There has been considerable recent interest in solving nonlocal equations of motion which contain an infinite number of derivatives. Here, focusing on inflation, we review how the problem can be reformulated as the question of finding solutions to a diffusionlike partial differential equation with nonlinear boundary conditions. Moreover, we show that this diffusionlike equation, and hence the nonlocal equations, can be solved as an initial value problem once nontrivial initial data consistent with the boundary conditions is found. This is done by considering linearized equations about any field value, for which we show that obtaining solutions using the diffusionlike equation is equivalent to solving a local but infinite field cosmology. These local fields are shown to consist of at most two canonically normalized or phantom fields together with an infinite number of quintoms. We then numerically solve the diffusionlike equation for the full nonlinear case for two string field theory motivated models.

Since the inhomogeneous instrument noise can produce extra non-Gaussianity in the cosmic microwave background (CMB) anisotropy, its effect should be carefully subtracted in the primordial non-Gaussianity estimation. We calculate the probability distribution function of the CMB anisotropy for a local type of non-Gaussianity, from which the optimal estimator in the general case (inhomogeneous noise and cut sky) is obtained. The new estimator obtained here is different from the popular one, since the inhomogeneous noise and cut sky effects are completely accounted for. The CMB anisotropy in the new estimator is noise weighted. The noise weight is different from that used by the WMAP Collaboration in their 5-year data analysis. Although it is still difficult to calculate the new estimator rigorously, for the case of the slightly inhomogeneous noise, there exists a series expansion method to compute the new estimator. Each order in the series is suppressed by two factors, $(\frac{{\sigma }^2}{{\sigma }_i^2}-1)$ and $\frac{C_l}{C_l^{\mathrm{tot}}}$, which make the method feasible. Through the Edgeworth expansion we can generalize our discussion to other types of non-Gaussianity.

It is an interesting possibility that the Universe underwent a period of thermal equilibrium at very early times. One expects a residue of this primordial state to be imprinted on the large scale structure of space time. In this paper, we study the morphology of this thermal residue in a universe whose early dynamics is governed by a scalar field. We calculate the amplitude of fluctuations on large scales and compare it with the imprint of vacuum fluctuations. We then use the observed power spectrum of fluctuations on the cosmic microwave background to place a constraint on the temperature of the Universe before and during inflation. We also present an alternative scenario, where the fluctuations are predominantly thermal and near scale-invariant.

Using the nonrelativisitc reduction of Coulomb gauge QCD we compute a spectrum of the low mass hybrid mesons containing a heavy quark-antiquark pair. The gluon degrees of freedom are treated in the mean field approximation calibrated to the gluelump spectrum. We discuss the role of the non-Abelian nature of the QCD Coulomb interaction in the ordering of the spin-parity levels.

We report a Dalitz-plot analysis of the charmless hadronic decays of neutral $B$ mesons to $K^{\pm }{\pi }^{\mp }{\pi }^0$. With a sample of $(231.8\pm 2.6)\times {10}^6\mathit{{\rm Y}}(4S)\to B\overline{B}$ decays collected by the BABAR detector at the PEP-II asymmetric-energy $B$ Factory at SLAC, we measure the magnitudes and phases of the intermediate resonant and nonresonant amplitudes for $B^0$ and ${\overline{B}}^0$ decays and determine the corresponding $CP$-averaged branching fractions and charge asymmetries. The inclusive branching fraction and $CP$-violating charge asymmetry are measured to be $\mathcal{B}(B^0\to K^{+}{\pi }^{-}{\pi }^0)=({35.7}_{-1.5}^{+2.6}\pm 2.2)\times {10}^{-6}$ and ${\mathcal{A}}_{CP}=-{0.030}_{-0.051}^{+0.045}\pm 0.055$ where the first errors are statistical and the second systematic. We observe the decay $B^0\to K^{*0}(892){\pi }^0$ with the branching fraction $\mathcal{B}(B^0\to K^{*0}(892){\pi }^0)=({3.6}_{-0.8}^{+0.7}\pm 0.4)\times {10}^{-6}$. This measurement differs from zero by 5.6 standard deviations (including the systematic uncertainties). The selected sample also contains $B^0\to {\overline{D}}^0{\pi }^0$ decays where ${\overline{D}}^0\to K^{+}{\pi }^{-}$, and we measure $\mathcal{B}(B^0\to {\overline{D}}^0{\pi }^0)=(2.93\pm 0.17\pm 0.18)\times {10}^{-4}$.

We present a high-statistics measurement of differential cross sections and the total cross section for the process $\gamma \gamma \to {\pi }^0{\pi }^0$ in the kinematic range $0.6\mathrm{GeV}\le W\le 4.0\mathrm{GeV}$ and $|\cos {\theta }^{*}|\le 0.8$, where $W$ and ${\theta }^{*}$ are the energy and pion scattering angle, respectively, in the $\gamma \gamma$ center-of-mass system. Differential cross sections are fitted to obtain information on S, ${\mathrm{D}}_0$, ${\mathrm{D}}_2$, ${\mathrm{G}}_0$, and ${\mathrm{G}}_2$ waves. The G waves are important above $W\simeq 1.6\mathrm{GeV}$. The general behavior of partial waves is studied by fitting differential cross sections in a simple parametrization where amplitudes contain resonant contributions and smooth background. The ${\mathrm{D}}_2$ wave is dominated by the $f_2(1270)$ meson whose parameters are consistent with the current world averages. The ${\mathrm{D}}_0$ wave contains a $f_2(1270)$ component, whose fraction is fitted. For the S wave, the $f_0(980)$ parameters are found to be consistent with the values determined from our recent ${\pi }^{+}{\pi }^{-}$ data. In addition to the $f_0(980)$, the S wave prefers to have another resonance-like contribution whose parameters are obtained.

We investigate the properties of the Sakai-Sugimoto model at finite magnetic field and baryon chemical potentials. We show that in a finite magnetic field, there exists a spatially homogeneous configuration carrying a finite-baryon number density. At a low magnetic field and baryon chemical potential, the equation of state of the matter coincides with that obtained from the chiral perturbation theory Lagrangian with an anomalous term. We discuss the behavior of the system at larger magnetic fields.

We analyze gauge coupling unification in the context of heterotic strings on anisotropic orbifolds. This construction is very much analogous to effective five-dimensional orbifold grand unified theory field theories. Our analysis assumes three fundamental scales: the string scale $M_{\mathrm{S}}$, a compactification scale $M_{\mathrm{C}}$, and a mass scale for some of the vectorlike exotics $M_{\mathrm{EX}}$; the other exotics are assumed to get mass at $M_{\mathrm{S}}$. In the particular models analyzed, we show that gauge coupling unification is not possible with $M_{\mathrm{EX}}=M_{\mathrm{C}}$, and in fact we require $M_{\mathrm{EX}}\ll M_{\mathrm{C}}\sim 3\times {10}^{16}\mathrm{GeV}$. We find that about 10% of the parameter space has a proton lifetime (from dimension six gauge exchange) ${10}^{33}\mathrm{yr}\lesssim \tau (p\to {\pi }^0{e}^{+})\lesssim {10}^{36}\mathrm{yr}$. The other 80% of the parameter space gives proton lifetimes below Super-Kamiokande bounds. The next generation of proton decay experiments should be sensitive to the remaining parameter space.

All modern routes leading to a quantum theory of gravity—i.e., perturbative quantum gravitational one-loop exact correction to the global chiral current in the standard model, string theory, and loop quantum gravity—require modification of the classical Einstein-Hilbert action for the spacetime metric by the addition of a parity-violating Chern-Simons term. The introduction of such a term leads to spacetimes that manifest an amplitude birefringence in the propagation of gravitational waves. While the degree of birefringence may be intrinsically small, its effects on a gravitational wave accumulate as the wave propagates. Observation of gravitational waves that have propagated over cosmological distances may allow the measurement of even a small birefringence, providing evidence of quantum gravitational effects. The proposed Laser Interferometer Space Antenna (LISA) will be sensitive enough to observe the gravitational waves from sources at cosmological distances great enough that interesting bounds on the Chern-Simons coupling may be found. Here we evaluate the effect of a Chern-Simons induced spacetime birefringence to the propagation of gravitational waves from such systems. Focusing attention on the gravitational waves from coalescing binary black holes systems, which LISA will be capable of observing at redshifts approaching 30, we find that the signature of Chern-Simons gravity is a time-dependent change in the apparent orientation of the binary’s orbital angular momentum with respect to the observer line-of-sight, with the magnitude of change reflecting the integrated history of the Chern-Simons coupling over the worldline of the radiation wave front. While spin-orbit coupling in the binary system will also lead to an evolution of the system’s orbital angular momentum, the time dependence and other details of this real effect are different than the apparent effect produced by Chern-Simons birefringence, allowing the two effects to be separately identified. In this way gravitational-wave observations with LISA may thus provide our first and only opportunity to probe the quantum structure of spacetime over cosmological distances.

We present the detailed properties of a self-consistent crystalline chiral condensate in the massless chiral Gross-Neveu model. We show that a suitable ansatz for the Gorkov resolvent reduces the functional gap equation, for the inhomogeneous condensate, to a nonlinear Schrödinger equation, which is exactly soluble. The general crystalline solution includes as special cases all previously known real and complex condensate solutions to the gap equation. Furthermore, the associated Bogoliubov-de Gennes equation is also soluble with this inhomogeneous chiral condensate, and the exact spectral properties are derived. We find an all-orders expansion of the Ginzburg-Landau effective Lagrangian and show how the gap equation is solved order by order.

Introducing new physically motivated ansätze, we explore both analytically and numerically the classical and absolute stabilities of a single $Q$-ball in an arbitrary number of spatial dimensions $D$, working in both the thin- and thick-wall limits.

We first review the result that the noncommutative principal chiral model has an infinite tower of conserved currents and discuss the special case of the noncommutative $\mathbb{C}{P}^1$ model in some detail. Next, we focus our attention to a submodel of the $\mathbb{C}{P}^1$ model in the noncommutative spacetime ${\mathcal{A}}_{\theta }({\mathbb{R}}^{2+1})$. By extending a generalized zero-curvature representation to ${\mathcal{A}}_{\theta }({\mathbb{R}}^{2+1})$ we discuss its integrability and construct its infinitely many conserved currents. A supersymmetric principal chiral model with and without the Wess-Zumino-Witten term and a supersymmetric extension of the $\mathbb{C}{P}^1$ submodel in noncommutative spacetime [i.e., in superspaces ${\mathcal{A}}_{\theta }({\mathbb{R}}^{1+1|2})$, ${\mathcal{A}}_{\theta }({\mathbb{R}}^{2+1|2})$] are also examined in detail and their infinitely many conserved currents are given in a systematic manner. Finally, we discuss the solutions of the aforementioned submodels with or without supersymmetry.

The Casimir interaction between two concentric corrugated cylinders provides the mechanism for noncontact gears. To this end, we calculate the Casimir torque between two such cylinders, described by $\delta$-potentials, which interact through a scalar field. We derive analytic expressions for the Casimir torque for the case when the corrugation amplitudes are small in comparison to the corrugation wavelengths. We derive explicit results for the Dirichlet case, and exact results for the weak coupling limit, in the leading order. The results for the corrugated cylinders approach the corresponding expressions for the case of corrugated parallel plates in the limit of large radii of cylinders (relative to the difference in their radii) while keeping the corrugation wavelength fixed.

We calculate the lateral Casimir force between corrugated parallel plates, described by $\delta$-function potentials, interacting through a scalar field, using the multiple scattering formalism. The contributions to the Casimir energy due to uncorrugated parallel plates is treated as a background from the outset. We derive the leading- and next-to-leading-order contribution to the lateral Casimir force for the case when the corrugation amplitudes are small in comparison to corrugation wavelengths. We present explicit results in terms of finite integrals for the case of the Dirichlet limit, and exact results for the weak-coupling limit, for the leading- and next-to-leading-orders. The correction due to the next-to-leading contribution is significant. In the weak coupling limit we calculate the lateral Casimir force exactly in terms of a single integral which we evaluate numerically. Exact results for the case of the weak limit allows us to estimate the error in the perturbative results. We show that the error in the lateral Casimir force, in the weak coupling limit, when the next-to-leading order contribution is included is remarkably low when the corrugation amplitudes are small in comparison to corrugation wavelengths. We expect similar conclusions to hold for the Dirichlet case. The analogous calculation for the electromagnetic case should reduce the theoretical error sufficiently for comparison with the experiments.

We propose a method to improve the quenched approximation. The method, based on the worldline formalism, takes into account effects of quark loops. The idea is mostly useful for AdS/CFT (holographic) calculations. To demonstrate the method we estimate screening (string breaking) effects by a simple holographic calculation.

We present a model-independent argument showing that massless particles interacting with gravity in a Minkowski background space can have at most spin two. This result is proven by extending a famous theorem due to Weinberg and Witten to theories that do not possess a gauge-invariant stress-energy tensor.

Considering both the nonlinear invariant terms constructed by the electromagnetic field and the Riemann tensor in gravity action, we obtain a new class of $(n+1)$-dimensional magnetic brane solutions in third order Lovelock-Born-Infeld gravity. This class of solutions yields a spacetime with a longitudinal nonlinear magnetic field generated by a static source. These solutions have no curvature singularity and no horizons but have a conic geometry with a deficit angle $\delta$. We find that, as the Born-Infeld parameter decreases, which is a measure of the increase of the nonlinearity of the electromagnetic field, the deficit angle increases. We generalize this class of solutions to the case of spinning magnetic solutions and find that, when one or more rotation parameters are nonzero, the brane has a net electric charge which is proportional to the magnitude of the rotation parameters. Finally, we use the counterterm method in third order Lovelock gravity and compute the conserved quantities of these spacetimes. We found that the conserved quantities do not depend on the Born-Infeld parameter, which is evident from the fact that the effects of the nonlinearity of the electromagnetic fields on the boundary at infinity are wiped away. We also find that the properties of our solution, such as deficit angle, are independent of Lovelock coefficients.

We study the absorption probability and Hawking radiation of the scalar field in the rotating Gödel black hole in minimal five-dimensional gauged supergravity. We find that Gödel parameter $j$ imprints in the greybody factor and Hawking radiation. It plays a different role from the angular momentum of the black hole in the Hawking radiation and super-radiance. This information can help us know more about rotating Gödel black holes in minimal five-dimensional gauged supergravity.

In the Lin-Lunin-Maldacena (LLM) bubbling geometries, we compute the entropies of black holes and estimate their horizon sizes from the fuzzball conjecture, based on coarse-graining on the gravity side. The differences of black hole microstates cannot be seen by classical observations. Conversely, by counting the possible deformations of the geometry which are not classically detectable, we can calculate the entropy. We carry out this method on the black holes of the LLM bubbling geometries, such as the superstar, and obtain the same result as was derived by coarse-graining directly on the conformal field theory (CFT) (fermion) side. Second, by application of this method, we can estimate the horizon sizes of those black holes, based on the fuzzball conjecture. The Bekenstein-Hawking entropy computed from this horizon agrees with that microscopic entropy above. This result supports the fuzzball conjecture.

Inspirals of stellar-mass compact objects into massive black holes are an important source for future gravitational wave detectors such as Advanced LIGO and LISA. The detection and analysis of these signals rely on accurate theoretical models of the binary dynamics. We cast the equations describing binary inspiral in the extreme mass ratio limit in terms of action-angle variables, and derive properties of general solutions using a two-timescale expansion. This provides a rigorous derivation of the prescription for computing the leading order orbital motion. As shown by Mino, this leading order or adiabatic motion requires only knowledge of the orbit-averaged, dissipative piece of the self-force. The two-timescale method also gives a framework for calculating the post-adiabatic corrections. For circular and for equatorial orbits, the leading order corrections are suppressed by one power of the mass ratio, and give rise to phase errors of order unity over a complete inspiral through the relativistic regime. These post-1-adiabatic corrections are generated by the fluctuating, dissipative piece of the first order self-force, by the conservative piece of the first order self-force, and by the orbit-averaged, dissipative piece of the second order self-force. We also sketch a two-timescale expansion of the Einstein equation, and deduce an analytic formula for the leading order, adiabatic gravitational waveforms generated by an inspiral.