In this paper we show that in the noncommutative chiral gauge theories the 4-fermion vertices are finite. The $4\psi$ vertices appear in linear order in quantization of the $\theta$-expanded noncommutative gauge theories; in all previously considered models, based on Dirac fermions, the $4\psi$ vertices were divergent and nonrenormalizable.

In $d>4$ dimensions, one can argue for the existence of small black rings using a scaling argument. We apply the same scaling argument to the $d=4$ case and demonstrate that it fails to say anything about the existence of $d=4$ small black rings, because stringy corrections get out of control. General relativity theorems say that there does not exist a black hole with toroidal topology for $d=4$, but we interpret this as saying that, for $d=4$ small black rings, stringy corrections are crucial which invalidate the assumptions those theorems are based on.

The thermodynamics of a first-order chiral phase transition is considered in the presence of spinodal phase separation within the Nambu–Jona-Lasinio model. The properties of the basic thermodynamic observables in the coexistence phase are discussed for zero and nonzero quark masses. We focus on observables that probe the chiral phase transition. In particular, the behavior of the specific heat and entropy as well as charge fluctuations are calculated and analyzed. We show that the specific heat and charge susceptibilities diverge at the isothermal spinodal lines. We determine the scaling behavior and compute the critical exponent $\gamma$ of the net quark number susceptibility at the isothermal spinodal lines within the Nambu–Jona-Lasinio model and the Ginsburg-Landau theory. We show that in the chiral limit the critical exponent $\gamma =1/2$ at the tricritical point as well as along the isothermal spinodal lines. On the other hand, for finite quark masses the critical exponent at the spinodal lines, $\gamma =1/2$, differs from that at the critical end point, $\gamma =2/3$, indicating a change in the universality class. These results are independent of the particular choice of the chiral Lagrangian and should be common for all mean-field approaches.

We evaluate generalized parton distributions of the pion in two chiral quark models: the spectral quark model and the Nambu–Jona-Lasinio model with a Pauli-Villars regularization. We proceed by the evaluation of double distributions through the use of a manifestly covariant calculation based on the $\alpha$ representation of propagators. As a result polynomiality is incorporated automatically and calculations become simple. In addition, positivity and normalization constraints, sum rules, and soft-pion theorems are fulfilled. We obtain explicit formulas, holding at the low-energy quark-model scale. The expressions exhibit no factorization in the $t$-dependence. The QCD evolution of those parton distributions is carried out to experimentally or lattice accessible scales. We argue for the need of evolution by comparing the parton distribution function and the parton distribution amplitude of the pion to the available experimental and lattice data, and confirm that the quark-model scale is low, about 320 MeV.

We study the transfer of color between a heavy quark pair and an unpaired heavy quark or antiquark moving at a nonrelativistic velocity with respect to the pair. We find that the open heavy quark or antiquark can catalyze the transformation of the pair from octet representation at short distances to singlet at long distances. This process is infrared sensitive in general, and we exhibit double poles in dimensional regularization at next-to-next-to-leading order in the transition probability. Because of their dependence on kinematic variables, these poles cannot be matched to the nonperturbative matrix elements of effective field theories based on a single heavy quark pair.

The decays of $J/\psi \to \omega K\overline{K}\pi$ and $J/\psi \to \varphi K\overline{K}\pi$ are studied using $5.8\times {10}^7$ $J/\psi$ events collected with the Beijing Spectrometer (BESII) at the Beijing Electron-Positron Collider (BEPC). The $K_S^0{K}^{\pm }{\pi }^{\mp }$ and $K^{+}{K}^{-}{\pi }^0$ systems, produced in $J/\psi \to \omega K\overline{K}\pi$, have enhancements in the invariant mass distributions at around $1.44\mathrm{GeV}/c^2$. However, there is no evidence for mass enhancements in the $K\overline{K}\pi$ system in $J/\psi \to \varphi K\overline{K}\pi$. The branching fractions of $J/\psi \to \omega K_S^0{K}^{\pm }{\pi }^{\mp }$, $\varphi K_S^0{K}^{\pm }{\pi }^{\mp }$, $\omega K^{*}\overline{K}+\mathrm{c}.\mathrm{c}.$, and $\varphi K^{*}\overline{K}+\mathrm{c}.\mathrm{c}.$ are obtained, and the $J/\psi \to \eta K_S^0{K}^{\pm }{\pi }^{\mp }$ branching fraction is measured for the first time.

We revisit type IIB supergravity backgrounds with null and spacelike singularities with natural gauge theory duals proposed in [S. R. Das, J. Michelson, K. Narayan, and S. P. Trivedi, Phys. Rev. D 74, 026002 (2006)] and [S. R. Das, J. Michelson, K. Narayan, and S. P. Trivedi, Phys. Rev. D 75, 026002 (2007)]. We show that for these backgrounds there are always choices of the boundaries of these deformed ${\mathrm{AdS}}_5\times S^5$ space-times, such that the dual gauge theories live on flat metrics and have space-time dependent couplings. We present a new time dependent solution of this kind where the effective string coupling is always bounded and vanishes at a spacelike singularity in the bulk, and the space-time becomes ${\mathrm{AdS}}_5\times S^5$ at early and late times. The holographic energy momentum tensor calculated with a choice of flat boundary is shown to vanish for null backgrounds and to be generically nonzero for time dependent backgrounds.

We consider the geometrical engineering constructions for the $N=1$ supersymmetric QCD vacua recently proposed by Giveon and Kutasov. After 1 T-duality, the geometries with wrapped D5 branes become $N=1$ brane configurations with NS branes and D4 branes. The field theories encoded by the geometries contain extra massive adjoint fields for the flavor group. After performing a flop, the geometries contain branes, antibranes and branes wrapped on nonholomorphic cycles. The various tachyon condensations between pairs of wrapped D5 branes and anti-D5 branes together with deformations of the cycles give rise to a variety of supersymmetric and metastable nonsupersymmetric vacua.

The Holst action containing the Immirzi parameter for pure gravity is generalized to supergravity theories. Supergravity equations of motion are not modified by such generalizations, thus preserving supersymmetry. Dependence on the Immirzi parameter does not emerge in the classical equations of motion. This is in contrast with the recent observation of Perez and Rovelli for gravity action containing the original Holst term and a minimally coupled Dirac fermion, where the classical equations of motion do develop a dependence on the Immirzi parameter.

The simplicity of the Morris-Thorne wormhole spacetime permits us to determine null and timelike geodesics by means of elliptic integral functions and Jacobian elliptic functions. This analytic solution makes it possible to find a geodesic which connects two distant events. An exact gravitational lensing, an illumination calculation, and even an interactive visualization become possible.

Fry (1996) showed that galaxy bias has the tendency to evolve towards unity, i.e. in the long run, the galaxy distribution tends to trace that of matter. Generalizing slightly Fry’s reasoning, we show that his conclusion remains valid in theories of modified gravity (or equivalently, complex clustered dark energy). This is not surprising: as long as both galaxies and matter are subject to the same force, dynamics would drive them towards tracing each other. This holds, for instance, in theories where both galaxies and matter move on geodesics. This relaxation of bias towards unity is tempered by cosmic acceleration, however: the bias tends towards unity but does not quite make it, unless the formation bias were close to unity. Our argument is extended in a straightforward manner to the case of a stochastic or nonlinear bias. An important corollary is that dynamical evolution could imprint a scale dependence on the large scale galaxy bias. This is especially pronounced if nonstandard gravity introduces new scales to the problem: the bias at different scales relaxes at different rates, the larger scales generally more slowly and retaining a longer memory of the initial bias. A consistency test of the current ($\mathrm{\text{general relativity}}+\mathrm{\text{uniform dark energy}}$) paradigm is therefore to look for departure from a scale-independent bias on large scales. A simple way is to measure the relative bias of different populations of galaxies which are at different stages of bias relaxation. Lastly, we comment on the possibility of directly testing the Poisson equation on cosmological scales, as opposed to indirectly through the growth factor.

Probabilities in the multiverse can be calculated by assuming that we are typical representatives in a given reference class. But is this class well defined? What should be included in the ensemble in which we are supposed to be typical? There is a widespread belief that this question is inherently vague, and that there are various possible choices for the types of reference objects which should be counted in. Here we argue that the “ideal” reference class (for the purpose of making predictions) can be defined unambiguously in a rather precise way, as the set of all observers with identical information content. When the observers in a given class perform an experiment, the class branches into subclasses who learn different information from the outcome of that experiment. The probabilities for the different outcomes are defined as the relative numbers of observers in each subclass. For practical purposes, wider reference classes can be used, where we trace over all information which is uncorrelated to the outcome of the experiment, or whose correlation with it is beyond our current understanding. We argue that, once we have gathered all practically available evidence, the optimal strategy for making predictions is to consider ourselves typical in any reference class we belong to, unless we have evidence to the contrary. In the latter case, the class must be correspondingly narrowed.

We make a detailed study of matter density perturbations in both metric and Palatini formalisms. Considering general theories whose Lagrangian density is a general function, $f(R)$, of the Ricci scalar $R$, we derive the equation of matter density perturbations in each case, in a number of gauges, including comoving, longitudinal and uniform density gauges. We show that for viable $f(R)$ models that satisfy cosmological and local gravity constraints (LGC), matter perturbation equations derived under a subhorizon approximation are valid even for super-Hubble scales provided the oscillating mode (scalaron) does not dominate over the matter-induced mode. Such approximate equations are especially reliable in the Palatini formalism because of the absence of scalarons. Using these equations we make a comparative study of the behavior of matter density perturbations as well as gravitational potentials for a number of classes of $f(R)$ theories. In the metric formalism the quantity $m=R{f}_{,RR}/f_{,R}$ that characterizes the deviation from the $\Lambda \mathrm{CDM}$ model is constrained to be very small during a matter era in order to ensure compatibility with LGC, but the models in which $m$ grows to the order of ${10}^{-1}$ around the present epoch can be allowed. These models also suffer from an additional fine-tuning due to the presence of scalaron oscillating modes which are absent in the Palatini case. In Palatini formalism LGC and background cosmological constraints provide only weak bounds on $|m|$ by constraining it to be smaller than $\sim 0.1$. This is in contrast to matter density perturbations which, on galactic scales, place far more stringent constraints on the present deviation parameter $m$ of the order of $|m|\lesssim {10}^{-5}–{10}^{-4}$. This is due to the peculiar evolution of matter perturbations in the Palatini case, which exhibits a rapid growth or a damped oscillation depending on the sign of $m$.

We compute the $\mathcal{O}({\alpha }_s)$ QCD corrections to the partonic process $gg\to t\overline{t}Z$ at the LHC. This partonic channel is the dominant component of the scattering process $pp\to t\overline{t}Z$, which will be important for measuring the $t\overline{t}Z$ electroweak couplings. We perform this calculation using a newly developed numerical technique for obtaining loop corrections. The $\mathcal{O}({\alpha }_s)$ corrections increase the total cross section by up to 75% for reasonable choices of the renormalization and factorization scales. Inclusion of these contributions decreases the residual scale dependence of the cross section coming from uncalculated higher order terms to $\pm 5\%$.

We discuss the phenomenology of strange-quark dynamics in the nucleon, based on experimental and theoretical results for electroweak form factors and for parton densities. In particular, we construct a model for the generalized parton distribution that relates the asymmetry $s(x)-\overline{s}(x)$ between the longitudinal momentum distributions of strange quarks and antiquarks with the form factor $F_1^s(t)$, which describes the distribution of strangeness in transverse position space.

A search for rare lepton decays of the $\eta$ meson was performed using the WASA detector at CELSIUS. Two candidates for double Dalitz decay $\eta \to e^{+}{e}^{-}{e}^{+}{e}^{-}$ events are reported with a background of $1.3\pm 0.2$ events. This allows to set an upper limit to the branching ratio of $9.7\times {10}^{-5}$ (90% CL). The branching ratio for the decay $\eta \to e^{+}{e}^{-}\gamma$ is determined to $(7.8\pm {0.5}_{\mathrm{stat}}\pm {0.8}_{\mathrm{syst}})\times {10}^{-3}$ in agreement with world average value. An upper limit (90% CL) for the branching ratio for the $\eta \to e^{+}{e}^{-}$ decay is $2.7\times {10}^{-5}$ and a limit for the sum of the $\eta \to {\mu }^{+}{\mu }^{-}{\mu }^{+}{\mu }^{-}$ and $\eta \to {\pi }^{+}{\pi }^{-}{\mu }^{+}{\mu }^{-}$ decays is $3.6\times {10}^{-4}$.

In this paper we study supersymmetric Wilson loops restricted to an $S^2$ submanifold of four-dimensional space in $\mathcal{N}=4$ super Yang-Mills theory. We provide evidence from both perturbation theory and the AdS dual that those loops are equal to the analogous observables in two-dimensional Yang-Mills on $S^2$ (excluding nonperturbative contributions). This relates a subsector of $\mathcal{N}=4$ SYM to a low-dimensional soluble model and also suggests that this subsector of $\mathcal{N}=4$ SYM is invariant under area preserving diffeomorphisms.

We study string theory duals of the expanding boost invariant conformal gauge theory plasmas at strong coupling. The dual supergravity background is constructed as an asymptotic late-time expansion, corresponding to equilibration of the gauge theory plasma. The absence of curvature singularities in the first few orders of the late-time expansion of the dual gravitational background unambiguously determines the equilibrium equation of state, and the shear viscosity of the gauge theory plasma. While the absence of the leading pole singularities in the gravitational curvature invariants at third order in late-time expansion determines the relaxation time of the plasma, the subleading logarithmic singularity cannot be canceled within a supergravity approximation. Thus, a supergravity approximation to a dual description of the strongly coupled boost invariant expanding plasma is inconsistent. Nevertheless we find that the relaxation time determined from the cancellation of pole singularities is quite robust.

We extend and develop a method for perturbative calculations of anomalous dimensions and mixing matrices of leading twist conformal primary operators in conformal field theories. Such operators lie on the unitarity bound and hence are conserved (irreducible) in the free theory. The technique relies on the known pattern of breaking of the irreducibility conditions in the interacting theory. We relate the divergence of the conformal operators via the field equations to their descendants involving an extra field and accompanied by an extra power of the coupling constant. The ratio of the two-point functions of descendants and of their primaries determines the anomalous dimension, allowing us to gain an order of perturbation theory. We demonstrate the efficiency of the formalism on the lowest-order analysis of anomalous dimensions and mixing matrices which is required for two-loop calculations of the former. We compare these results to another method based on anomalous conformal Ward identities and constraints from the conformal algebra. It also permits us to gain a perturbative order in computations of mixing matrices. We show the complete equivalence of both approaches.