Restricted Schur polynomials have been posited as orthonormal operators for the change of basis from $\mathcal{N}=4$ SYM to type IIB string theory. In this paper we briefly expound the relationship between the restricted Schur polynomials and the operators forwarded by Brown, Heslop, and Ramgoolam. We then briefly examine the finite $N$ counting of the restricted Schur polynomials.

Investigations of quantum Einstein gravity (QEG) based upon the effective average action employ a flow equation which does not contain any ultraviolet (UV) regulator. Its renormalization group trajectories emanating from a non-Gaussian fixed point define asymptotically safe quantum field theories. A priori these theories are, somewhat unusually, given in terms of their effective rather than bare action. In this paper we construct a functional integral representation of these theories. We fix a regularized measure and show that every trajectory of effective average actions, depending on an IR cutoff only, induces an associated trajectory of bare actions which depend on a UV cutoff. Together with the regularized measure these bare actions give rise to a functional integral which reproduces the prescribed effective action when the UV cutoff is removed. In this way we are able to reconstruct the underlying microscopic (classical) system and identify its fundamental degrees of freedom and interactions. The bare action of the Einstein-Hilbert truncation is computed and its flow is analyzed as an example. Various conceptual issues related to the completion of the asymptotic safety program are discussed.

We consider the decay of a metastable domain wall. The transition proceeds through quantum tunneling, and we calculate in an arbitrary number of dimensions the preexponential factor multiplying the leading semiclassical exponential expression for the rate of the process. We find that the effect of the motion in transverse directions reduces to a renormalization of the tension of the edge of the wall in the semiclassical exponent. This behavior is similar to the one previously found for breaking of a metastable string. However, this simple property is generally lost for spontaneous decay of higher-dimensional branes.

Standard entropy calculations in quantum field theory, when applied to a subsystem of definite volume, exhibit area-dependent UV divergences that make a thermodynamic interpretation troublesome. In this paper we define a renormalized entropy which is related with the Newton-Wigner position operator. Accordingly, whenever we trace over a region of space, we trace away degrees of freedom that are localized according to Newton-Wigner localization but not in the usual sense. We consider a free scalar field in $d+1$ spacetime dimensions prepared in a thermal state and we show that our entropy is free of divergences and has a perfectly sound thermodynamic behavior. In the high temperature/big volume limit our results agree with the standard QFT calculations once the divergent contributions are subtracted from the latter. In the limit of low temperature/small volume the entropy goes to zero but with a different dependence on the temperature.

The dynamical breaking of gauge symmetry in the supersymmetric quantum electrodynamics in three-dimensional spacetime is studied at two-loop approximation. At this level, the effective superpotential is evaluated in a supersymmetric phase. At one-loop order, we observe a generation of the Chern-Simons term due to a parity violating term present in the classical action. At two-loop order, the scalar background superfield acquires a nonvanishing vacuum expectation value, generating a mass term $A^{\alpha }{A}_{\alpha }$ through the Coleman-Weinberg mechanism. It is observed that the mass of gauge superfield is predominantly an effect of the topological Chern-Simons term.

We study the properties of the space of thermodynamic equilibrium states of the Bañados-Teitelboim-Zanelli (BTZ) black hole in ($2+1$) gravity. We use the formalism of geometrothermodynamics to introduce in the space of equilibrium states a two-dimensional thermodynamic metric whose curvature is nonvanishing, indicating the presence of thermodynamic interaction, and free of singularities, indicating the absence of phase transitions. Similar results are obtained for generalizations of the BTZ black hole which include a Chern-Simons term and a dilatonic field. Small logarithmic corrections of the entropy turn out to be represented by small corrections of the thermodynamic curvature, reinforcing the idea that thermodynamic curvature is a measure of thermodynamic interaction.

It is known that the total gravitational energy in localized sources that have static spherical symmetry and satisfy energy conditions is negative (attractive gravity). A natural query is how the gravitational energy behaves under circumstances where energy conditions are violated. To answer this, the known expression for the gravitational energy is suitably adapted to account for situations like the ones occurring in wormhole spacetime. It is then exemplified that in many cases the modified expression yields desirable answers. The implications are discussed.

We study an extension of the minimal supersymmetric standard model with a singlet supermultiplet $S$ with coupling $S{H}_1{H}_2$ in order to solve the $\mu$ problem as in the next-to-minimal supersymmetric standard model, and right-handed neutrino supermultiplets $N$ with couplings $SNN$ in order to generate dynamically electroweak-scale Majorana masses. We show how in this model a purely right-handed sneutrino can be a viable candidate for cold dark matter in the Universe. Through the direct coupling to the singlet, the sneutrino cannot only be thermal relic dark matter but also have a large enough scattering cross section with nuclei to detect it directly in the near future, in contrast with most other right-handed sneutrino dark matter models.

For an unsteady baryonic gamma-ray burst (GRB) outflow, the fast and slow proton shells collide with each other and produce energetic soft gamma-ray emission. If the outflow has a significant neutron component, the ultrarelativistic neutrons initially expand freely until decaying at a larger radius. The late-time proton shells ejected from the GRB central engine, after powering the regular internal shocks, will sweep these $\beta$-decay products and give rise to very bright UV/optical emission. The naked-eye optical flash from GRB 080319B, an energetic explosion in the distant Universe, can be well explained in this way.

In this work we study the predominantly orbital and radial excitations of hadrons containing a single heavy quark. We present meson and baryon mass splittings and ratios of meson decay constants (e.g., $f_{B_s}/f_B$ and $f_{B_s^{\prime }}/f_{B_s}$) resulting from quenched and dynamical two-flavor configurations. Light quarks are simulated using the chirally improved lattice Dirac operator at valence masses as light as $M_{\pi }\approx 350\mathrm{MeV}$. The heavy quark is approximated by a static propagator, appropriate for the $b$ quark on our lattices ($1/a\sim 1–2\mathrm{GeV}$). We also include some preliminary calculations of the $O(1/m_Q)$ kinetic corrections to the states, showing, in the process, a viable way of applying the variational method to three-point functions involving excited states. We compare our results with recent experimental findings.

We present a new model, based on color rearrangements, which at the same time can describe both hidden and open charm production in $B$-meson decays. The model is successfully compared to both inclusive decays, such as $B\to J/\psi X$ and $B\to D_{s}X$, as well as exclusive ones, such as $B\to J/\psi K^{(*)}$ and $B\to D^{(*)}{D}^{(*)}K$. It also gives a good description of the momentum distribution of direct $J/\psi$’s, especially in the low-momentum region, which earlier has been claimed as a possible signal for new exotic states.

Exclusive photoproduction of dileptons, $\gamma N\to {\ell }^{+}{\ell }^{-}N$, is and will be measured in ultraperipheral collisions at hadron colliders, such as the Tevatron, Relativistic Heavy Ion Collider, and the LHC. We demonstrate that the timelike deeply virtual Compton scattering mechanism $\gamma q\to {\ell }^{+}{\ell }^{-}q$ where the lepton pair comes from the subprocess $\gamma q\to {\gamma }^{*}q$ dominates in some accessible kinematical regions, thus opening a new way to study generalized parton distributions in the nucleon. High energy kinematics enables one to probe parton distributions at small skewedness. This subprocess interferes at the amplitude level with the pure QED subprocess $\gamma {\gamma }^{*}\to {\ell }^{+}{\ell }^{-}$ where the virtual photon is radiated from the nucleon.

The up- and down-quark masses are determined from an optimized QCD finite-energy sum rule involving the correlator of axial-vector divergences, to five-loop order in perturbative QCD, and including leading nonperturbative QCD and higher order quark-mass corrections. This finite-energy sum rule is designed to reduce considerably the systematic uncertainties arising from the (unmeasured) hadronic resonance sector, which in this framework contributes less than 3–4% to the quark mass. This is achieved by introducing an integration kernel in the form of a second degree polynomial, restricted to vanish at the peak of the two lowest lying resonances. The driving hadronic contribution is then the pion pole, with parameters well known from experiment. The determination is done in the framework of contour improved perturbation theory, which exhibits a very good convergence, leading to a remarkably stable result in the unusually wide window $s_0=1.0–4.0{\mathrm{GeV}}^2$, where $s_0$ is the radius of the integration contour in the complex energy (squared) plane. The results are $m_u(Q=2\mathrm{GeV})=2.9\pm 0.2\mathrm{MeV}$, $m_d(Q=2\mathrm{GeV})=5.3\pm 0.4\mathrm{MeV}$, and $(m_u+m_d)/2=4.1\pm 0.2\mathrm{MeV}$ (at a scale $Q=2\mathrm{GeV}$).

We investigate the possibility of generating neutrino masses in the context of split supersymmetric scenarios where all sfermions are very heavy. All relevant contributions coming from the R-parity violating terms to the neutrino mass matrix up to one-loop level are computed showing the importance of the Higgs bosons one-loop corrections. We conclude that it is not possible to generate all neutrino masses and mixings in split SUSY with bilinear R-parity violating interactions. In the case of partial split SUSY, the one-loop Higgs bosons contributions are enough to generate the neutrino masses and mixings in agreement with the experiment. In the context of minimal SUSY SU(5), we find new contributions that help us to generate neutrino masses in the case of split SUSY.

Semileptonic $\overline{B}$ decays to $DX\ell \overline{\nu }$ ($\ell =e$ or $\mu$) are selected by reconstructing $D^0\ell$ and $D^{+}\ell$ combinations from a sample of $230\times {10}^6$ ${\rm Y}(4S)\to B\overline{B}$ decays recorded with the BABAR detector at the PEP-II $e^{+}{e}^{-}$ collider at SLAC. A global fit to these samples in a three-dimensional space of kinematic variables is used to determine the branching fractions $\mathcal{B}(B^{-}\to D^0\ell \overline{\nu })=(2.34\pm 0.03\pm 0.13)\%$ and $\mathcal{B}(B^{-}\to D^{*0}\ell \overline{\nu })=(5.40\pm 0.02\pm 0.21)\%$ where the errors are statistical and systematic, respectively. The fit also determines form-factor parameters in a parametrization based on heavy quark effective theory, resulting in ${\rho }_D^2=1.20\pm 0.04\pm 0.07$ for $\overline{B}\to D\ell \overline{\nu }$ and ${\rho }_{D^{*}}^2=1.22\pm 0.02\pm 0.07$ for $\overline{B}\to D^{*}\ell \overline{\nu }$. These values are used to obtain the product of the Cabibbo-Kobayashi-Maskawa matrix element $|V_{cb}|$ times the form factor at the zero recoil point for both $\overline{B}\to D\ell \overline{\nu }$ decays, $\mathcal{G}(1)|V_{cb}|=(43.1\pm 0.8\pm 2.3)\times {10}^{-3}$, and for $\overline{B}\to D^{*}\ell \overline{\nu }$ decays, $\mathcal{F}(1)|V_{cb}|=(35.9\pm 0.2\pm 1.2)\times {10}^{-3}$.

We present measurements of the $CP$-violation parameters $S$ and $C$ for the radiative decay $B^0\to \eta K_S^0\gamma$; for $B\to \eta K\gamma$ we also measure the branching fractions and for $B^{+}\to \eta K^{+}\gamma$ the time-integrated charge asymmetry ${\mathcal{A}}_{ch}$. The data, collected with the BABAR detector at the Stanford Linear Accelerator Center, represent $465\times {10}^6$ $B\overline{B}$ pairs produced in $e^{+}{e}^{-}$ annihilation. The results are $S=-{0.18}_{-0.46}^{+0.49}\pm 0.12$, $C=-{0.32}_{-0.39}^{+0.40}\pm 0.07$, $\mathcal{B}(B^0\to \eta K^0\gamma )=({7.1}_{-2.0}^{+2.1}\pm 0.4)\times {10}^{-6}$, $\mathcal{B}(B^{+}\to \eta K^{+}\gamma )=(7.7\pm 1.0\pm 0.4)\times {10}^{-6}$, and ${\mathcal{A}}_{ch}=(-{9.0}_{-9.8}^{+10.4}\pm 1.4)\times {10}^{-2}$. The first error quoted is statistical and the second systematic.

We construct a solution of two black holes on a Kaluza-Klein bubble in Einstein-Maxwell-dilaton theory. We explore the consequences of the presence of charge for the properties of this solution, and obtain a generalized Smarr relation and first law.

Although $f(R)$ modified gravity models can be made to satisfy solar system and cosmological constraints, it has been shown that they have the serious drawback of the nonexistence of stars with strong gravitational fields. In this paper, we discuss whether or not higher curvature corrections can remedy the nonexistence consistently. The following problems are shown to arise as the costs one must pay for the $f(R)$ models that allow for neutrons stars: (i) the leading correction must be fine-tuned to have the typical energy scale $\mu \lesssim {10}^{-19}\mathrm{GeV}$, which essentially comes from the free fall time of a relativistic star; (ii) the leading correction must be further fine-tuned so that it is not given by the quadratic curvature term. The second problem is caused because there appears an intermediate curvature scale, and laboratory experiments of gravity will be under the influence of higher curvature corrections. Our analysis thus implies that it is a challenge to construct viable $f(R)$ models without very careful and unnatural fine-tuning.

In this paper we study the Landau levels in the nonrelativistic dynamics of a neutral particle which possesses a permanent magnetic dipole moment interacting with an external electric field in the curved space-time background with the presence or absence of a torsion field. The eigenfunction and eigenvalues of the Hamiltonian are obtained. We show that the presence of the topological defect breaks the infinite degeneracy of the Landau levels arising in this system. We also apply a duality transformation to discuss this same quantization for a dynamics of a neutral particle with a permanent electric dipole moment.

Control of systematic uncertainties in the use of type Ia supernovae as standardized distance indicators can be achieved through contrasting subsets of observationally characterized, like supernovae. Essentially, like supernovae at different redshifts reveal the cosmology, and differing supernovae at the same redshift reveal systematics, including evolution not already corrected for by the standardization. Here we examine the strategy for use of empirically defined subsets to minimize the cosmological parameter risk, the quadratic sum of the parameter uncertainty and systematic bias. We investigate the optimal recognition of subsets within the sample and discuss some issues of observational requirements on accurately measuring subset properties. Neglecting like vs like comparison (i.e. creating only a single Hubble diagram) can cause cosmological constraints on dark energy to be biased by $1\sigma$ or degraded by a factor of 1.6 for a total drift of 0.02 mag. Recognition of subsets at the 0.016 mag level (relative differences) erases bias and reduces the degradation to 2%.