Complete gauge fixing beyond perturbation theory in non-Abelian gauge theories is a nontrivial problem. This is particularly evident in covariant gauges, where the Gribov-Singer ambiguity gives an explicit formulation of the problem. In practice, this is a problem if gauge-dependent quantities between different methods, especially lattice and continuum methods, should be compared: Only when treating the Gribov-Singer ambiguity in the same way is the comparison meaningful. To provide a better basis for such a comparison the structure of the first Gribov region in Landau gauge, a subset of all possible gauge copies satisfying the perturbative Landau gauge condition, will be investigated. To this end, lattice gauge theory will be used to investigate a two-dimensional projection of the region for SU(2) Yang-Mills theory in two, three, and four dimensions for a wide range of volumes and discretizations.

We investigate constraints on the interactions of light dark matter with Standard Model quarks in a framework with effective contact operators mediating the decay of heavy flavor bound state quarkonium to dark matter and a photon. When considered in combination with decays to purely invisible final states, constraints from heavy quarkonium decays at high intensity electron-positron colliders can complement missing energy searches at high energy colliders and provide sensitivity to dark matter masses difficult to probe at direct and indirect detection experiments. We calculate the approximate limits on the branching fraction for $\mathrm{\Upsilon }(1S)$ decays to dark matter and a photon. Given the approximate limits on the branching fractions for all dimension six or lower contact operators, we present the corresponding limits on the interaction strength for each operator and the inferred limits on dark matter-nucleon scattering. Complementary constraints on dark matter annihilation from gamma-ray searches from dwarf spheroidal galaxies are also considered.

I present approximate next-to-next-to-leading-order (aNNLO) transverse-momentum ($p_T$) distributions in single-top production processes. The aNNLO results are derived from the next-to-next-to-leading-logarithm resummation of soft-gluon corrections in the differential cross section. Single-top as well as single-antitop $p_T$ distributions are shown in $t$-channel, $s$-channel, and $tW$ production for LHC energies.

It is shown that an idea proposed in 1996 that relates in a qualitatively correct way the interfamily mass hierarchies of the up quarks, down quarks, charged leptons, and neutrinos, can be combined with a predictive scheme recently proposed for relating quark mixing and neutrino mixing. In the resulting model, the entire flavor structure of the quarks and leptons is expressible in terms of two “master matrices”: a diagonal matrix that gives the interfamily mass ratios, and an off-diagonal matrix that controls all flavor mixing.

We study analytically the effect of a weak random chemical potential of zero average in an Einstein-Maxwell background. For uncorrelated disorder this perturbation is relevant; however we show that it can become marginal or even irrelevant by tuning disorder correlations. At zero temperature we find that, to leading order in the disorder strength, the correction to the conductivity for irrelevant perturbations vanishes. In the marginal case, in order to renormalize a logarithmic divergence, we carry out a resummation of the perturbative expansion of the metric that leads to a Lifshitz-like geometry in the infrared. Disorder in this case also induces a positive correction to the conductivity. At finite temperature the black hole acquires an effective charge and the thermal conductivity has the expected Drude peak that signals the breaking of translational invariance. However the electric conductivity is not affected by the random chemical potential to leading order in the disorder strength.

Employing the coset approach we construct component actions for a superparticle moving in ${\mathrm{AdS}}_3$ with $N=(2,0)$, $D=3$ supersymmetry partially broken to $N=2$, $d=1$. These actions may contain higher time-derivative terms, which are chosen to possess the same (super)symmetries as the free superparticle. In terms of the nonlinear-realization superfields, the component actions always take a simpler form when written in terms of covariant Cartan forms. We also consider in detail the reduction to the nonrelativistic case and construct the corresponding action of a Newton-Hooke superparticle and its higher-derivative generalizations. The structure of these higher time-derivative generalizations is completely fixed by invariance under the supersymmetric Newton-Hooke algebra extended by two central charges.

We study the Higgs inflation model realized in the supersymmetric $SU(5)$ grand unified theory (GUT), focusing on its multifield dynamics and prediction of cosmological observables. The requirement for GUT symmetry breaking during inflation imposes tight constraints on the model parameters. We find, nevertheless, that with an appropriately chosen noncanonical Kähler potential the model is in excellent agreement with the present cosmological observations. The effects from multifield dynamics are found to be minor and thus, unlike other similar supersymmetric implementations of nonminimally coupled Higgs inflation, the prediction of this model is robust against multifield ambiguities.

We relate the unconstrained “double metric” of the “${\alpha }^{\prime }$-geometry” formulation of double field theory to the constrained generalized metric encoding the spacetime metric and $b$-field. This is achieved by integrating out auxiliary field components of the double metric in an iterative procedure that induces an infinite number of higher-derivative corrections. As an application, we prove that, to first order in ${\alpha }^{\prime }$ and to all orders in fields, the deformed gauge transformations are Green-Schwarz–deformed diffeomorphisms. We also prove that to first order in ${\alpha }^{\prime }$ the spacetime action encodes precisely the Green-Schwarz deformation with Chern-Simons forms based on the torsionless gravitational connection. This seems to be in tension with suggestions in the literature that T-duality requires a torsionful connection, but we explain that these assertions are ambiguous since actions that use different connections are related by field redefinitions.

We consider the spectral action within the context of a four-dimensional manifold with torsion and show that, in the vacuum case, the equations of motion reduce to Einstein’s equations, securing the linear stability of the theory. To subsequently investigate the nonvacuum case, we consider the spectral action of an almost commutative torsion geometry and show that the Hamiltonian is bounded from below, a result which guarantees the linear stability of the theory.

The relativistic analogue of the Hall-Vinen-Bekarevich-Khalatnikov (HVBK) hydrodynamics is derived making use of the phenomenological method similar to that used by Bekarevich and Khalatnikov [1] in their derivation of HVBK hydrodynamics. The resulting equations describe a finite-temperature superfluid liquid with the distributed vorticity. The main dissipative effects, including mutual friction, are taken into account. The proposed hydrodynamics is needed for reliable modeling of the dynamical properties of superfluid neutron stars.

By neglecting the self-force, self-energy, and radiative effects, it has been shown that an extremal or near-extremal Kerr-Newman black hole can turn into a naked singularity when it captures charged and spinning massive particles. A straightforward question then arises: do charged and rotating black holes in string theory possess the same property? In this paper we apply Wald’s gedanken experiment, in his study on the possibility of destroying extremal Kerr-Newman black holes, to the case of (near-)extremal Kerr-Sen black holes. We find that feeding a test particle into a (near-)extremal Kerr-Sen black hole could lead to a violation of the extremal bound for the black hole.

Eternal inflation is studied in the context of warm inflation. We focus on different tools to analyze the effects of dissipation and the presence of a thermal radiation bath on the fluctuation-dominated regime, for which the self-reproduction of Hubble regions can take place. The tools we explore are the threshold inflaton field and threshold number of e-folds necessary to establish a self-reproduction regime and the counting of Hubble regions, using generalized conditions for the occurrence of a fluctuation-dominated regime. We obtain the functional dependence of these quantities on the dissipation and temperature. A Sturm-Liouville analysis of the Fokker-Planck equation for the probability of having eternal inflation and an analysis for the probability of having eternal points are performed. We have considered the representative cases of inflation models with monomial potentials of the form of chaotic and hilltop ones. Our results show that warm inflation tends to initially favor the onset of a self-reproduction regime for smaller values of the dissipation. As the dissipation increases, it becomes harder than in cold inflation (i.e., in the absence of dissipation) to achieve a self-reproduction regime for both types of models analyzed. The results are interpreted, and explicit analytical expressions are given whenever that is possible.

The linear halo bias is the response of the dark matter halo number density to a long-wavelength fluctuation in the dark matter density. Using abundance matching between separate universe simulations which absorb the latter into a change in the background, we test the consistency relation between the change in a one-point function, the halo mass function, and a two-point function, the halo-matter cross-correlation in the long-wavelength limit. We find excellent agreement between the two at the 1%–2% level for average halo biases between $1\lesssim {\overline{b}}_1\lesssim 4$ and no statistically significant deviations at the 4%–5% level out to ${\overline{b}}_1\approx 8$. The halo bias inferred assuming instead a universal mass function is significantly different and inaccurate at the 10% level or more. The separate universe technique provides a way of calibrating the linear halo bias efficiently for even highly biased rare halos in the $\mathrm{\Lambda }$ cold dark matter model. Observational violation of the consistency relation would indicate new physics, e.g. in the dark matter, dark energy, or primordial non-Gaussianity sectors.

Being able to reliably track perturbations across bounces and turnarounds in cyclic and bouncing cosmology lies at the heart of being able to compare the predictions of these models with the cosmic microwave background observations. This has been a challenging task due to the unknown nature of the physics involved during the bounce as well as the technical challenge of matching perturbations precisely between the expansion and contraction phases. In this paper, we present some general techniques (analytical and numerical) that can be applied to understand the physics of the fluctuations, especially those with “long” wavelengths, and apply our techniques to nonsingular cosmological models such as the bounce inflation and cyclic inflation.

When the Higgs field starts oscillation after Higgs inflation, gauge bosons are produced nonperturbatively near the enhanced symmetry point (ESP). Just after the particle production, when the Higgs field is going away from the ESP, these gauge bosons gain mass and decay or annihilate into Standard Model (SM) fermions. Left-handed neutrinos can be generated in that way. If one assumes the seesaw mechanism, the mass matrix of a pair of left- and right-handed neutrinos is nondiagonal. Although their mixing in the mass eigenstates is negligible in the true vacuum, it could be significant near the edge of the Higgs oscillation, where the off-diagonal component is large. Therefore, the left-handed neutrinos generated from the gauge bosons can start neutrino oscillation between the right-handed neutrinos. We study the particle production when such left-right (L-R) neutrino oscillation is significant. For a working example, the nonthermal leptogenesis scenario after Higgs inflation is examined, which cannot be realized without the L-R neutrino oscillation. The same mechanism could be applied to other singlet particles whose abundance has been neglected.

Observations using the Fermi Large Area Telescope (Fermi-LAT) have found a significant $\gamma$-ray excess surrounding the center of the Milky Way (GC). One possible interpretation of this excess invokes $\gamma$-ray emission from an undiscovered population of either young or recycled pulsars densely clustered throughout the inner kiloparsec of the Milky Way. While these systems, by construction, have individual fluxes that lie below the point-source sensitivity of the Fermi-LAT, they may already be observed in multiwavelength observations. Notably the Australia Telescope National Facility (ATNF) catalog of radio pulsars includes 270 sources observed in the inner 10° around the GC. We calculate the $\gamma$-ray emission observed from these 270 sources and obtain three key results: (1) point-source searches in the GC region produce a plethora of highly significant $\gamma$-ray “hot spots” compared to searches far from the Galactic Plane, (2) there is no statistical correlation between the positions of these $\gamma$-ray hot spots and the locations of ATNF pulsars, and (3) the spectrum of the most statistically significant $\gamma$-ray hot spots is substantially softer than the spectrum of the GC $\gamma$-ray excess. These results place strong constraints on models where young pulsars produce the majority of the $\gamma$-ray excess, and disfavor some models where millisecond pulsars produce the $\gamma$-ray excess.

Observable states are gauge invariant. In a non-Abelian gauge theory, these are necessarily composite operators. We investigate the spectrum of these operators in the two-Higgs-doublet model. For this purpose, we are working along the lines of the Fröhlich-Morchio-Strocchi mechanism to relate the physical spectrum to the spectrum of the elementary particles. We also investigate the consequences of spontaneous breaking of the global (custodial) symmetry group. Finally, we briefly comment on how to test the results using lattice methods.

We show how the Higgs boson mass is protected from the potentially large corrections due to the introduction of minimal dark matter if the new physics sector is made supersymmetric. The fermionic dark matter candidate (a 5-plet of $SU(2{)}_L$) is accompanied by a scalar state. The weak gauge sector is made supersymmetric, and the Higgs boson is embedded in a supersymmetric multiplet. The remaining standard model states are nonsupersymmetric. Nonvanishing corrections to the Higgs boson mass only appear at three-loop level, and the model is natural for dark matter masses up to 15 TeV—a value larger than the one required by the cosmological relic density. The construction presented stands as an example of a general approach to naturalness that solves the little hierarchy problem which arises when new physics is added beyond the standard model at an energy scale around 10 TeV.

We present the first calculation of the electromagnetic form factor of the $\pi$ meson at physical light quark masses. We use configurations generated by the MILC Collaboration including the effect of $u$, $d$, $s$ and $c$ sea quarks with the highly improved staggered quark formalism. We work at three values of the lattice spacing on large volumes and with $u/d$ quark masses going down to the physical value. We study scalar and vector form factors for a range in spacelike $q^2$ from 0.0 to $-0.13{\mathrm{GeV}}^2$ and from their shape we extract mean square radii. Our vector form factor agrees well with experiment and we find $⟨r^2{⟩}_V=0.403(18)(6){\mathrm{fm}}^2$. For the scalar form factor we include quark-line disconnected contributions which have a significant impact on the radius. We give the first results for SU(3) flavor-singlet and flavor-octet scalar mean square radii, obtaining $⟨r^2{⟩}_S^{\text{singlet}}=0.506(38)(53){\mathrm{fm}}^2$ and $⟨r^2{⟩}_S^{\text{octet}}=0.431(38)(46){\mathrm{fm}}^2$. We discuss the comparison with expectations from chiral perturbation theory.