We study the correlation functions of scalar operators in the theory defined as the holographic dual of the Schrödinger background with dynamical exponent $z=2$ at zero temperature and zero chemical potential. We offer a closed expression of the correlation functions at tree level in terms of Fourier transforms of the corresponding $n$-point functions computed from pure AdS in the light-cone frame. At the loop level this mapping does not hold and one has to use the full Schrödinger background, after proper regularization. We explicitly compute the 3-point function comparing it with the specific 3-point function of the nonrelativistic theory of cold atoms at unitarity. We find agreement of both 3-point functions, including the part not fixed by the symmetry, up to an overall normalization constant.

We identify the nonlinear evolution equation in impact-parameter space for the “Supercritical Pomeron” in Reggeon field theory as a two-dimensional stochastic Fisher-Kolmogorov-Petrovski-Piscounov equation. It exactly preserves unitarity and leads in its radial form to a high-energy traveling wave solution corresponding to a “universal” behavior of the impact-parameter front profile of the elastic amplitude; its rapidity dependence and form depend only on one parameter, the noise strength, independently of the initial conditions and of the nonlinear terms restoring unitarity. Theoretical predictions are presented for the three typical distinct regimes corresponding to zero, weak, and strong noise.

We present numerical evidences for the existence of rotating black holes in $d$-dimensional Einstein-Maxwell theory with a cosmological constant and for an odd number of dimensions. The metric used possesses $(d+1)/2$ Killing vectors and the black holes have $(d-1)/2$ equal angular momenta. The Schwarzschild-like coordinate system used clearly reveals the influence of the electromagnetic field on the vacuum black holes where analytic expressions are available. The domain of existence of the charged rotating black holes is then characterized for both signs of the cosmological constant. The generic solutions are specified by their event horizon and by two additional parameters: the magnetic field and the angular velocity at the horizon. The dependence of several physical quantities—surface gravity, mass, angular momentum, etc.—is studied as a function of these parameters; Smarr-like relations are derived.

It is well known that, for a wide class of spacetimes with horizons, Einstein equations near the horizon can be written as a thermodynamic identity. It is also known that the Einstein tensor acquires a highly symmetric form near static, as well as stationary, horizons. We show that, for generic static spacetimes, this highly symmetric form of the Einstein tensor leads quite naturally and generically to the interpretation of the near-horizon field equations as a thermodynamic identity. We further extend this result to generic static spacetimes in Lanczos-Lovelock gravity, and show that the near-horizon field equations again represent a thermodynamic identity in all these models. These results confirm the conjecture that this thermodynamic perspective of gravity extends far beyond Einstein’s theory.

The generation of non-Gaussianity is studied in a three-fluid curvaton model. By utilizing second order perturbation theory we derive general formulae for the large scale temperature fluctuation and non-Gaussianity parameter $f_{\mathrm{NL}}$ that includes the possibility of a nonadiabatic final state. In the adiabatic limit we recover previously known results. The results are applied to a three-fluid curvaton model where radiation and all of the cold dark matter are produced by the curvaton field decay. We find that the amount of non-Gaussianity in this model decreases as the final state of the system becomes more adiabatic and that the generated non-Gaussianity in the scenario is small, $|f_{\mathrm{NL}}|\sim \mathcal{O}(1)$, in contrast to the two-fluid curvaton model.

Predecoupling magnetic fields affect the scalar modes of the geometry and produce observable effects which can be constrained also through the use of current (as opposed to forthcoming) data stemming from the cosmic microwave nackground observations. The dependence of the temperature and polarization angular power spectra upon the parameters of an ambient magnetic field is encoded in the scaling properties of a set of basic integrals whose derivation is simplified in the limit of small angular scales. The magnetically-induced distortions patterns of the relevant observables can be computed analytically by employing scaling considerations which are corroborated by numerical results. The parameter space of the magnetized cosmic microwave background anisotropies is also discussed in the light of the obtained analytical results.

Our model consists of intersecting ${22}^{\prime }{55}^{\prime }$ branes in M theory distributed uniformly in the common transverse space. Equations of state follow from $U$ duality symmetries. In this model, three spatial directions expand, and seven directions stabilize to constant sizes. From a string theory perspective, the dilaton is hence stabilized. The constant sizes depend on certain imbalance among initial values. One naturally obtains $M_{11}\simeq M_s\simeq M_4$ and $g_s\simeq 1$ within a few orders of magnitude. Smaller numbers, for example, $M_s\simeq {10}^{-16}{M}_4$, are also possible but require fine-tuning.

We show that it is possible to accommodate the observed size of the phase in $B_s^0-{\overline{B}}_s^0$ mixing in the framework of a model with violation of $3\times 3$ unitarity. This violation is associated to the presence of a new $Q=2/3$ isosinglet quark $T$, which mixes both with $t$ and $c$ and has a mass not exceeding 500 GeV. The crucial point is the fact that this framework allows for $\chi \equiv \arg (-V_{ts}{V}_{cb}{V}_{tb}^{*}{V}_{cs}^{*})$ of order $\lambda$, to be contrasted with the situation in the standard model, where $\chi$ is constrained to be of order ${\lambda }^2$. We point out that this scenario implies rare top decays $t\to cZ$ at a rate observable at the LHC and $|V_{tb}|$ significantly different from unity. In this framework, one may also account for the observed size of $D^0-{\overline{D}}^0$ mixing without having to invoke long-distance contributions. It is also shown that in the present scenario, the observed size of $D^0-{\overline{D}}^0$ mixing constrains ${\chi }^{\prime }\equiv \arg (-V_{cd}{V}_{us}{V}_{cs}^{*}{V}_{ud}^{*})$ to be of order ${\lambda }^4$, which is significantly smaller than what is allowed in generic models with violations of $3\times 3$ unitarity.

Charged and neutral, pion and kaon electric polarizabilities are extracted from lattice QCD using an ensemble of anisotropic gauge configurations with dynamical clover fermions. We utilize classical background fields to access the polarizabilities from two-point correlation functions. Uniform background fields are achieved by quantizing the electric field strength with the proper treatment of boundary flux. These external fields, however, are implemented only in the valence quark sector. A novel method to extract charge particle polarizabilities is successfully demonstrated for the first time.

We compute, for the first time using lattice QCD methods, charmonium radiative transition rates involving states of high spin and exotics. Utilizing a large basis of interpolating fields we are able to project out various excited-state contributions to three-point correlators computed on quenched anisotropic lattices. In the first lattice QCD calculation of the exotic $1^{-+}$ ${\eta }_{c1}$ radiative decay, we find a large partial width $\Gamma ({\eta }_{c1}\to J/\psi \gamma )\sim 100\mathrm{keV}$. We find clear signals for electric dipole and magnetic quadrupole transition form factors in ${\chi }_{c2}\to J/\psi \gamma$, calculated for the first time in this framework, and study transitions involving excited $\psi$ and ${\chi }_{c1,2}$ states. We calculate hindered magnetic dipole transition widths without the sensitivity to assumptions made in model studies and find statistically significant signals, including a nonexotic vector hybrid candidate $Y_{\mathrm{hyb}?}\to {\eta }_c\gamma$. As well as comparison to experimental data, we discuss in some detail the phenomenology suggested by our results and the extent to which it mirrors that of quark-potential models, and make suggestions for the interpretation of our results involving exotic quantum numbered states.

We obtain a novel result in QCD for long range rapidity correlations between gluons produced in the collision of saturated high energy hadrons or nuclei. This result, obtained in a high energy factorization framework, provides strong justification for the Glasma flux tube picture of coherent strong color fields. Our formalism can be applied to “near side ridge” events at the Relativistic Heavy Ion Collider and in future studies of long range rapidity correlations at the LHC.

In the traditional nonrelativistic bound state calculation, the two-photon decay amplitudes of the $P$-wave ${\chi }_{c0,2}$ and ${\chi }_{b0,2}$ states depend on the derivative of the wave function at the origin, which can only be obtained from potential models. However, by neglecting the relative quark momenta, the decay amplitude can be written as the matrix element of a local heavy quark field operator which could be obtained from other processes or computed with the QCD sum rules technique or lattice simulation. Following the same lines as in recent work for the two-photon decays of the $S$-wave ${\eta }_c$ and ${\eta }_b$ quarkonia, we show that the effective Lagrangian for the two-photon decays of the $P$-wave ${\chi }_{c0,2}$ and ${\chi }_{b0,2}$ states is given by the heavy quark energy-momentum tensor local operator or its trace, the $\overline{Q}Q$ scalar density, and that the expression for ${\chi }_{c0}$ two-photon and two-gluon decay rates is given by the $f_{{\chi }_{c0}}$ decay constant and is similar to that of ${\eta }_c$ which is given by $f_{{\eta }_c}$. From the existing QCD sum rules value for $f_{{\chi }_{c0}}$, we get 5 keV for the ${\chi }_{c0}$ two-photon width, somewhat larger than the measurements, but possibly with large uncertainties.

We study two-loop anomalous dimension matrices in QCD and related gauge theories for products of Wilson lines coupled at a point. We verify by an analysis in Euclidean space that the contributions to these matrices from diagrams that link three massive Wilson lines do not vanish in general. We show, however, that for two-to-two processes the two-loop anomalous dimension matrix is diagonal in the same color-exchange basis as the one-loop matrix for arbitrary masses at absolute threshold and for scattering at 90 degrees in the center of mass. This result is important for applications of threshold resummation in heavy quark production.

We compare a recent lattice determination of the nucleon distribution amplitudes with other approaches and models. We study the nucleon distribution amplitudes up to twist 6 in next-to-leading conformal spin and we also investigate conformal $d$-wave contributions to the leading-twist distribution amplitude. With the help of light-cone sum rules one can relate the distribution amplitudes to the form factors of the nucleon or the $N\to \Delta$ transition at intermediate values of the momentum transfer. We compare our results with experimental data in the range $1{\mathrm{GeV}}^2\le Q^2\le 10{\mathrm{GeV}}^2$. Keeping in mind that we are working only in leading order QCD and next-to-leading order QCD corrections might be sizeable, we already obtain a surprisingly good agreement for the nucleon form factors $G_M^n$, $G_M^p$, $G_A^p$, and $G_T^p$ and for the $N\to \Delta$ transition form factor ratios $R_{\mathrm{EM}}$ and $R_{\mathrm{SM}}$.

We examine various direct and indirect experimental constraints on the nearly minimal supersymmetric standard model (nMSSM) and obtain the following observations: (i) Current experiments stringently constrain the parameter space, setting a range of $1\sim 37\mathrm{GeV}$ for the lightest neutralino ${\tilde{\chi }}_1^0$, $30\sim 140\mathrm{GeV}$ ($1\sim 250\mathrm{GeV}$) for the lightest $CP$-even ($CP$-odd) Higgs boson, and $1.5\sim 10$ for $\tan \beta$; (ii) To account for the dark matter relic density, besides the $s$-channel exchange of a $Z$ boson, the $s$-channel exchange of a light $A_1$ (the lightest $CP$-odd Higgs boson) can also play an important role in lightest supersymmetric particle annihilation. Compared with the $Z$-exchange annihilation channel, the $A_1$-exchange channel is more favored by muon $g-2$ data and allows much broader regions for the parameters; (iii) In a large part of the allowed parameter space the SM-like Higgs boson may dominantly decay to ${\tilde{\chi }}_1^0{\tilde{\chi }}_1^0$ or $A_1{A}_1$ and the conventional visible decays (e.g. into bottom quarks) are severely suppressed.

$B$ modes in CMB polarization from patchy reionization arise from two effects: generation of polarization from scattering of quadrupole moments by reionization bubbles and fluctuations in the screening of $E$ modes from recombination. The scattering contribution has been studied previously, but the screening contribution has not yet been calculated. We show that on scales smaller than the acoustic scale ($\ell \gtrsim 300$), the $B$-mode power from screening is larger than the $B$-mode power from scattering. The ratio approaches a constant $\sim 2.5$ below the damping scale ($\ell \gtrsim 2000$). On degree scales relevant for gravitational waves ($\ell \lesssim 100$), screening $B$ modes have a white noise tail and are subdominant to the scattering effect. These results are robust to uncertainties in the modeling of patchy reionization.

We discuss classification of defects of various codimensions within a holographic model of pure Yang-Mills theories or gauge theories with fundamental matter. We focus on their role below and above the phase transition point as well as their weights in the partition function. The general result is that objects which are stable and heavy in one phase are becoming very light (tensionless) in the other phase. We argue that the $\theta$ dependence of the partition function drastically changes at the phase transition point, and therefore it correlates with stability properties of configurations. We also explore the possibility that novel stable glueballlike particles, with mass which scales like $N_c$ and which are analogous to carbon Fullerenes, may exist in nature on the QCD scale. Some possible applications for studying the QCD vacuum properties above and below the phase transition are also discussed.

We analyze the thermodynamical properties, at finite density and nonzero temperature, of the ($1+1$) dimensional chiral Gross-Neveu model (the ${\mathrm{NJL}}_2$ model), using the exact inhomogeneous (crystalline) condensate solutions to the gap equation. The continuous chiral symmetry of the model plays a crucial role, and the thermodynamics leads to a broken phase with a periodic spiral condensate, the “chiral spiral,” as a thermodynamically preferred limit of the more general “twisted kink crystal” solution of the gap equation. This situation should be contrasted with the Gross-Neveu model, which has a discrete chiral symmetry, and for which the phase diagram has a crystalline phase with a periodic kink crystal. We use a combination of analytic, numerical, and Ginzburg-Landau techniques to study various parts of the phase diagram.

In ($2+1$)-dimensional gravity with negative cosmological constant, the states in the negative energy range, between anti-de Sitter (AdS) ($M=-1$) and the so-called Bañados-Teitelboim-Zanelli black hole ($M\ge 0$), correspond to topological defects with angular deficit $0<\alpha <2\pi$. These defects are produced by (static or spinning) 0-branes which, in the extreme case $M\ell =-|J|$, admit globally-defined covariantly constant spinors. Thus, these branes correspond to Bogomol’nyi-Prasad-Sommerfield solitons and are stable ground state candidates for the corresponding supersymmetric extension of $2+1$ AdS gravity. These branes constitute external currents that couple in a gauge-invariant way to three-dimensional AdS gravity.