We apply the background field (BF) method to nonrelativistic QCD (NRQCD) on the lattice in order to determine the one-loop radiative corrections to the coefficients of the NRQCD action in a manifestly gauge-covariant manner by matching the NRQCD prediction for particular on-shell processes with those of relativistic continuum QCD. We explain how the BF method is implemented in automated perturbation theory and discuss the technique for matching the relativistic and nonrelativistic theories. We compute the one-loop radiative corrections to the $\mathit{\sigma }·\mathit{B}$ and Darwin terms for the NRQCD action currently used in simulations, as well as the one-loop coefficients of the spin-dependent $O({\alpha }^2)$ four-fermion contact terms. The effect of the corrections on the hyperfine splitting of bottomonium is estimated using earlier simulation results [A. Gray et al., Phys. Rev. D 72, 094507 (2005)]; the corrected lattice prediction is found to be in agreement with experiment. Agreement of the hyperfine splitting of bottomonium and the $B$-meson system is confirmed by recent simulation studies [R. J. Dowdall et al., Phys. Rev. D 85, 054509 (2012); Phys. Rev. D 86, 094510 (2012)]. which include our NRQCD radiative corrections for the first time.

Lattice simulations for the electromagnetic form factors of the nucleon yield insights into the internal structure of hadrons. The logarithmic divergence of the charge radius in the chiral limit poses an interesting challenge in achieving reliable predictions from finite-volume lattice simulations. Recent results near the physical pion mass ($m_{\pi }\sim 180\mathrm{MeV}$) are examined in order to confront the issue of how the chiral regime is approached. The electric charge radius of the nucleon isovector presents a forum for achieving consistent finite-volume corrections. Newly developed techniques within the framework of chiral effective field theory ($\chi \mathrm{EFT}$) are used to achieve a robust extrapolation of the electric charge radius to the physical pion mass and to infinite volume. The chiral extrapolations exhibit considerable finite-volume dependence; lattice box sizes of $L\gtrsim 7\mathrm{fm}$ are required in order to achieve a direct lattice simulation result within 2% of the infinite-volume value at the physical point. Predictions of the volume dependence are provided to guide the interpretation of future lattice results.

Effects of an external magnetic field on the fluctuations of quark number, fluctuations, and correlations of conserved charges, including baryon number, electric charge, and strangeness, are studied in the $2+1$ flavor Polyakov-Nambu-Jona-Lasinio model. We find that a magnetic field increases fluctuations and correlations in the regime of chiral crossover. It makes the transition of quadratic fluctuations more abrupt, and the peak structure of quartic fluctuations more pronounced. Our calculations indicate that ${\chi }_4^B/{\chi }_2^B$, ${\chi }_4^Q/{\chi }_2^Q$, and ${\chi }_{11}^{BQ}$ are very sensitive to the external magnetic field and can possibly be used for probes for the strong magnetic field produced in the early stage of noncentral collisions.

We study the transverse single spin asymmetry in ${\eta }_{c,b}$ production in polarized hadron collisions, employing the collinear twist-3 approach in combination with the color singlet model. Our main focus lies on the contribution from the twist-3 Efremov-Teryaev-Qiu-Sterman function. By extrapolating the derived spin-dependent cross section to the small transverse momentum region, consistency between the collinear twist-3 approach and the transverse-momentum-dependent factorization approach is confirmed. As a byproduct of this work, we identify a term contributing to the scale evolution of trigluon correlations in the flavor-singlet case which was originally missed, see also V. M. Braun, A. N. Manashov, and B. Pirnay [Phys. Rev. D 80, 114002 (2009); 86, 119902(E) (2012)].

A modification of the action of the general relativity produces a different pattern for the growth of the cosmic structures below a certain length scale leaving an imprint on the cosmic microwave background anisotropies. We reexamine the upper limits on the length-scale parameter $B_0$ of $f(R)$ models using the recent data from the Planck satellite experiment. We also investigate the combined constraints obtained when including the Hubble Space Telescope $H_0$ measurement and the baryon acoustic oscillations measurements from the SDSS, WiggleZ and BOSS surveys.

We extend an infrared-deformed soft-wall anti–de Sitter/QCD model at zero temperature to a model at finite temperature and perform hydrodynamics. To have the infalling boundary condition to make the hydrodynamic analysis possible, we treat the infrared energy scale factor in our metric as a temperature-depending parameter. Then, by carrying out the hydrodynamic analysis, we compute the transport coefficients, the diffusion constant, and the shear viscosity through the linear response theory.

In Lorentzian AdS/CFT there exists a mapping between local bulk operators and nonlocal conformal field theory (CFT) operators. In global anti-de Sitter (AdS) this mapping can be found through use of bulk equations of motion and allows the nonlocal CFT operator to be expressed as a local operator smeared over a range of positions and times. We argue that such a construction is not possible if there are bulk normal modes with exponentially small near boundary imprint. We show that the AdS-Schwarzschild background is such a case, with the horizon introducing modes with angular momentum much larger than frequency, causing them to be trapped by the centrifugal barrier. More generally, we argue that any barrier in the radial effective potential which prevents null geodesics from reaching the boundary will lead to modes with vanishingly small near boundary imprint, thereby obstructing the existence of a smearing function. While one may have thought the bulk-boundary dictionary for low curvature regions, such as the exterior of a black hole, should be as in empty AdS, our results demonstrate otherwise.

We consider ${\mathrm{AdS}}_2\times R^2$ solutions supported by a magnetic field, such as those which arise in the near-horizon limit of magnetically charged ${\mathrm{AdS}}_4$ Reissner-Nordstrom black branes. In the presence of an electrically charged scalar field, such magnetic solutions can be unstable to spontaneous formation of a vortex lattice. We solve the coupled partial differential equations that govern the charged scalar, gauge field, and metric degrees of freedom to lowest nontrivial order in an expansion around the critical point and discuss the corrections to the free energy and thermodynamic functions arising from the formation of the lattice. We describe how such solutions can also be interpreted, via S-duality, as characterizing infrared crystalline phases of conformal field theories doped by a chemical potential, but in zero magnetic field; the doped conformal field theories are dual to geometries that exhibit dynamical scaling and hyperscaling violation.

We discuss properties of the electroweak vacuum as a function of an external magnetic field. The interest in these properties arises due to possible existence of the electromagnetically superconducting phase of QCD in the background of a sufficiently strong magnetic field. In the electroweak theory, a superconducting vacuum exists for a well defined range of magnetic background fields, and the interest of the current paper is the behavior near the upper critical magnetic field. We determine this critical field and calculate the vacuum condensates to leading order.

We present the mechanism of the dynamical supersymmetry breaking at the metastable vacuum recently uncovered in the $\mathcal{N}=1$ $U(N)$ supersymmetric gauge theory that contains adjoint superfields and that is specified by Kähler and noncanonical gauge kinetic functions and a superpotential whose tree vacua preserve $\mathcal{N}=1$ supersymmetry. The overall $U(1)$ serves as the hidden sector, and no messenger superfield is required. The dynamical supersymmetry breaking is triggered by the nonvanishing $D$ term coupled to the observable sector and is realized by the self-consistent Hartree-Fock approximation of the Nambu-Jona-Lasinio type while it eventually brings us the nonvanishing $F$ term as well. It is shown that theoretical analysis is resolved as a variational problem of the effective potential for three kinds of background fields, namely, the complex scalar, and the two order parameters $D$ and $F$ of supersymmetry, the last one being treated perturbatively. We determine the stationary point and numerically check the consistency of such treatment as well as the local stability of the scalar potential. The coupling to the $\mathcal{N}=1$ supergravity is given, and the gravitino mass formula is derived.

We present the calculation of the spectral function of an unstable scalar boson coupled to fermions as resulting from the resummation of the one-loop diagrams in the scalar particle self-energy. We work with a large but finite high-energy cutoff; in this way, the spectral function of the scalar field is always correctly normalized to unity, independent of the value of the cutoff. We show that this high-energy cutoff affects the Breit-Wigner width of the unstable particle: the larger the cutoff, the smaller is the width at fixed coupling. Thus, the existence of a high-energy cutoff (alias minimal length), and for instance the possible opening of new degrees of freedom beyond that energy scale, could then be in principle proven by measuring, at lower energy scales, the line shape of the unstable scalar state. Although the Lagrangian here considered represents only a toy model, we discuss possible future extensions of our work which could be relevant for particle physics phenomenology.

We construct an equation of state of strange quark matter in a strong magnetic field within a confining model. The confinement is modeled by means of the Richardson potential for quark-quark interaction modified suitably to account for a strong magnetic field. We compare our results for the equation of state and magnetization of matter to those derived within the MIT bag model. The differences between these models arise mainly due to the momentum dependence of the strong interaction between quarks in the Richardson model. Specifically, we find that the magnetization of strange quark matter in this model has much more pronounced de Haas-van Alfvén oscillations than in the MIT bag model, which is the consequence of the (static) gluon-exchange structure of the confining potential.

Three dimensional Eddington-inspired Born-Infeld gravity is studied with the goal of finding new solutions. Beginning with cosmology, we obtain analytical and numerical solutions for the scale factor $a(t)$, in spatially flat ($k=0$) and spatially curved ($k=\pm 1$) Friedmann-Roberston-Walker universes with (i) pressureless dust ($P=0$) and (ii) perfect fluid ($P=\frac{\rho }{2}$), as matter sources. When the theory parameter $\kappa >0$, our cosmological solutions are generically singular (except for the open universe, with a specific condition). On the other hand, for $\kappa <0$ we do find nonsingular cosmologies. We then move on towards finding static, circularly symmetric line elements with matter obeying (i) $p=0$ and (ii) $p=\frac{\rho }{2}$. For $p=0$, the solution found is nonsingular for $\kappa <0$ with the matter-stress-energy representing inhomogeneous dust. For $p=\frac{\rho }{2}$ we obtain nonsingular solutions, for all $\kappa$, and discuss some interesting characteristics of these solutions. Finally, we look at the rather simple $p=-\rho$ case where the solutions are either de Sitter or anti–de Sitter or flat spacetime.

We forecast the constraints on both the Hu-Sawicki model and the Bertschinger-Zukin model of $f(R)$ modified gravity within the parametrized post-Friedmann formalism for the Planck satellite experiment by performing the joint analysis of the integrated-Sachs-Wolfe-lensing bispectrum and cosmic microwave background power spectrum. We find that, even considering the temperature-temperature mode of cosmic microwave background power spectrum only, Planck data are expected to reduce the error bars on the modified gravity parameter $B_0$ (related to the present value of the Compton wavelength of the extra scalar degree of freedom) at least one order magnitude compared with Wilkinson microwave anisotropy probe. The spectrum-bispectrum joint analysis can further improve the results by a factor ranging from 1.14 to 5.32 depending on the specific modified gravity model. One of our main results is that the cross correlation between the integrated-Sachs-Wolfe-lensing bispectrum and the power spectrum can be safely neglected when performing the joint analysis. For simplicity, we investigate only the likelihood of one parameter ($B_0$) and fix all other cosmological parameters to their best-fit values in Wilkinson microwave anisotropy probe 7-yr results.

We calculate the most divergent contribution to the nondegenerate sector of the self-energy (or “melonic”) graph in the context of the Lorentzian Engle-Pereira-Rovelli-Livine and Freidel-Krasnov spin foam model of quantum gravity. We find that such a contribution is logarithmically divergent in the cutoff over the $SU(2)$ representation spins when one chooses the face amplitude guaranteeing the face-splitting invariance of the foam. We also find that the dependence on the boundary data is different from that of the bare propagator. This fact has its origin in the noncommutativity of the Engle-Pereira-Rovelli-Livine and Freidel-Krasnov ${\mathrm{Y}}_{\gamma }$ map with the projector onto $SL(2,\mathbb{C})$-invariant states. In the course of the paper, we discuss in detail the approximations used during the calculations, their geometrical interpretation, and the physical consequences of our result.

Following a recent proposal, we consider the most general structure possible for the Hamiltonian operator associated with the quantum isolated horizon (QIH) with explanations of the underlying physical motivations. After a brief overview of the microcanonical ensemble results, thermodynamic analysis with this model Hamiltonian is presented considering the usual canonical energy ensemble for a fixed number of punctures. It is shown that for a quantum spacetime admitting a thermodynamically stable QIH as its internal boundary, there must exist a specific bound on the Barbero-Immirzi parameter if the entropy of the QIH obeys the Bekenstein-Hawking area law. Arguing that the known classical results must follow in the correspondence limit, the model is fixed, yielding the energy spectrum of the QIH.

Motivated by the previous work on the fermion resonances on symmetric thick branes [Phys. Rev. D 80, 065020 (2009)], we extend the idea to the Kalb-Ramond (KR) resonances on the asymmetric thick branes. The localization and resonance of the KR field on symmetric and asymmetric thick branes are investigated in detail. In order to analyze the effect of scalar and KR field interaction on the spectrum of KR field Kaluza-Klein modes, we introduce a coupling between the background kink field and KR field, and find that there exist some resonant modes. In the case of a symmetric brane, we seek the resonances by using both the relative probability and transfer matrix methods, and show the consistency of results with the two methods. While for the asymmetric case, it is found that we can only apply one of the above two methods, i.e., the transfer matrix method, which reveals that the asymmetry reduces the number of the resonant modes of the KR field.

A single fluid approximation which treats perturbations in baryons and dark matter as equal has sometimes been used to calculate the growth of linear matter density perturbations in the Universe. We demonstrate that properly accounting for the separate growth of baryon and dark matter fluctuations can change some predictions of structure formation in the linear domain in a way that can alter conclusions about the consistency between predictions and observations for $\Lambda \mathrm{CDM}$ models vs modified gravity scenarios. Our results may also be useful for 21 cm tomography constraints on alternative cosmological models for the formation of large scale structure.

We suggest one of the possible ways to compensate the large negative quantum-topological QCD contribution to the vacuum energy density of the Universe by means of a positive constant contribution from a cosmological Yang-Mills field. An important role of the exact particular solution for the Yang-Mills field corresponding to the finite-time instantons is discussed. An interesting connection of the compensation mechanism to the color confinement in the framework of instanton models has been pointed out. Besides the ${\Lambda }_{\mathrm{QCD}}$ scale, this proposal relies on one dimensionless normalization constant which cannot be fixed by the perturbative QCD theory, and thus should be fine-tuned for the exact compensation to hold.

An inflationary model in the framework of noncommutative space-time may generate a nontrivial running of the scalar spectral index, but usually induces a large tensor-to-scalar ratio simultaneously. With the latest observational data from the Planck mission, we reexamine the inflationary scenarios in a noncommutative space-time. We find that either the running of the spectral index is tiny compared with the recent observational result, or the tensor-to-scalar ratio is too large to allow a sufficient number of e-folds. As examples, we show that the chaotic and power-law inflation models with the noncommutative effects are not favored by the current Planck data.