Wess-Zumino-Witten (WZW) models are abstract conformal field theories with an infinite-dimensional symmetry which accounts for their integrability, and at the same time they have a sigma-model description of closed-string propagation on group manifolds which, in turn, endows the models with an intuitive geometric meaning. We exploit this dual algebraic and geometric property of WZW models to construct an explicit example of a field-dependent reflection matrix for open strings in the Nappi-Witten model. Demanding the momentum outflow at the boundary to be zero determines a certain combination of the left and right chiral currents at the boundary. This same reflection matrix is obtained algebraically from an inner automorphism, giving rise to a space-filling D-brane. Half of the infinite-dimensional affine Kac-Moody symmetry present in the closed-string theory is preserved by this unique combination of the left and the right chiral currents. The operator-product expansions of these boundary currents are computed explicitly and they are shown to obey the same current algebra as those of the closed-string chiral currents. Different choices of the inner automorphisms correspond to different background gauge field configurations. Only those B-field configurations, and the corresponding D-branes, that preserve the diagonal part of the infinite-dimensional chiral algebras are allowed. In this way the existence of the D-branes in curved spaces is further constrained by the underlying symmetry of the ambient spacetime.

The quantization of the giant magnon away from the infinite size limit is discussed. We argue that this quantization inevitably leads to string theory on a $Z_M$ orbifold of $S^5$. This is shown explicitly and examined in detail in the near plane-wave limit.

We study baryons as Skyrmions in holographic QCD with $\mathrm{D}4/\mathrm{D}8/\overline{\mathrm{D}8}$ multi-D brane system in type IIA superstring theory, and also in the nonlinear sigma model with hidden local symmetry. Comparing these two models, we find that the extra dimension and its nontrivial curvature can largely change the role of (axial) vector mesons for baryons in four-dimensional space-time. In the hidden local symmetry approach, the $\rho$-meson field as a massive Yang-Mills field has a singular configuration in Skyrmion, which gives a strong repulsion for the baryon as a stabilizer. When the $a_1$ meson is added in this approach, the stability of Skyrmion is lost by the cancellation of $\rho$ and $a_1$ contributions. On the contrary, in holographic QCD, the $\rho$-meson field does not appear as a massive Yang-Mills field due to the extra dimension and its nontrivial curvature. We show that the $\rho$-meson field has a regular configuration in Skyrmion, which gives a weak attraction for the baryon in holographic QCD. We argue that Skyrmion with $\pi$, $\rho$, and $a_1$ mesons become stable due to the curved extra dimension and also the presence of the Skyrme term in holographic QCD. From this result, we also discuss the features of our truncated-resonance analysis on baryon properties with $\pi$ and $\rho$ mesons below the cutoff scale $M_{\mathrm{KK}}\sim 1\mathrm{GeV}$ in holographic QCD, which is compared with other 5D instanton analysis.

We study “holographic superconductors” in various spacetime dimensions. We compute most of the static critical exponents in the linear perturbations and show that they take the standard mean-field values. We also consider the dynamic universality class for these models and show that they belong to model A with dynamic critical exponent $z=2$.

The model of the position-dependent noncommutativity in quantum mechanics is proposed. We start with given commutation relations between the operators of coordinates $[{\widehat{x}}^i,{\widehat{x}}^j]={\omega }^{ij}(\widehat{x})$, and construct the complete algebra of commutation relations, including the operators of momenta. The constructed algebra is a deformation of a standard Heisenberg algebra and obeys the Jacobi identity. The key point of our construction is a proposed first-order Lagrangian, which after quantization reproduces the desired commutation relations. Also we study the possibility to localize the noncommutativity.

We consider the Bekenstein-Hawking entropy-area formula in four dimensional extended ungauged supergravity and its electric-magnetic duality property. Symmetries of both “large” and “small” extremal black holes are considered, as well as the ADM mass formula for $\mathcal{N}=4$ and $\mathcal{N}=8$ supergravity, preserving different fraction of supersymmetry. The interplay between BPS conditions and duality properties is an important aspect of this investigation.

We use the harmonic maps ansatz to find exact solutions of the Einstein-Maxwell-dilaton-axion (EMDA) equations. The solutions are harmonic maps invariant to the symplectic real group in four dimensions $Sp(4,\mathbb{R})\sim O(5)$. We find solutions of the EMDA field equations for the one- and two-dimensional subspaces of the symplectic group. Specially, for illustration of the method, we find space-times that generalize the Schwarzschild solution with dilaton, axion, and electromagnetic fields.

AdS/CFT correspondence is now widely used for the study of strongly coupled plasmas, such as those produced in ultrarelativistic heavy ion collisions at the Relativistic Heavy Ion Collider. While properties of equilibrated plasma and small deviations from equilibrium are by now reasonably well understood, the plasma’s initial formation and thermal equilibration is a much more challenging issue which remains to be studied. In the dual gravity language, these problems are related to the formation of bulk black holes, and studying trapped surfaces, as we do in this work, is a way to estimate the properties (temperature and entropy) of such black holes. Extending the work by Gubser et al. for central collisions, we find numerically trapped surfaces for noncentral collisions of ultrarelativistic black holes (gravitational shock waves) with different energies. We observe that beyond a certain critical impact parameter, the trapped surface does not exist, and we argue that there are some experimental indications for a similar jump in entropy production as a function of the impact parameter in real heavy ion collisions. We also present a simple solvable example of the so-called wall-on-wall collision, for colliding objects that depend on the holographic coordinate only. Finally, we critically discuss the applicability of the AdS/CFT approach to real-world heavy ion collisions.

In paper I in this series, we found exact expressions for the equatorial homoclinic orbits: the separatrix between bound and plunging, whirling and not whirling motion. As a companion to that physical space study, in this paper we paint a phase space portrait of the homoclinic orbits that includes exact expressions for the actions and fundamental frequencies. Additionally, we develop a reduced Hamiltonian description of Kerr motion that allows us to track groups of trajectories with a single global clock. This facilitates a variational analysis, whose stability exponents and eigenvectors could potentially be useful for future studies of families of black hole orbits and their associated gravitational waveforms.

For equatorial Kerr orbits, we show that each separatrix between bound and plunging geodesics is a homoclinic orbit—an orbit that asymptotes to an energetically-bound, unstable circular orbit. We derive exact expressions for these trajectories in terms of elementary functions. We also clarify the formal connection between the separatrix and zoom-whirl orbits and show that, contrary to popular belief, zoom-whirl behavior is not intrinsically a near-separatrix phenomenon. This paper focuses on homoclinic behavior in physical space, while in a companion paper we paint the complementary phase space portrait. Although they refer to geodesic motion, the exact solutions for the Kerr separatrix could be useful for analytic or numerical studies of eccentric transitions from orbital to plunging motion under the dissipative effects of gravitational radiation.

Spontaneous Lorentz symmetry breaking can occur when the dynamics of a tensor field cause it to take on a nonzero expectation value in vacuo, thereby providing one or more “preferred directions” in spacetime. Couplings between such fields and spacetime curvature will then affect the dynamics of the metric, leading to interesting gravitational effects. Bailey and Kostelecký [Q. G. Bailey and V. A. Kostelecký, Phys. Rev. D 74, 045001 (2006)] developed a post-Newtonian formalism that, under certain conditions concerning the field’s couplings and stress-energy, allows for the analysis of gravitational effects in the presence of Lorentz symmetry breaking. We perform a systematic survey of vector models of spontaneous Lorentz symmetry breaking. We find that a two-parameter class of vector models, those with kinetic terms we call “pseudo-Maxwell,” can be successfully analyzed under the Bailey-Kostelecký formalism, and that one of these two “dimensions” in parameter space has not yet been explored as a possible mechanism of spontaneous Lorentz symmetry breaking.

This work deals with the dynamics of inflation in the context of a scalar-vector-tensor theory of gravity exhibiting spontaneous Lorentz violation at early times. We describe a first-order formalism which we use to obtain new exact Lorentz violating inflationary solutions for a broad family of models, some in the absence of a potential for the inflaton field. Our results show that different conditions are required to solve the horizon and flatness problems. In particular, we find a necessary condition for inflation to provide a solution to both problems and we show that in inflationary models with no inflaton potential a period of superinflation might be necessary to solve the flatness problem.

The structural properties of geodesic currents in an ambient Kerr background are studied from an analytical point of view. The geodesics in this congruence may correspond to charged particles that carry energy and angular momentum from the black hole through the Blandford-Znajek mechanism. It is shown that the resulting magnetosphere naturally satisfies the Znajek regularity condition. Particular attention is paid here to the energy extracted by matter currents rather than by electromagnetic Poynting fluxes. This analytic study is motivated by the mathematical structure behind the Blandford-Znajek process, and may only have limited applications to the astrophysics of supermassive black holes.

The application of higher-order Laguerre-Gauss (LG) modes in large-scale gravitational wave detectors has recently been proposed. In comparison to the fundamental mode, some higher-order Laguerre-Gauss modes can significantly reduce the contribution of coating Brownian noise. Using frequency domain simulations we give a detailed analysis of the longitudinal and angular control signals derived with a ${\mathrm{LG}}_{33}$ mode in comparison to the fundamental transverse electromagnetic ${\mathrm{TEM}}_{00}$ mode. The performance regarding interferometric sensing and control of the ${\mathrm{LG}}_{33}$ mode is found to be similar, if not even better in all aspects of interest. In addition, we evaluate the sensitivity gain of the implementation of ${\mathrm{LG}}_{33}$ modes into the Advanced Virgo instrument. Our analysis shows that the application of the ${\mathrm{LG}}_{33}$ mode results in a broadband improvement of the Advanced Virgo sensitivity, increasing the potential detection rate of binary neutron star inspirals by a factor 2.1.

Using numerical methods we present the first full nonlinear study of a phantom scalar field accreted into a black hole. We study different initial configurations and find that the accretion of the field into the black hole can reduce its area down to 50 percent within time scales of the order of few masses of the initial horizon. The analysis includes the cases where the total energy of the space-time is positive or negative. The confirmation of this effect in full nonlinear general relativity implies that the accretion of exotic matter could be considered an evaporation process. We speculate that if this sort of exotic matter has some cosmological significance, this black hole area reduction process might have played a crucial role in black hole formation and population.

In the limit of large $N_c$ we first consider the $N_c$ ordering of the various parity-violating $\pi$, $N$, $\Delta$ couplings. Then we derive the relations among these couplings and consistency relations from the stability of these couplings under the chiral loop corrections with and without the mass splitting between $N$ and $\Delta$. Especially we find that $h_{\Delta }=-\frac{3}{\sqrt{5}}{h}_{\pi }$ in the large $N_c$ limit, which correctly reproduces the relative sign and magnitude of the Desplanques-Donoghue-Holstein values for these parity-violating couplings.

We investigate the QCD effects in the production of neutral Higgs bosons via bottom quark fusion in both the standard model and the minimal supersymmetric standard model at the CERN Large Hadron Collider. We include the next-to-leading order (NLO) QCD corrections (including supersymmetric QCD) and the threshold resummation effects. We use the soft-collinear effective theory to resum the large logarithms near threshold from soft gluon emission. Our results show that the resummation effects can enhance the total cross sections by about 5% compared with the NLO results.

We report on a Dalitz plot analysis of $B^{-}\to D^{+}{\pi }^{-}{\pi }^{-}$ decays, based on a sample of about $383\times {10}^6$ ${\rm Y}(4\mathrm{S})\to B\overline{B}$ decays collected with the BABAR detector at the PEP-II asymmetric-energy $B$ Factory at SLAC. We find the total branching fraction of the three-body decay: $\mathcal{B}(B^{-}\to D^{+}{\pi }^{-}{\pi }^{-})=(1.08\pm 0.03\pm 0.05)\times {10}^{-3}$. We observe the established $D_2^{*0}$ and confirm the existence of $D_0^{*0}$ in their decays to $D^{+}{\pi }^{-}$, where the $D_2^{*0}$ and $D_0^{*0}$ are the $2^{+}$ and $0^{+}c\overline{u}$ $P$-wave states, respectively. We measure the masses and widths of $D_2^{*0}$ and $D_0^{*0}$ to be: $m_{D_2^{*0}}=(2460.4\pm 1.2\pm 1.2\pm 1.9)\mathrm{MeV}/c^2$, ${\Gamma }_{D_2^{*0}}=(41.8\pm 2.5\pm 2.1\pm 2.0)\mathrm{MeV}$, $m_{D_0^{*0}}=(2297\pm 8\pm 5\pm 19)\mathrm{MeV}/c^2$, and ${\Gamma }_{D_0^{*0}}=(273\pm 12\pm 17\pm 45)\mathrm{MeV}$. The stated errors reflect the statistical and systematic uncertainties, and the uncertainty related to the assumed composition of signal events and the theoretical model.

We use operator product expansion (OPE) techniques to study the spectral functions of currents and stress tensors at finite temperature, in the high-energy timelike region $\omega \gg T$. The leading corrections to these spectral functions are proportional to $\sim T^4$ expectation values in general, and the leading corrections $\sim g^2{T}^4$ are calculated at weak coupling, up to an undetermined coefficient in the shear viscosity channel. Spectral functions are shown to be infrared safe, in the deeply virtual regime, up to order $g^8{T}^4$. The convergence of (vacuum subtracted) sum rules in the shear and bulk viscosity channels is established in QCD to all orders in perturbation theory, though numerically significant tails $\sim T^4/(\log \omega {)}^3$ are shown to exist in the bulk viscosity channel. We argue that the spectral functions of currents and stress tensors in infinitely coupled $\mathcal{N}=4$ super Yang-Mills theory do not receive any medium-dependent power correction.

By applying the recently developed loop regularization (LR) with string-mode regulators to supersymmetric field theories, we explicitly verify the supersymmetric Ward identities in several supersymmetric models at one-loop level. It is interesting to observe that supersymmetry is such a remarkable symmetry that the supersymmetric Ward identities hold as long as a regularization scheme is realized in the exact four-dimensional space-time with translational invariance for the momentum integration, and the gauge symmetry can be maintained once the regularization scheme preserves supersymmetry and satisfies the consistency condition for logarithmic divergences. As a manifest demonstration, we carry out a complete one-loop renormalization for the massive Wess-Zumino model by adopting the LR method, and it is found that all the quadratic divergences cancel out and the relations among masses and coupling constants hold after renormalization, which agrees with the well-known nonrenormalization theorem. It is concluded that the LR method preserves not only gauge symmetry but also supersymmetry. A simple and definite derivation of Majorana Feynman rules is found to be very useful.