “first law” for the inner Cauchy horizons of black holes. The validity of this formula, which seems to be universal, was explicitly checked in all cases.

We consider a theory of gravity with a hidden extra dimension and metric-dependent torsion. A set of physically motivated constraints are imposed on the geometry so that the torsion stays confined to the extra dimension and the extra dimension stays hidden at the level of four-dimensional geodesic motion. At the kinematic level, the theory maps onto general relativity, but the dynamical field equations that follow from the action principle deviate markedly from the standard Einstein equations. We study static spherically symmetric vacuum solutions and homogeneous-isotropic cosmological solutions that emerge from the field equations. In both cases, we find solutions of significant physical interest. Most notably, we find positive mass solutions with naked singularity that match the well-known Schwarzschild solution at large distances but lack an event horizon. In the cosmological context, we find an oscillatory scenario, in contrast to the inevitable singular big bang of the standard cosmology.

We find the connection between thermodynamic quantities and quasinormal frequencies in Lifshitz black holes. It is shown that the globally stable Lifshitz black holes have pure imaginary quasinormal frequencies. We also show that by employing the Maggiore’s method, both the horizon area and the entropy can be quantized for these black holes.

If the Hamiltonian of a quantum field theory is taken to be a timelike isometry, the vacuum state remains empty for all time. We search for such stationary vacua in anti-de Sitter space. By considering conjugacy classes of the Lorentz group, we find interesting one-parameter families of stationary vacua in three-dimensional anti-de Sitter space. In particular, there exists a family of rotating Rindler vacua, labeled by the rotation parameter $\beta$, which are related to the usual Rindler vacuum by nontrivial Bogolubov transformations. Rotating Rindler-AdS space possesses not only an observer-dependent event horizon but even an observer-dependent ergosphere. We also find rotating vacua in global AdS provided a certain region of spacetime is excluded.

A new variational approach for general relativity and modified theories of gravity is presented. In addition to the metric tensor, two independent affine connections enter the action as dynamical variables. In the matter action the dependence upon one of the connections is left completely unspecified. When the variation is applied to the Einstein-Hilbert action the Einstein field equations are recovered. However when applied to $f(R)$ and scalar-tensor theories, it yields gravitational field equations which differ from their equivalents obtained with a metric or Palatini variation and reduce to the former ones only when no connections appear in the matter action.

We quantize to completion an inflationary universe with small inhomogeneities in the framework of loop quantum cosmology. The homogeneous setting consists of a massive scalar field propagating in a closed, homogeneous scenario. We provide a complete quantum description of the system employing loop quantization techniques. After introducing small inhomogeneities as scalar perturbations, we identify the true physical degrees of freedom by means of a partial gauge fixing, removing all the local degrees of freedom except the matter perturbations. We finally combine a Fock description for the inhomogeneities with the polymeric quantization of the homogeneous background, providing the quantum Hamiltonian constraint of the composed system. Its solutions are then completely characterized, owing to the suitable choice of quantum constraint, and the physical Hilbert space is constructed. Finally, we consider the analog description for an alternate gauge and, moreover, in terms of gauge-invariant quantities. In the deparametrized model, all these descriptions are unitarily equivalent at the quantum level.

We analyze the scalar synchrotron radiation emitted by a source in circular orbits, stable and unstable, direct and retrograde, around a rotating black hole within the framework of quantum field theory in curved spacetimes at tree level. We also analyze the radiation which escapes to infinity, showing that, in accordance with superradiance, it can be amplified for the case of direct orbits.

We find constant scalar curvature Type-N and Type-D solutions in all higher curvature gravity theories with actions of the form $f(R_{\mu \nu })$ that are built on the Ricci tensor, but not on its derivatives. In our construction, these higher derivative theories inherit some of the previously studied solutions of the cosmological topologically massive gravity and the new massive gravity field equations, once the parameters of the theories are adjusted. Besides the generic higher curvature theory, we have considered in some detail the examples of the quadratic curvature theory, the cubic curvature theory, and the Born-Infeld extension of the new massive gravity.

We compute the vector and tensor contributions to the luminosity distance fluctuations in first order perturbation theory, and we expand them in spherical harmonics. This work presents the formalism with a first application to a stochastic background of primordial gravitational waves.

We argue that in an inflationary cosmology a consequence of the lack of time translational invariance is that spontaneous breaking of a continuous symmetry and Goldstone’s theorem do not imply the existence of massless Goldstone modes. We study spontaneous symmetry breaking in an $O(2)$ model, and implications for $O(N)$ in de Sitter space-time. The Goldstone mode acquires a radiatively generated mass as a consequence of infrared divergences, and the continuous symmetry is spontaneously broken for any finite $N$; however there is a first order phase transition as a function of the Hawking temperature $T_H=H/2\pi$. For $O(2)$ the symmetry is spontaneously broken for $T_H<T_c={\lambda }^{1/4}v/2.419$ where $\lambda$ is the quartic coupling and $v$ is the tree-level vacuum expectation value and the Goldstone mode acquires a radiatively generated mass ${\mathcal{M}}_{\pi }^2\propto {\lambda }^{1/4}H$. The first order nature of the transition is a consequence of the strong infrared behavior of minimally coupled scalar fields in de Sitter space-time; the jump in the order parameter at $T_H=T_c$ is ${\sigma }_{0c}\simeq 0.61H/{\lambda }^{1/4}$. In the strict $N\to \infty$ the symmetry cannot be spontaneously broken. Furthermore, the lack of kinematic thresholds imply that the Goldstone modes decay into Goldstone and Higgs modes by emission and absorption of superhorizon quanta.

This paper is concerned with string cosmology and the dynamics of multiple scalar fields in potentials that can become negative, and their features as (early) dark energy models. Our point of departure is the “string axiverse,” a scenario that motivates the existence of cosmologically light axion fields as a generic consequence of string theory. We couple such an axion to its corresponding modulus. We give a detailed presentation of the rich cosmology of such a model, ranging from the setting of initial conditions on the fields during inflation, to the asymptotic future. We present some simplifying assumptions based on the fixing of the axion decay constant $f_a$, and on the effective field theory when the modulus trajectory is adiabatic, and find the conditions under which these assumptions break down. As a by-product of our analysis, we find that relaxing the assumption of fixed $f_a$ leads to the appearance of a new metastable de Sitter region for the modulus without the need for uplifting by an additional constant. A dynamical systems analysis reveals the existence of many fixed point attractors, repellers and saddle points, which we analyze in detail. We also provide geometric interpretations of the phase space. The fixed points can be used to bound the couplings in the model. A systematic scan of certain regions of parameter space reveals that the future evolution of the Universe in this model can be rich, containing multiple epochs of accelerated expansion.

We discuss irreducible statistical limitations of future ton-scale dark matter direct detection experiments. We focus in particular on the coverage of confidence intervals, which quantifies the reliability of the statistical method used to reconstruct the dark matter parameters and the bias of the reconstructed parameters. We study 36 benchmark dark matter models within the reach of upcoming ton-scale experiments. We find that approximate confidence intervals from a profile-likelihood analysis exactly cover or overcover the true values of the weakly interacting massive particle (WIMP) parameters, and hence are conservative. We evaluate the probability that unavoidable statistical fluctuations in the data might lead to a biased reconstruction of the dark matter parameters, or large uncertainties on the reconstructed parameter values. We show that this probability can be surprisingly large, even for benchmark models leading to a large event rate of order a hundred counts. We find that combining data sets from two different targets leads to improved coverage properties, as well as a substantial reduction of statistical bias and uncertainty on the dark matter parameters.

If dark matter (DM) is a weakly interacting massive particle (WIMP) that is a thermal relic of the early Universe, then its total self-annihilation cross section is revealed by its present-day mass density. This result for a generic WIMP is usually stated as $⟨\sigma v⟩\approx 3\times {10}^{-26}{\mathrm{cm}}^3{\mathrm{s}}^{-1}$, with unspecified uncertainty, and taken to be independent of WIMP mass. Recent searches for annihilation products of DM annihilation have just reached the sensitivity to exclude this canonical cross section for 100% branching ratio to certain final states and small WIMP masses. The ultimate goal is to probe all kinematically allowed final states as a function of mass and, if all states are adequately excluded, set a lower limit to the WIMP mass. Probing the low-mass region is further motivated due to recent hints for a light WIMP in direct and indirect searches. We revisit the thermal relic abundance calculation for a generic WIMP and show that the required cross section can be calculated precisely. It varies significantly with mass at masses below 10 GeV, reaching a maximum of $5.2\times {10}^{-26}{\mathrm{cm}}^3{\mathrm{s}}^{-1}$ at $m\approx 0.3\mathrm{GeV}$, and is $2.2\times {10}^{-26}{\mathrm{cm}}^3{\mathrm{s}}^{-1}$ with feeble mass dependence for masses above 10 GeV. These results, which differ significantly from the canonical value and have not been taken into account in searches for annihilation products from generic WIMPs, have a noticeable impact on the interpretation of present limits from Fermi-LAT and $\mathrm{WMAP}+\mathrm{ACT}$.

We implement slow roll reconstruction—an optimal solution to the inverse problem for inflationary cosmology—within ModeCode, a publicly available solver for the inflationary dynamics. We obtain up-to-date constraints on the reconstructed inflationary potential, derived from the WMAP 7 year data set and South Pole Telescope observations, combined with large scale structure data derived from SDSS Data Release 7. Using ModeCode in conjunction with the MultiNest sampler, we compute Bayesian evidence for the reconstructed potential at each order in the truncated slow roll hierarchy. We find that the data are well-described by the first two slow roll parameters, $ϵ$ and $\eta$, and that there is no need to include a nontrivial $\xi$ parameter.