We show that scalar perturbations of the eternal, rotating Banados-Teitelboim-Zanelli (BTZ) black hole should lead to an instability of the inner (Cauchy) horizon, preserving strong cosmic censorship. Because of backscattering from the geometry, plane-wave modes have a divergent stress tensor at the event horizon, but suitable wave packets avoid this difficulty, and are dominated at late times by quasinormal behavior. The wave packets have cuts in the complexified coordinate plane that are controlled by requirements of continuity, single-valuedness, and positive energy. Due to a focusing effect, regular wave packets nevertheless have a divergent stress energy at the inner horizon, signaling an instability. We propose that this instability, which is localized behind the event horizon, is detected holographically as a breakdown in the semiclassical computation of dual conformal field theory (CFT) expectation values in which the analytic behavior of wave packets in the complexified coordinate plane plays an integral role. In the dual field theory, this is interpreted as an encoding of physics behind the horizon in the entanglement between otherwise independent CFTs.

We consider premetric electrodynamics with a local and linear constitutive law for the vacuum. Within this framework, we find quartic Fresnel wave surfaces for the propagation of light. If we require (i) the Fresnel equation to have only real solutions and (ii) the vanishing of birefringence in vacuum, then a Riemannian light cone is implied. No proper Finslerian structure can occur. This is generalized to dynamical equations of any order.

The Yang-Mills Schrödinger equation is solved in Coulomb gauge for the vacuum by the variational principle using an Ansatz for the wave functional, which is strongly peaked at the Gribov horizon. A coupled set of Schwinger-Dyson equations for the gluon and ghost propagators in the Yang-Mills vacuum as well as for the curvature of gauge orbit space is derived and solved in one-loop approximation. We find an infrared suppressed gluon propagator, an infrared singular ghost propagator, and an almost linearly rising confinement potential.

The inflationary mechanism of mode amplification predicts that the state of each mode with a given wave vector is correlated to that of its partner mode with the opposite vector. This implies nonlocal correlations which leave their imprint on temperature anisotropies in the cosmic microwave background. Their spatial properties are best revealed by using local wave packets. This analysis shows that all density fluctuations giving rise to the large scale structures originate in pairs which are born near the reheating. In fact each local density fluctuation is paired with an oppositely moving partner with opposite amplitude. To obtain these results we first apply a “wave packet transformation” with respect to one argument of the two-point correlation function. A finer understanding of the correlations is then reached by making use of coherent states. A knowledge of the velocity field is required to extract the contribution of a single pair of wave packets. Otherwise, there is a two-folded degeneracy which gives three aligned wave packets arising from two pairs. The applicability of these methods to observational data is briefly discussed.

We consider several classes of noncommutative inflationary models within an extended version of patch cosmological braneworlds, starting from a maximally invariant generalization of the action for scalar and tensor perturbations to a noncommutative brane embedded in a commutative bulk. Slow-roll expressions and consistency relations for the cosmological observables are provided, both in the UV and IR region of the spectrum; the inflaton field is assumed to be either an ordinary scalar field or a Born-Infeld tachyon. The effects of noncommutativity are then analyzed in a number of ways and energy regimes.

We present a new approach to gauge-invariant cosmological perturbations at second-order, which is also covariant. We examine two cases, in particular, for a dust Friedman-Lemaître-Robertson-Walker model of any curvature: we investigate gravity waves generated from clustering matter, that is, induced tensor modes from scalar modes; and we discuss the generation of density fluctuations induced by gravity waves-scalar modes from tensor perturbations. We derive a linear system of evolution equations for second-order gauge-invariant variables which characterize fully the induced modes of interest, with a source formed from variables quadratic in first-order quantities; these we transform into fully-fledged second-order gauge-invariant variables. Both the invariantly defined variables and the key evolution equations are considerably simpler than similar gauge-invariant results derived by other methods. By finding analytical solutions, we demonstrate that nonlinear effects can significantly amplify or dampen modes present in standard linearized cosmological perturbation theory, thereby providing an important source of potential error in, and refinement of, the standard model. Moreover, these effects can dominate at late times, and on super-Hubble scales.

We performed lattice Landau gauge QCD simulation on $\beta =6.0,{16}^4,{24}^4,{32}^4$ and $\beta =6.4,{32}^4,{48}^4$ and ${56}^4$ by adopting the gauge fixing that minimizes the norm of the gauge field, and measured the running coupling by using the gluon propagator and the ghost propagator. In view of ambiguity in the vertex renormalization factor ${\tilde{Z}}_1$ in the lattice, we adjust the normalization of the running coupling by the perturbative QCD results near the highest momentum point. It has a maximum ${\alpha }_s(q)\simeq 2.1(3)$ at around $q=0.5\mathrm{G}\mathrm{e}\mathrm{V}$ and decreases as $q$ approaches 0, and the Kugo-Ojima parameter reached $-0.83(2)$. The infrared exponent of the ghost propagator at $0.4\mathrm{G}\mathrm{e}\mathrm{V}$ region is ${\alpha }_G=0.20$ but there is an exceptional Gribov copy with ${\alpha }_G=0.27$. The features of the exceptional Gribov copy are investigated by measuring four one-dimensional Fourier transform (1-d FT) of the gluon propagator transverse to each lattice axis. We observe, in general, correlation between absolute value of the Kugo-Ojima parameter and the degree of reflection positivity violation in the 1-d FT of the gluon propagator. The 1-d FT of the exceptional Gribov copy has an axis whose samplewise gluon propagator manifestly violates reflection positivity, and the average of the Cartan subalgebra components of the Kugo-Ojima parameter along this axis is consistent to $-1$. The running coupling of the ensemble average shows a suppression at 0 momentum, but when the ghost propagator of the exceptional Gribov copy is adopted, the suppression disappears and the data implies presence of the infrared fixed point ${\alpha }_s(0)\sim 2.5(5)$ and $\kappa =0.5$ suggested by the Dyson-Schwinger approach in the multiplicative renormalizable scheme. Comparison with the SU(2) QCD and $N_f=2$ unquenched SU(3) QCD are also made.

We study the role of finite widths of resonances in a nonlocal version of the Wick-Cutkosky model. The spectrum of bound states is known analytically in this model and forms linear Regge tragectories. We compute the widths of resonances, calculate the spectral density in an extension of the Breit-Wigner ansatz and discuss a mechanism for the damping of unphysical exponential growth of observables at high energy due to finite widths of resonances.

We compute the 1-loop chiral corrections to the bag parameters which are needed for the discussion of the supersymmetric (SUSY) $K^0-\overline{K^0}$ mixing problem in both finite and infinite volume. We then show how the bag parameters can be combined among themselves and with some auxiliary quantities and thus sensibly reduce the systematic errors due to chiral extrapolations as well as those due to finite volume artefacts that are present in the results obtained from lattice QCD. We also show that in some cases these advantages remain as such even after including the 2-loop chiral corrections. Similar discussion is also made for the $K\to \pi$ electroweak penguin operators.

We calculate the radiative corrections to the angular correlation between the polarization of the decaying and the direction of the emitted spin one-half baryons in the semileptonic decay mode to order $(\alpha /\pi )(q/M_1)$, where $q$ is the momentum transfer and $M_1$ is the mass of the decaying baryon. The final results are presented, first, with the triple integration of the bremsstrahlung photon ready to be performed numerically and, second, in an analytical form. A third presentation of our results in the form of numerical arrays of coefficients to be multiplied by the quadratic products of form factors is discussed. This latter may be the most practical one to use in Monte Carlo simulations. A series of cross-checks is performed. This paper is organized to make it accessible and reliable in the analysis of the Dalitz plot of precision experiments involving heavy quarks and is not compromised to fixing the form factors at predetermined values. It is assumed that the real photons are kinematically discriminated. Otherwise, our results have a general model-independent applicability.

We show analytically that the vacuum electromagnetic stress-energy tensor outside a ball with constant dielectric constant and permeability always obeys the weak, null, dominant, and strong energy conditions. There are still no known examples in quantum field theory in which the averaged null energy condition in flat spacetime is violated.

We construct the large radius limit of the metric of three-charge supertubes and three-charge BPS black rings by using the fact that supertubes preserve the same supersymmetries as their component branes. Our solutions reproduce a few of the properties of three-charge supertubes found recently using the Born-Infeld description. Moreover, we find that these solutions pass a number of rather nontrivial tests which they should pass if they are to describe some of the hair of three-charge black holes and three-charge black rings.

We investigate the possibility of cosmic censorship violation in string theory using a characteristic double-null code, which penetrates horizons and is capable of resolving the spacetime all the way to the singularity. We perform high-resolution numerical simulations of the evolution of negative mass initial scalar field profiles, which were argued to provide a counterexample to cosmic censorship conjecture for AdS-asymptotic spacetimes in five-dimensional supergravity. In no instances formation of naked singularity is seen. Instead, numerical evidence indicates that black holes form in the collapse. Our results are consistent with earlier numerical studies, and explicitly show where the 'no black hole' argument breaks.

By utilizing the gauge symmetries of two-time physics (2T physics), a superstring with linearly realized global $\mathrm{S}\mathrm{U}(2,2|4)$ supersymmetry in $4+2$ dimensions (plus internal degrees of freedom) is constructed. It is shown that the dynamics of the Witten-Berkovits twistor superstring in $3+1$ dimensions emerges as one of the many one-time (1T) holographic pictures of the $4+2$ dimensional string obtained via gauge fixing of the 2T gauge symmetries. In 2T physics the twistor language can be transformed to usual spacetime language and vice versa, off shell, as different gauge fixings of the same 2T string theory. Further holographic string pictures in $3+1$ dimensions that are dual theories also can be derived. The 2T superstring is further generalized in the $\mathrm{S}\mathrm{U}(4)=\mathrm{S}\mathrm{O}(6)$ sector of $\mathrm{S}\mathrm{U}(2,2|4)$ by the addition of six bosonic dimensions, for a total of $10+2$ dimensions. Excitations of the extra bosons produce a $\mathrm{S}\mathrm{U}(2,2|4)$ current algebra spectrum that matches the classification of the high-spin currents of $N=4,$ $d=4$ super Yang-Mills theory which are conserved in the weak coupling limit. This spectrum is interpreted as the extension of the $\mathrm{S}\mathrm{U}(2,2|4)$ classification of the Kaluza-Klein towers of typeII-B supergravity compactified on ${\mathrm{A}\mathrm{d}\mathrm{S}}_5\times {\mathrm{S}}^5$, into the full string theory, and is speculated to have a covariant $10+2$ origin in F-theory or S-theory. Further generalizations of the superstring theory to $3+2$, $5+2$, and $6+2$ dimensions based on the supergroups $\mathrm{O}\mathrm{S}\mathrm{p}(8|4),$ F(4), $\mathrm{O}\mathrm{S}\mathrm{p}(8^{*}|4)$, respectively, and other cases, are discussed also. The $\mathrm{O}\mathrm{S}\mathrm{p}(8^{*}|4)$ case in $6+2$ dimensions can be gauge fixed to $5+1$ dimensions to provide a formulation of the special superconformal theory in six dimensions either in terms of ordinary spacetime or in terms of twistors.

An example of interpolation by means of local field theories between the case of normal Kogut-Susskind fermions and the case of keeping just the fourth root of the Kogut-Susskind determinant is given. For the fourth root trick to be a valid approximation, certain limits need to be smooth. The question about the validity of the fourth root trick is not resolved, only cast into a local field theoretical framework.

An analysis of soft breaking under the constraint of modular invariance is given. The role of dilaton and moduli dependent front factors in achieving a modular invariant $V_{\mathrm{s}\mathrm{o}\mathrm{f}\mathrm{t}}$ is emphasized. Further, it is shown that in string models $\tan \beta$ is no longer a free parameter but is determined in terms of ${\alpha }_{\mathrm{s}\mathrm{t}\mathrm{r}\mathrm{i}\mathrm{n}\mathrm{g}}$ and the other soft parameters by the constraints of modular invariance and radiative electroweak symmetry breaking. The above framework is then used to analyze the neutralino relic density consistent with the Wilkinson Microwave Anisotropy Probe (WMAP) data at self-dual points in the Kähler and complex structure moduli. One finds that the combined set of constraints arising from modular invariant soft breaking, radiative electroweak symmetry breaking, and WMAP lead to upper limits on sparticle masses for $\mu >0$. These limits are investigated for a class of models and found to lie within reach of the Tevatron and the Large Hadron Collider. Further, an analysis of the neutralino-proton cross section shows that dark matter in these models can be explored in CDMS (Soudan), GENIUS, and ZEPLIN. While the analysis is carried out within the general framework of heterotic strings, the possibility that the results of the analysis may extend to a broader class of string models, such as models based on intersecting D branes, is also discussed.

This is an exploratory study of the lightest nonsinglet scalar $q\overline{q}$ state on the lattice with two dynamical quarks. Domain wall fermions are used for both sea and valence quarks on a ${16}^3\times 32$ lattice with an inverse lattice spacing of 1.7 GeV. We extract the scalar meson mass $1.58\pm 0.34\mathrm{G}\mathrm{e}\mathrm{V}$ from the exponential time dependence of the dynamical correlators with $m_{\mathrm{v}\mathrm{a}\mathrm{l}}=m_{\mathrm{s}\mathrm{e}\mathrm{a}}$ and $N_f=2$. Since this statistical error bar from dynamical correlators is rather large, we analyze also the partially quenched lattice correlators with $m_{\mathrm{v}\mathrm{a}\mathrm{l}}\ne m_{\mathrm{s}\mathrm{e}\mathrm{a}}$. They are positive for $m_{\mathrm{v}\mathrm{a}\mathrm{l}}\ge m_{\mathrm{s}\mathrm{e}\mathrm{a}}$ and negative for $m_{\mathrm{v}\mathrm{a}\mathrm{l}}<m_{\mathrm{s}\mathrm{e}\mathrm{a}}$. In order to understand this striking effect of partial quenching, we derive the scalar correlator within the partially quenched chiral perturbation theory (ChPT) and find it describes lattice correlators well. The leading unphysical contribution in partially quenched ChPT comes from the exchange of the two pseudoscalar fields and is also positive for $m_{\mathrm{v}\mathrm{a}\mathrm{l}}\ge m_{\mathrm{s}\mathrm{e}\mathrm{a}}$ and negative for $m_{\mathrm{v}\mathrm{a}\mathrm{l}}<m_{\mathrm{s}\mathrm{e}\mathrm{a}}$ at large $t$. After the subtraction of this unphysical contribution from the partially quenched lattice correlators, the correlators are positive and exponentially falling. The resulting scalar meson mass $1.51\pm 0.19\mathrm{G}\mathrm{e}\mathrm{V}$ from the partially quenched correlators is consistent with the dynamical result and has an appreciably smaller error bar.

We study the photoproduction of a $D^{*\pm }$ meson in association with a hadron jet at next-to-leading order in the parton model of QCD with nonperturbative fragmentation functions extracted from LEP1 data of $e^{+}{e}^{-}$ annihilation. The transverse-momentum and rapidity distributions recently measured at DESY HERA in various kinematic ranges nicely agree with our theoretical predictions. This provides a useful test of the universality and the scaling violations of the fragmentation functions predicted by the factorization theorem. These comparisons also illustrate the significance of the charm component in the resolved photon. This is elaborated by investigating the cross section distributions in $x_{\mathrm{o}\mathrm{b}\mathrm{s}}^{\gamma }$ and $\cos {\theta }^{*}$.

The Lattice results for the pion and kaon decay constants are analyzed within the Resonance Chiral Theory framework in the large $N_C$ limit. The approximately linear behavior of the observable at large light-quark mass is explained through the interaction with the lightest multiplet of scalar resonances. The analysis of the Lattice results allows to obtain the resonance mass $M_S=1049\pm 25\mathrm{M}\mathrm{e}\mathrm{V}$ and some of the Chiral Perturbation Theory parameters at leading order in $1/N_C$.

We study the production of hadron pairs in proton-proton collisions, selecting pairs with large total transverse momentum with respect to the beam, and small relative transverse momentum, i.e., belonging to a single jet with large transverse momentum. We describe the process in terms of dihadron fragmentation functions. We consider the production of one pair in polarized collisions (with one transversely polarized proton) and the production of two pairs in unpolarized collisions. In the first case, we discuss how to observe the quark transversity distribution in connection with a specific class of dihadron fragmentation functions, named interference fragmentation functions. In the second case, we suggest how to determine the latter and also how to observe linearly polarized gluons.