We consider how to take an orbifold reduction for the multiple $M2$-brane theory recently proposed by Bagger and Lambert, and discuss its relation to Chern-Simons theories. Starting from the infinite dimensional 3 algebra realized as Nambu bracket on a 3 torus, we first suggest an orbifolding prescription for various fields. Then we introduce a second truncation, which effectively reduces the internal space to a 2 torus. Eventually, one obtains a large-$N$ limit of Chern-Simons gauge theories coupled to matter fields. We consider an Abelian orbifold ${\mathbb{C}}^4/{\mathbb{Z}}_n$, and illustrate how one can arrive at the $\mathcal{N}=6$ supersymmetric theories with gauge groups $U(N)\times U(N)$ and Chern-Simons levels ($k,-k$), as recently constructed by Aharony, Bergman, Jafferis, and Maldacena.

We develop an internal gauge theory using a covariant star product. The space-time is a symplectic manifold endowed only with torsion but no curvature. It is shown that, in order to assure the restrictions imposed by the associativity property of the star product, the torsion of the space-time has to be covariant constant. An illustrative example is given and it is concluded that in this case the conditions necessary to define a covariant star product on a symplectic manifold completely determine its connection.

Many extensions of the standard model predict the existence of hidden sectors that may contain unbroken Abelian gauge groups. We argue that in the presence of quantum decoherence photons may convert into hidden photons on sufficiently long time scales and show that this effect is strongly constrained by CMB and supernova data. In particular, Planck-scale suppressed decoherence scales $D\propto {\omega }^2/M_{\mathrm{Pl}}$ (characteristic for noncritical string theories) are incompatible with the presence of even a single hidden U(1). The absence of photon decoherence in this simple standard model extension complements other strong bounds derived from solar, reactor, and atmospheric neutrinos.

We describe a background independent quantization of the scalar field that provides an explicit realization of Fock-like states and associated operators in a polymer Hilbert space. The vacuum expectation values of the commutator and anticommutator of the creation and annihilation operators become energy dependent, and exhibit a surprising transition to fermionic behavior at high energy. Furthermore, the approach yields a modified dispersion relation with a leading correction proportional to the momentum cubed. These results suggests a fundamental change in the ultraviolet properties of quantum fields.

We show that the black hole laser effect discovered by Corley and Jacobson should be described in terms of frequency eigenmodes that are spatially bound. The spectrum contains a discrete and finite set of complex frequency modes, which appear in pairs and which encode the laser effect. In addition, it contains real frequency modes that form a continuous set when space is infinite, and which are only elastically scattered, i.e., not subject to any Bogoliubov transformation. The quantization is straightforward, but the calculation of the asymptotic fluxes is rather involved. When the number of complex frequency modes is small, our expressions differ from those given earlier. In particular, when the region between the horizons shrinks, there is a minimal distance under which no complex frequency mode exists, and no radiation is emitted. Finally, we relate this effect to other dynamical instabilities found for rotating black holes and in electric fields, and we give the conditions to get this type of instability.

We present the first attempt at calibrating the effective-one-body (EOB) model to accurate numerical relativity simulations of spinning, nonprecessing black-hole binaries. Aligning the EOB and numerical waveforms at low frequency over a time interval of $1000M$, we first estimate the phase and amplitude errors in the numerical waveforms and then minimize the difference between numerical and EOB waveforms by calibrating a handful of EOB-adjustable parameters. In the equal-mass, spin aligned case, we find that phase and fractional amplitude differences between the numerical and EOB $(2,2)$ mode can be reduced to 0.01 radian and 1%, respectively, over the entire inspiral waveforms. In the equal-mass, spin antialigned case, these differences can be reduced to 0.13 radian and 1% during inspiral and plunge, and to 0.4 radian and 10% during merger and ringdown. The waveform agreement is within numerical errors in the spin aligned case while slightly over numerical errors in the spin antialigned case. Using Enhanced LIGO and Advanced LIGO noise curves, we find that the overlap between the EOB and the numerical $(2,2)$ mode, maximized over the initial phase and time of arrival, is larger than 0.999 for binaries with total mass $30M_{\odot }–200M_{\odot }$. In addition to the leading $(2,2)$ mode, we compare four subleading modes. We find good amplitude and frequency agreements between the EOB and numerical modes for both spin configurations considered, except for the $(3,2)$ mode in the spin antialigned case. We believe that the larger difference in the $(3,2)$ mode is due to the lack of knowledge of post-Newtonian spin effects in the higher modes.

We study thermodynamic instability of a class of ($n+1$)-dimensional charged dilatonic spherically symmetric black holes in the background of the anti–de Sitter universe. We calculate the quasilocal mass of the anti–de Sitter dilaton black hole through the use of the subtraction method of Brown and York. We find a Smarr-type formula and perform a stability analysis in the canonical ensemble and disclose the effect of the dilaton field on the thermal stability of the solutions. Our study shows that the solutions are thermally stable for small $\alpha$, while for large $\alpha$ the system has an unstable phase, where $\alpha$ is a coupling constant between the dilaton and matter field.

We present a calculation of the scalar-field self-force (SSF) acting on a scalar-charge particle in a strong-field orbit around a Kerr black hole. Our calculation specializes to circular and equatorial geodesic orbits. The analysis is an implementation of the standard mode-sum regularization scheme: We first calculate the multipole modes of the scalar-field perturbation using numerical integration in the frequency domain, and then apply a certain regularization procedure to each of the modes. The dissipative piece of the SSF is found to be consistent with the flux of energy and angular-momentum carried by the scalar waves through the event horizon and out to infinity. The conservative (radial) component of the SSF is calculated here for the first time. When the motion is retrograde this component is found to be repulsive (outward pointing, as in the Schwarzschild case) for any spin parameter $a$ and (Boyer-Lindquist) orbital radius $r_0$. However, for prograde orbits we find that the radial SSF becomes attractive (inward pointing) for $r_0>r_c(a)$, where $r_c$ is a critical $a$-dependent radius at which the radial SSF vanishes. The dominant conservative effect of the SSF in Schwarzschild spacetime is known to be of third post-Newtonian (3PN) order (with a logarithmic running). Our numerical results suggest that the leading-order PN correction due to the black hole’s spin arises from spin-orbit coupling at 3PN order, which dominates the overall SSF effect at large $r_0$. In PN language, the change of sign of the radial SSF is attributed to an interplay between the spin-orbit term ($\propto -a{r}_0^{-4.5}$) and the Schwarzschild term ($\propto r_0^{-5}\log r_0$).

We argue that the total number of distinguishable locally Friedmann “universes” generated by eternal inflation is proportional to the exponent of the entropy of inflationary perturbations and is limited by $e^{e^{3N}}$, where $N$ is the number of $e$-folds of slow-roll posteternal inflation. For simplest models of chaotic inflation, $N$ is approximately equal to de Sitter entropy at the end of eternal inflation; it can be exponentially large. However, not all of these universes can be observed by a local observer. In the presence of a cosmological constant $\Lambda$ the number of distinguishable universes is bounded by $e^{|\Lambda {|}^{-3/4}}$. In the context of the string theory landscape, the overall number of different universes is expected to be exponentially greater than the total number of vacua in the landscape. We discuss the possibility that the strongest constraint on the number of distinguishable universes may be related not to the properties of the multiverse but to the properties of observers.

We study how direct detection of the inflationary gravitational wave background constrains inflationary parameters and complements CMB polarization measurements. The error ellipsoids calculated using the Fisher information matrix approach with Planck and the direct detection experiment, Big Bang Observer (BBO), show different directions of parameter degeneracy, and the degeneracy is broken when they are combined. For a slow-roll parametrization, we show that BBO could significantly improve the constraints on the tensor-to-scalar ratio compared with Planck alone. We also look at a quadratic and a natural inflation model. In both cases, if the temperature of reheating is also treated as a free parameter, then the addition of BBO can significantly improve the error bars. In the case of natural inflation, we find that the addition of BBO could even partially improve the error bars of a cosmic variance-limited CMB experiment.

We address the challenging issue of how $CP$ violation is realized in higher dimensional gauge theories without higher dimensional elementary scalar fields. In such theories interactions are basically governed by a gauge principle and therefore to get $CP$ violating phases is a nontrivial task. It is demonstrated that $CP$ violation is achieved as the result of compactification of extra dimensions, which is incompatible with the 4-dimensional $CP$ transformation. As a simple example we adopt a 6-dimensional U(1) model compactified on a 2-dimensional orbifold $T^2/Z_4$. We argue that the 4-dimensional $CP$ transformation is related to the complex structure of the extra space and show how the $Z_4$ orbifolding leads to $CP$ violation. We confirm by explicit calculation of the interaction vertices that $CP$ violating phases remain even after the rephasing of relevant fields. For completeness, we derive a rephasing invariant $CP$ violating quantity, following a similar argument in the Kobayashi-Maskawa model which led to the Jarlskog parameter. As an example of a $CP$ violating observable we briefly comment on the electric dipole moment of the electron.

We explore, within the warped extra dimensional framework, the possibility of finding antimatter signals in cosmic rays (CRs) from dark matter (DM) annihilation. We find that exchange of order 100 GeV radion, an integral part of this class of models, generically results in a sizable Sommerfeld enhancement of the annihilation rate for DM mass at the TeV scale. No ad hoc dark sector is required to obtain boosted annihilation cross sections and hence signals. Such a mild hierarchy between the radion and DM masses can be natural due to the pseudo-Goldstone boson nature of the radion. We study the implications of a Sommerfeld enhancement specifically in warped grand unified theory (GUT) models, where proton stability implies a DM candidate. We show, via a partially unified Pati-Salam group, how to incorporate a custodial symmetry for $Z\to b\overline{b}$ into the GUT framework such that a few TeV Kaluza-Klein (KK) mass scale is allowed by electroweak precision tests. Among such models, the one with the smallest $SO(10)$ (fully unified) representation, with $SU(5)$ hypercharge normalization, allows us to decouple the DM from the electroweak gauge bosons. Thus, a correct DM relic density can be obtained and direct detection bounds are satisfied. Looking at robust CR observables, we find a possible future signal in the $\overline{p}/p$ flux ratio consistent with current constraints. Using a different choice of representations, we show how to embed in this GUT model a similar custodial symmetry for the right-handed tau, allowing it to be strongly coupled to KK particles. Such a scenario might lead to an observed signal in CR positrons; however, the DM candidate in this case cannot constitute all of the DM in the Universe. As an aside and independent of the GUT or DM model, the strong coupling between KK particles and tau’s can lead to striking LHC signals.

Using a covariant spectator quark model we estimate valence quark contributions to the $F_1^{*}(Q^2)$ and $F_2^{*}(Q^2)$ transition form factors for the $\gamma N\to P_{11}(1440)$ reaction. The Roper resonance, $P_{11}(1440)$, is assumed to be the first radial excitation of the nucleon. The present model requires no extra parameters except for those already fixed by previous studies of the nucleon. Our results are consistent with the experimental data in the high $Q^2$ region, and those from lattice QCD. We also estimate the meson cloud contributions, focusing on the low $Q^2$ region, where they are expected to be dominant.

We report a search for single top quark production with the CDF II detector using $2.1{\mathrm{fb}}^{-1}$ of integrated luminosity of $p\overline{p}$ collisions at $\sqrt{s}=1.96\mathrm{TeV}$. The data selected consist of events characterized by large energy imbalance in the transverse plane and hadronic jets, and no identified electrons and muons, so the sample is enriched in $W\to \tau \nu$ decays. In order to suppress backgrounds, additional kinematic and topological requirements are imposed through a neural network, and at least one of the jets must be identified as a $b$ quark jet. We measure an excess of signal-like events in agreement with the standard model prediction, but inconsistent with a model without single top quark production by 2.1 standard deviations ($\sigma$), with a median expected sensitivity of $1.4\sigma$. Assuming a top quark mass of $175\mathrm{GeV}/c^2$ and ascribing the excess to single top quark production, the cross section is measured to be ${4.9}_{-2.2}^{+2.5}(\mathrm{stat}+\mathrm{syst})\mathrm{pb}$, consistent with measurements performed in independent data sets and with the standard model prediction.

Using the Berezin-Marinov pseudoclassical formulation of the spin particle we propose a classical model of spin noncommutativity. In the nonrelativistic case, the Poisson brackets between the coordinates are proportional to the spin angular momentum. The quantization of the model leads to the noncommutativity with mixed spatial and spin degrees of freedom. A modified Pauli equation, describing a spin half particle in an external electromagnetic field is obtained. We show that nonlocality caused by the spin noncommutativity depends on the spin of the particle; for spin zero, nonlocality does not appear, for spin half, $\Delta x\Delta y\ge {\theta }^2/2$, etc. In the relativistic case the noncommutative Dirac equation was derived. For that we introduce a new star product. The advantage of our model is that in spite of the presence of noncommutativity and nonlocality, it is Lorentz invariant. Also, in the quasiclassical approximation it gives noncommutativity with a nilpotent parameter.

In this article I argue that the expression for entropic force, used as a starting point in Verlinde’s derivation of Newton’s law [E. P. Verlinde, arXiv:1001.0785], can be deduced from the first principles if one assumes that the microscopic theory behind his construction is the topological $\mathsf{S}\mathsf{O}(4,1)$ BF theory coupled to particles.

We show a uniqueness theorem for charged dipole rotating black rings in the bosonic sector of five-dimensional minimal supergravity, generalizing our previous work [arXiv:0901.4724] on the uniqueness of charged rotating black holes with topologically spherical horizon in the same theory. More precisely, assuming the existence of two commuting axial Killing vector fields and the same rod structure as the known solutions, we prove that an asymptotically flat, stationary charged rotating black hole with nondegenerate connected event horizon of cross-section topology $S^1\times S^2$ in the five-dimensional Einstein-Maxwell-Chern-Simons theory—if exists—is characterized by the mass, charge, two independent angular momenta, dipole charge, and the ratio of the $S^2$ radius to the $S^1$ radius. As anticipated, the necessity of specifying dipole charge—which is not a conserved charge—is the new, distinguished ingredient that highlights difference between the present theorem and the corresponding theorem for vacuum case, as well as difference from the case of topologically spherical horizon within the same minimal supergravity. We also consider a similar boundary value problem for other topologically nontrivial black holes within the same theory, and in particular, discuss some nontrivial issues that arise when attempting to generalize the present uniqueness results to include black lenses—provided there exists such a solution in the theory.

Motivated by the possible extension into a supersymmetric Randall-Sundrum (RS) model, we investigate the properties of the vacuum expectation value (VEV) of the stress-energy tensor for a quantized bulk Dirac spinor field in the RS geometry and compare it with that for a real scalar field. This is carried out via the Green function method based on first principles without invoking the degeneracy factor, whose validity in a warp geometry is a priori unassured. In addition, we investigate the local behavior of the Casimir energy near the two branes. One salient feature we found is that the surface divergences near the two branes have opposite signs. We argue that this is a generic feature of the fermionic Casimir energy density due to its parity transformation in the fifth dimension. Furthermore, we investigate the self-consistency of the RS metric under the quantum correction due to the stress-energy tensor. It is shown that the VEV of the stress-energy tensor and the classical one become comparable near the visible brane if $k\simeq M\simeq M_{\mathrm{Pl}}$ (the requirement of no hierarchy problem), where $k$ is the curvature of the RS warped geometry and $M$ the five-dimensional Planck mass. In that case the self-consistency of the RS model that includes bulk fields is in doubt. If, however, $k\lesssim M$, then an approximate self-consistency of the RS-type metric may still be satisfied.

According to the standard cosmology, near the last scattering surface, the photons scattered via Compton scattering are just linearly polarized and then the primordial circular polarization of the cosmic microwave background (CMB) photons is zero. In this work we show that CMB polarization acquires a small degree of circular polarization when a background magnetic field is considered or the quantum electrodynamic sector of standard model is extended by Lorentz-noninvariant operators as well as noncommutativity. The existence of circular polarization for the CMB radiation may be verified during future observation programs, and it represents a possible new channel for investigating new physics effects.

The vacuum average value of the stress-energy tensor of a massive scalar field with nonminimal coupling $\xi$ to the curvature on the short-throat flat-space wormhole background is calculated. The final analysis is made numerically. It was shown that the energy-momentum tensor does not violate the null energy condition near the throat. Therefore, the vacuum polarization cannot self-consistently support the wormhole.