I extend the results of hep-th/0310137 to show that a general classical action for $D=2$, $\mathcal{N}=2$ sigma models on a non(anti)commutative superspace is not standard and contains infinite number of terms, which depend on the determinant of the non(anti)commutativity parameter $C^{\alpha \beta }$. I show that using Kähler normal coordinates the action can be written in a manifestly covariant manner. I introduce vector multiplets and obtain the $\mathcal{N}=1/2$ supersymmetry transformations of the theory in the Wess-Zumino gauge. By explicitly deriving the expressions for vector and twisted superfields on non(anti)commutative superspace, I study the classical aspects of gauged linear sigma models.

Many properties of black holes can be studied using acoustic analogues in the laboratory through the propagation of sound waves. We investigate in detail sound wave propagation in a rotating acoustic $(2+1)$-dimensional black hole, which corresponds to the “draining bathtub” fluid flow. We compute the quasinormal mode frequencies of this system and discuss late-time power-law tails. Because of the presence of an ergoregion, waves in a rotating acoustic black hole can be superradiantly amplified. We also compute superradiant reflection coefficients and instability time scales for the acoustic black hole bomb, the equivalent of the Press-Teukolsky black hole bomb. Finally we discuss quasinormal modes and late-time tails in a nonrotating canonical acoustic black hole, corresponding to an incompressible, spherically symmetric $(3+1)$-dimensional fluid flow.

In this article we lay foundations for a formal relationship of spin foam models of gravity and BF theory to their continuum canonical formulations. First the derivation of the spin foam model of the BF theory from the discrete BF theory action in $n$ dimensions is reviewed briefly. By foliating the underlying $n$ dimensional simplicial manifold using $n-1$ dimensional simplicial hypersurfaces, the spin foam model is reformulated. Then it is shown that spin network functionals arise naturally on the foliations. The graphs of these spin network functionals are dual to the triangulations of the foliating hypersurfaces. Quantum Transition amplitudes are defined. We calculate the transition amplitudes related to $2D$ BF theory explicitly. The application to the spin foam models of gravity is discussed briefly.

The existence of a minimum time uncertainty is usually argued to be a consequence of the combination of quantum mechanics and general relativity. Most of the studies that point to this result are nonetheless based on perturbative quantization approaches, in which the effect of matter on the geometry is regarded as a correction to a classical background. In this paper, we consider rainbow spacetimes constructed from doubly special relativity by using a modification of the proposals of Magueijo and Smolin. In these models, gravitational effects are incorporated (at least to a certain extent) in the definition of the energy-momentum of particles without adhering to a perturbative treatment of the backreaction. In this context, we derive and compare the expressions of the time uncertainty in quantizations that use as evolution parameter either the background or the rainbow time coordinates. These two possibilities can be regarded as corresponding to perturbative and nonperturbative quantization schemes, respectively. We show that, while a nonvanishing time uncertainty is generically unavoidable in a perturbative framework, an infinite time resolution can in fact be achieved in a nonperturbative quantization for the whole family of doubly special relativity theories with unbounded physical energy.

We study stationary and axisymmetric solutions of General Relativity, i.e., pure gravity, in four or higher dimensions. $D$-dimensional stationary and axisymmetric solutions are defined as having $D-2$ commuting Killing vector fields. We derive a canonical form of the metric for such solutions that effectively reduces the Einstein equations to a differential equation on an axisymmetric $D-2$ by $D-2$ matrix field living in three-dimensional flat space (apart from a subclass of solutions that instead reduce to a set of equations on a $D-2$ by $D-2$ matrix field living in two-dimensional flat space). This generalizes the Papapetrou form of the metric for stationary and axisymmetric solutions in four dimensions, and furthermore generalizes the work on Weyl solutions in four and higher dimensions. We analyze then the sources for the solutions, which are in the form of thin rods along a line in the three-dimensional flat space that the matrix field can be seen to live in. As examples of stationary and axisymmetric solutions, we study the five-dimensional rotating black hole and the rotating black ring, write the metrics in the canonical form and analyze the structure of the rods for each solution.

Soliton type solutions of a scalar model with a ${\Phi }^6$ self-interaction are analyzed for their density profiles as toy model of dark matter halos. We construct exact solutions with nontrivial ellipticity due to angular momentum and propose a “nonlinear superposition” of round and flattened halos in order to improve the scaling relations and the correspondence of the predicted rotation curves to the empirical Burkert fit.

Mirror matter has been proposed as a dark matter candidate. It has several very attractive features, including automatic stability and darkness, the ability to mimic the broad features of cold dark matter while in the linear density perturbation regime, and consistency with all direct dark matter search experiments, both negative (e.g. CDMS II) and positive (DAMA). In this paper we consider an important unsolved problem: Are there plausible reasons to explain why most of the mirror matter in spiral galaxies exists in the form of gaseous spheroidal galactic halos around ordinary matter disks? We compute an order-of-magnitude estimate that the mirror-photon luminosity of a typical spiral galaxy today is around ${10}^{44}\mathrm{e}\mathrm{r}\mathrm{g}/\mathrm{s}$. Interestingly, this rate of energy loss is similar to the power supplied by ordinary supernova explosions. We discuss circumstances under which supernova power can be used to heat the gaseous part of the mirror matter halo and hence prevent its collapse to a disk. The macroscopic ordinary-mirror asymmetry plays a fundamental role in our analysis.

This paper introduces a systematic treatment of the linear theory of scalar gravitational perturbations in the presence of a fully inhomogeneous magnetic field. The analysis is conducted both in the synchronous and in the conformally Newtonian gauges. The cosmological plasma is assumed to be composed of cold dark matter, baryons, photons, neutrinos. The problem of superhorizon initial conditions for the fluid variables of the various species and for the coupled system of Boltzmann-Einstein equations is discussed in the presence of an inhomogeneous magnetic field. The tight-coupling approximation for the Boltzmann hierarchy is extended to the case where gravitating magnetic fields are included.

Here we study the creation of a brane world using an instanton solution with Hartle-Hawking’s no-boundary approach. We analyze brane models with a Gauss-Bonnet term in a bulk spacetime. The curvature of 3-brane is assumed to be closed, flat, or open. We construct instanton solutions with branes for our models, and calculate the value of the actions to discuss the initial state of a brane universe.

We analyze the spectrum of density perturbations generated in models of the recently discovered “D-cceleration” mechanism of inflation. In this scenario, strong coupling quantum field theoretic effects sum to provide a Dirac-Born-Infeld–like action for the inflaton. We show that the model has a strict lower bound on the non-Gaussianity of the cosmic microwave background radiation power spectrum at an observable level, and is thus falsifiable. This, in particular, observationally distinguishes this mechanism from traditional slow-roll inflation generated by weakly interacting scalar fields. The model also favors a large observable tensor component to the cosmic microwave background radiation spectrum.

The motivation for studying the rolling tachyon and noncommutative inflation comes from string theory. In the tachyon inflation scenario, metric perturbations are created by tachyon field fluctuations during inflation. We drive the exact mode equation for scalar perturbations of the metric and investigate the cosmological perturbations in the commutative and noncommutative inflationary spacetime driven by the tachyon field which have a Born-Infeld Lagrangian. Although at lowest order the predictions of tachyon inflation are no different than those from standard slow-roll inflation, due to the modified inflationary dynamics there exists modifications to the power spectra of fluctuations generated during inflation. In the noncommutative tachyon inflation scenario, the stringy noncommutativity of spacetime results in corrections to the primordial power spectrum that lead to a spectral index that is greater than 1 on large scales and less than 1 on small scales as the first-year results of the Wilkinson Microwave Anisotropy Probe indicate.

We calculate the diurnal and annual modulation of the signals in axion and weakly interacting massive particle (WIMP) dark matter detectors on Earth caused by a cold flow of dark matter in the solar neighborhood. The effects of the Sun’s and the Earth’s gravity, and of the orbital and rotational motions of the Earth are included. A cold flow on Earth produces a peak in the spectrum of microwave photons in cavity detectors of dark matter axions, and a plateau in the nuclear recoil energy spectrum in WIMP detectors. Formulas are given for the positions and heights of these peaks and plateaux as a function of time in the course of day and year, including all corrections down to the 0.1% level of precision. The results can be applied to an arbitrary dark matter velocity distribution $f(\overrightarrow{v})$ by integrating the one-flow results over velocities. We apply them to the set of flows predicted by the caustic ring model of the Galactic halo. The caustic ring model predicts the dark matter flux on Earth to be largest in December $\pm$ one month. Nonetheless, because of the role of energy thresholds, the model is consistent with the annual modulation results published by the DAMA Collaboration provided the WIMP mass is larger than approximately 100 GeV.

The behavior of perturbations is studied in cosmological models which consist of two different homogeneous regions connected in a spherical shell boundary. The junction conditions for the metric perturbations and the displacements of the shell boundary are analyzed and the surface densities of the perturbed energy and momentum in the shell are derived, using Mukohyama’s gauge-invariant formalism and the Israel discontinuity condition. In both homogeneous regions, the perturbations of scalar, vector, and tensor types are expanded using the three-dimensional harmonic functions, but the mode coupling among them is caused in the shell by the inhomogeneity. By treating the perturbations with odd and even parities separately, it is found, however, that we can have consistent displacements and surface densities for given metric perturbations.

In a recent investigation of chiral behavior in quenched lattice QCD, the flavor-singlet pseudoscalar “hairpin” vertex associated with the ${\eta }^{\prime }$ mass was studied for pion masses ranging from $\approx 275$ to 675 MeV. It has been observed by Sharpe that, with a consistent NLO calculation in quenched chiral perturbation theory, the quark-mass dependence of the hairpin vertex is uniquely predicted in terms of the single-pole coefficient ${\alpha }_{\Phi }$ and the Leutwyler parameter $L_5$. Since ${\alpha }_{\Phi }$ is found to be $\approx 0$, the chiral slope of the double-pole residue determines a value for $L_5$, providing a consistency check between the chiral slope of the hairpin mass insertion and that of the pion decay constant. We investigate the consistency of these mass dependences in our Monte Carlo results at two values of lattice spacing. Within statistics, the slopes are found to be consistent with the $Q\chi PT$ prediction.

We investigate a possible background of the type ${\Omega }_c^0\to {\Xi }_c^{+}{\pi }^{-}$ to the CLEO ${\Xi }_c^{+}$ lifetime measurement. This decay mode may lead to an overestimate of the ${\Xi }_c^{+}$ decay length and, therefore, increase the measured ${\Xi }_c^{+}$ lifetime. The branching ratio $\Gamma ({\Omega }_c^0\to {\Xi }_c^{+}{\pi }^{-})/\Gamma ({\Omega }_c^0\to {\Omega }^{-}{\pi }^{+})$ is analyzed in the framework of the pole model and the modified current algebra. We find that the ${\Omega }_c^0\to {\Xi }_c^{+}{\pi }^{-}$ decay mode could not generate a substantial systematic error in the ${\Xi }_c^{+}$ lifetime measurement.

We calculate the corrections to the partial widths of the light Higgs boson in the Littlest Higgs model due to effects of the TeV-scale physics. We focus on the loop-induced Higgs coupling to photon pairs, which is especially sensitive to the effects of new particles running in the loop. This coupling can be probed with high precision at a photon collider in the process $\gamma \gamma \to H\to b\overline{b}$ for a light Higgs boson with mass $115\mathrm{G}\mathrm{e}\mathrm{V}\le M_H\lesssim 140\mathrm{G}\mathrm{e}\mathrm{V}$. Using future LHC measurements of the parameters of the Littlest Higgs model, one can calculate a prediction for this process, which will serve as a test of the model and as a probe for a strongly coupled UV completion at the 10 TeV scale. We outline the prospects for measuring these parameters with sufficient precision to match the expected experimental uncertainty on $\gamma \gamma \to H\to b\overline{b}$.

We present a model-independent description of the exclusive rare decays $\overline{B}\to K^{*}{e}^{+}{e}^{-}$ in the low recoil region (large lepton invariant mass $q^2\sim m_b^2$). In this region the long-distance effects from quark loops can be computed with the help of an operator product expansion in $1/Q$, with $Q=\{m_b,\sqrt{q^2}\}$. Nonperturbative effects up to and including terms suppressed by $\Lambda /Q$ and $m_c^2/m_b^2$ relative to the short-distance amplitude can be included in a model-independent way. Based on these results, we propose an improved method for determining the Cabibbo-Kobayashi-Maskawa matrix element $|V_{ub}|$ from a combination of rare and semileptonic $B$ and $D$ decays near the zero recoil point. The residual theoretical uncertainty from long-distance effects in this $|V_{ub}|$ determination comes from terms in the operator product expansion of order ${\alpha }_s(Q)\Lambda /m_b$, ${\alpha }_s^2(Q)$, $m_c^4/m_b^4$, and duality violations, and is estimated to be below 10%.

We extract the next-to-next-to-leading order results for spin-flip generalized polarizabilities (GPs) of the nucleon from the spin-dependent amplitudes for virtual Compton scattering at $\mathcal{O}(p^4)$ in heavy baryon chiral perturbation theory. At this order, no unknown low-energy constants enter the theory, allowing us to make absolute predictions for all spin-flip GPs. Furthermore, by using constraint equations between the GPs due to nucleon crossing combined with charge conjugation symmetry of the virtual Compton scattering amplitudes, we get a next-to-next-to-next-to-leading order prediction for one of the GPs. We provide estimates for forthcoming double-polarization experiments which allow one to access these spin-flip GPs of the nucleon.

We discuss the hadronic light-by-light scattering contribution to the muon anomalous magnetic moment $a_{\mu }^{\mathrm{l}\mathrm{b}\mathrm{l}}$, paying particular attention to the consistent matching between the short- and the long-distance behavior of the light-by-light scattering amplitude. We argue that short-distance QCD imposes strong constraints on this amplitude overlooked in previous analyses. We find that accounting for these constraints leads to approximately 50% increase in the central value of $a_{\mu }^{\mathrm{l}\mathrm{b}\mathrm{l}}$, compared to commonly accepted estimates (see, e.g., [M. Davier, S. Eidelman, A. Hocker, and Z. Zhang, Eur. Phys. J. C 31, 503 (2003).]). The hadronic light-by-light scattering contribution becomes $a_{\mu }^{\mathrm{l}\mathrm{b}\mathrm{l}}=136(25)\times {10}^{-11}$, thereby shifting the standard model prediction closer to the experimental value.