We consider world-sheet theories for non-Abelian strings assuming compactification on a cylinder with a finite circumference $L$ and periodic boundary conditions. The dynamics of the orientational modes is described by the two-dimensional $CP(N-1)$ model. We analyze both the nonsupersymmetric (bosonic) model and the $\mathcal{N}=(2,2)$ supersymmetric $CP(N-1)$ emerging in the case of $1/2$-BPS saturated strings (Bogomol’nyi–Prasad–Sommerfteld saturated string that breaks only half of supersymmetry) in $\mathcal{N}=2$ supersymmetric QCD with $N_f=N$. The nonsupersymmetric case was studied previously; technically our results agree with those obtained previously, although our interpretation is totally different. In the large-$N$ limit we detect a phase transition at $L\sim {\mathrm{\Lambda }}_{CP}^{-1}$ (which is expected to become a rapid crossover at finite $N$). If at large $L$ the $CP(N-1)$ model develops a mass gap and is in the Coulomb/confinement phase, with exponentially suppressed finite-$L$ effects, at small $L$ it is in the deconfinement phase, and the orientational modes contribute to the Lüsher term. The latter becomes dependent on the rank of the bulk gauge group. In the supersymmetric $CP(N-1)$ models at finite $L$ we find a large-$N$ solution which was not known previously. We observe a single phase independently of the value of $L{\mathrm{\Lambda }}_{CP}$. For any value of this parameter a mass gap develops and supersymmetry remains unbroken. So does the $SU(N)$ symmetry of the target space. The mass gap turns out to be independent of the string length. The Lüscher term is absent due to supersymmetry.

By explicit construction, we show that one can in a simple way introduce and measure gravitational holonomies and Wilson loops in lattice formulations of nonperturbative quantum gravity based on (causal) dynamical triangulations. We use this setup to investigate a class of Wilson line observables associated with the world line of a point particle coupled to quantum gravity, and deduce from their expectation values that the underlying holonomies cover the group manifold of SO(4) uniformly.

The deformability of a compact object induced by a perturbing tidal field is encoded in the tidal Love numbers, which depend sensibly on the object’s internal structure. These numbers are known only for static, spherically-symmetric objects. As a first step to compute the tidal Love numbers of a spinning compact star, here we extend powerful perturbative techniques to compute the exterior geometry of a spinning object distorted by an axisymmetric tidal field to second order in the angular momentum. The spin of the object introduces couplings between electric and magnetic deformations and new classes of induced Love numbers emerge. For example, a spinning object immersed in a quadrupolar, electric tidal field can acquire some induced mass, spin, quadrupole, octupole and hexadecapole moments to second order in the spin. The deformations are encoded in a set of inhomogeneous differential equations which, remarkably, can be solved analytically in vacuum. We discuss certain subtleties in defining the tidal Love numbers in general relativity, which are due to the difficulty in separating the tidal field from the linear response of the object in the solution, even in the static case. By extending the standard procedure to identify the linear response in the static case, we prove analytically that the Love numbers of a Kerr black hole remain zero to second order in the spin. As a by-product, we provide the explicit form for a slowly-rotating, tidally-deformed Kerr black hole to quadratic order in the spin, and discuss its geodesic and geometrical properties.

The gamma-ray excess observed by the Fermi-LAT in the Galactic Center can be interpreted by the dark matter annihilation to $b\overline{b}$ via a light pseudoscalar in the next-to-minimal supersymmetric standard model (NMSSM). It is interesting to note that the corresponding singlet scalar is useful to achieve a strongly first-order phase transition required by the electroweak baryogenesis. In this paper, we investigate the possibility that the NMSSM model can simultaneously accommodate these two issues. The phase transition strength can be characterized by the vacua energy gap at zero temperature and be sufficiently enhanced by the tree-level effect in the NMSSM. We find that the annihilation of singlino/Higgsino dark matter (DM) particles occurring close to the light pseudoscalar resonance is favored by the Galactic Center excess and the observed DM relic density, and some resulting regions in the parameter space with a small $\kappa /\lambda$ and a negative $A_{\kappa }$ can simultaneously account for a successful strongly first-order electroweak phase transition.

We extend our calculation of the atmospheric neutrino fluxes to polar and tropical regions. It is well known that the air density profiles in the polar and the tropical regions are different from the mid-latitude region. Also there are large seasonal variations in the polar region. In this extension, we use the NRLMSISE-00 global atmospheric model J. M. Picone, J. Geophys. Res. 107, SIA 15 (2002), replacing the U.S.-standard 1976 atmospheric model, which has no positional or seasonal variations. With the NRLMSISE-00 atmospheric model, we study the atmospheric neutrino flux at the polar and tropical regions with seasonal variations. The geomagnetic model international geomagnetic reference field (IGRF) we have used in our calculations seems accurate enough in the polar regions also. However, the polar and the equatorial regions are the two extremes in the IGRF model, and the magnetic field configurations are largely different from one another. Note that the equatorial region is also the tropical region generally. We study the effect of the geomagnetic field on the atmospheric neutrino flux in these extreme regions.

We present constraints on testing general relativity (GR) at cosmological scales using recent data sets and assess the impact of galaxy intrinsic alignment in the CFHTLenS lensing data on those constraints. We consider data from Planck temperature anisotropies, the galaxy power spectrum from the WiggleZ survey, weak-lensing tomography shear-shear cross-correlations from the CFHTLenS survey, integrated Sachs Wolfe-galaxy cross-correlations, and baryon acoustic oscillation data. We use three different parametrizations of modified gravity (MG), one that is binned in redshift and scale, a parametrization that evolves monotonically in scale but is binned in redshift, and a functional parametrization that evolves only in redshift. We present the results in terms of the MG parameters $Q$ and $\mathrm{\Sigma }$. We employ an intrinsic alignment model with an amplitude $A_{\text{CFHTLenS}}$ that is included in the parameter analysis. We find an improvement in the constraints on the MG parameters corresponding to a 40–53% increase on the figure of merit compared to previous studies, and GR is found consistent with the data at the 95% confidence level. The bounds found on $A_{\text{CFHTLenS}}$ are sensitive to the MG parametrization used, and the correlations between $A_{\text{CFHTLenS}}$ and MG parameters are found to be weak to moderate. For all three MG parametrizations $A_{\text{CFHTLenS}}$ is found to be consistent with zero when the whole lensing sample is used; however, when using the optimized early-type galaxy sample a significantly nonzero $A_{\text{CFHTLenS}}$ is found for GR and the scale-independent MG parametrization. We find that the tensions observed in previous studies persist, and there is an indication that cosmic microwave background (CMB) data and lensing data prefer different values for MG parameters, particularly for the parameter $\mathrm{\Sigma }$. The analysis of the confidence contours and probability distributions suggest that the bimodality found follows that of the known tension in the ${\sigma }_8$ parameter.

We consider a two-Higgs doublet scenario containing three $SU(2{)}_L$ singlet heavy neutrinos with Majorana masses. The second scalar doublet as well as the neutrinos are odd under a $Z_2$ symmetry. This scenario not only generates Majorana masses for the light neutrinos radiatively but also makes the lighter of the neutral $Z_2$-odd scalars an eligible dark matter candidate, in addition to triggering leptogenesis at the scale of the heavy neutrino masses. Taking two representative values of this mass scale, we identify the allowed regions of the parameter space of the model, which are consistent with all dark matter constraints. At the same time, the running of quartic couplings in the scalar potential to high scales is studied, thus subjecting the regions consistent with dark matter constraints to further requirements of vacuum stability, perturbativity and unitarity. It is found that part of the parameter space is consistent with all of these requirements all the way up to the Planck scale, and also yields the correct signal strength in the diphoton channel for the scalar observed at the Large Hadron Collider.

We report on our exploratory study for the direct evaluation of the parton distribution functions from lattice QCD, based on a recently proposed new approach. We present encouraging results using $N_f=2+1+1$ twisted mass fermions with a pion mass of about 370 MeV. The focus of this work is a detailed description of the computation, including the lattice calculation, the matching to an infinite momentum and the nucleon mass correction. In addition, we test the effect of gauge link smearing in the operator to estimate the influence of the Wilson line renormalization, which is yet to be done.

The symmetric and traceless part of the matrix element $\mathcal{S}\mathcal{T}⟨N|\overline{q}{D}_{\mu }{D}_{\nu }q|N⟩$ can be determined from the second moment of the twist-3 parton distribution function $e(x)$. Recently, novel experimental data on $e(x)$ have become available, which enables us to evaluate the magnitude of the above matrix element with considerably reduced systematic uncertainties. Based on the new experimental data, we show that $\mathcal{S}\mathcal{T}⟨N|\overline{q}{D}_{\mu }{D}_{\nu }q|N⟩$ is likely to be at least an order of magnitude smaller than what previous model-based estimates have so far suggested. We discuss the consequences of this observation for the analysis of deep inelastic scattering and QCD sum rules studies at finite density for the vector meson and the nucleon in which this matrix element is being used as an input parameter.

Electroweak vector-boson production, accompanied by multiple jets, is an important background to searches for physics beyond the standard model. A precise and quantitative understanding of this process is helpful in constraining deviations from known physics. We study four key ratios in $W+n$-jet production at the LHC. We compute the ratio of cross sections for $W+n$- to $W+(n-1)$-jet production as a function of the minimum jet transverse momentum. We also study the ratio differentially, as a function of the $W$-boson transverse momentum; as a function of the scalar sum of the jet transverse energy, $H_{\mathrm{T}}^{\text{jets}}$; and as a function of certain jet transverse momenta. We show how to use such ratios to extrapolate differential cross sections to $W+6$-jet production at next-to-leading order, and we cross-check the method against a direct calculation at leading order. We predict the differential distribution in $H_{\mathrm{T}}^{\text{jets}}$ for $W+6$ jets at next-to-leading order using such an extrapolation. We use the BlackHat software library together with SHERPA to perform the computations.

The capability of the LHC to study the electromagnetic dipole moments of the top quark is discussed. In particular, the process $pp\to p\gamma \gamma p\to pt\overline{t}p$, which is supposed to be tagged by the forward/backward detectors at the LHC experiments, is used to explore the top quark electric and magnetic moments. We perform analytical calculations and then a numerical analysis on the sensitivity of the total cross section of the top quark pair production in $\gamma \gamma$ scattering at the LHC to the anomalous top quark couplings with photon. It is shown that improvements in the bounds on the electromagnetic dipole moments of the top quark can be achieved in this channel in comparison with the constraints from the former studies.

In order to test different models proposed for some states discovered recently in the charmonium mass range that do not fit into the pattern predicted by the conventional quark model, we derive predictions for the spectrum within the hadro-charmonium picture, the tetraquark picture as well as the hadronic molecular approach. We exploit heavy quark spin symmetry for the hadro-charmonium and hadronic molecule scenarios. The patterns that emerge from the different models turn out to be quite distinct. For example, only within the hadro-charmonium picture a pseudoscalar state emerges that is lighter than the $Y(4260)$. Possible discovery channels of these additional states are discussed.

If the recently discovered Higgs boson’s couplings deviate from the Standard Model expectation, we may anticipate new resonant physics in the weak boson fusion channels resulting from high scale unitarity sum rules of longitudinal gauge boson scattering. Motivated by excesses in analyses of multi-leptons $+$ missing energy $+$ jets final states during run 1, we perform a phenomenological investigation of these channels at the LHC bounded by current Higgs coupling constraints. Such an approach constrains the prospects to observe such new physics at the LHC as a function of very few and generic parameters and allows the investigation of the strong requirement of probability conservation in the electroweak sector to high energies.

We consider a spin-$s$ Heisenberg model coupled to two-dimensional quantum gravity. We quantize the model using the Feynman path integral, summing over all possible two-dimensional geometries and spin configurations. We regularize this path integral by starting with the R-matrices defining the spin-$s$ Heisenberg model on a regular 2d Manhattan lattice. Two-dimensional quantum gravity is included by defining the R-matrices on random Manhattan lattices and summing over these, in the same way as one sums over 2d geometries using random triangulations in noncritical string theory. We formulate a random matrix model where the partition function reproduces the annealed average of the spin-$s$ Heisenberg model over all random Manhattan lattices. A technique is presented which reduces the random matrix integration in the partition function to an integration over their eigenvalues.

We study the $\mu$-term matrix of Higgs pairs induced by the D-brane instanton effects in intersecting D6-brane models compactified on $T^6$. It is found that the $\mu$-term matrix has a certain permutation symmetry and its eigenvalues have large hierarchical structure without fine-tuning.

Entanglement entropy of gauge fields is calculated using the partition function in curved spacetime with a boundary. Deriving a Gibbons-Hawking-like term from a Becchi-Rouet-Stora-Tyutin (BRST) action produces a Wald-entropy-like codimension-2 surface term. It is further suggested that boundary degrees of freedom localized on the entanglement surface generated from the gauge redundancy could be used to resolve a subtle mismatch in a universal conformal anomaly-entanglement entropy relation.

We study nonperturbative pair production in electric fields with lightlike inhomogeneities, using complex worldline instantons. We show that the instanton contribution to the pair production probability is a complex contour integral over the instanton itself, and that pair production in the considered fields can be recast in terms of Cauchy’s residue theorem. The instantons contribute residues from the poles they circulate (i.e. give local contributions), and the invariance of complex integrals under contour deformation manifests in the instanton contributions as invariance under a set of generalized, complex, reparametrizations.

We study the statistical mechanics of a general Hamiltonian system in the context of symplectic structure of the corresponding phase space. This covariant formalism reveals some interesting correspondences between properties of the phase space and the associated statistical physics. While topology, as a global property, turns out to be related to the total number of microstates, the invariant measure which assigns a priori probability distribution over the microstates is determined by the local form of the symplectic structure. As an example of a model for which the phase space has a nontrivial topology, we apply our formulation on the Snyder noncommutative space-time with de Sitter four-momentum space and analyze the results. Finally, in the framework of such a setup, we examine our formalism by studying the thermodynamical properties of a harmonic oscillator system.