Strong coupling dynamics of Yang-Mills theories with chiral fermion content remained largely elusive despite much effort over the years. In this work, we propose a dynamical framework in which we can address nonperturbative properties of chiral, nonsupersymmetric gauge theories, in particular, chiral quiver theories on $S_1\times R_3$. Double-trace deformations are used to stabilize the center-symmetric vacuum. This allows one to smoothly connect small-$r(S_1)$ to large-$r(S_1)$ physics ($R_4$ is the limiting case) where the double-trace deformations are switched off. In particular, the occurrence of the mass gap in the gauge sector and linear confinement due to bions are analytically demonstrated. We find the pattern of the chiral symmetry realization which depends on the structure of the monopole-ring operators, a novel class of topological excitations. The deformed chiral theory, unlike the undeformed one, satisfies volume independence down to arbitrarily small volumes (a working Eguchi-Kawai reduction) in the large $N$ limit. This equivalence may open new perspectives on strong coupling chiral gauge theories on $R_4$.

We write an integral equation that incorporates finite corrections to the large spin asymptotics of $\mathcal{N}=4$ supersymmetric Yang-Mills theory twist operators from the nonlinear integral equation. We show that these corrections are an all-loop result, not affected by wrapping effects, and agree, after determining the strong coupling expansion, with string theory predictions.

It is shown that the existence of static, cylindrically symmetric wormholes does not require violation of the weak or null energy conditions near the throat, and cylindrically symmetric wormhole geometries can appear with less exotic sources than wormholes whose throats have a spherical topology. Examples of exact wormhole solutions are given with scalar, spinor and electromagnetic fields as sources, and these fields are not necessarily phantom. In particular, there are wormhole solutions for a massless, minimally coupled scalar field in the presence of a negative cosmological constant, and for an azimuthal Maxwell electromagnetic field. All these solutions are not asymptotically flat. A no-go theorem is proved, according to which a flat (or string) asymptotic behavior on both sides of a cylindrical wormhole throat is impossible if the energy density of matter is everywhere nonnegative.

We extend the discussion of the “Kerr/CFT correspondence” and its recent developments to the more general gauge/gravity correspondence in the full extremal black hole space-time of the bulk by using a technique of the holographic renormalization group (RG) flow. It is conjectured that the extremal black hole space-time is holographically dual to the chiral two-dimensional field theory. Our example is a typical four-dimensional Reissner-Nordstrom black hole, a system in which the M5-brane is wrapped on four cycles of Calabi-Yau threefold. In the five-dimensional supergravity viewpoint, this near horizon geometry is ${\mathrm{AdS}}_3\times {\mathrm{S}}^2$, and three-dimensional gravity coupled to moduli fields is effectively obtained after a dimensional reduction on ${\mathrm{S}}^2$. Constructing the Hamilton-Jacobi equation, we define the holographic RG flow from the three-dimensional gravity. The central charge of the Virasoro algebra is calculable from the conformal anomaly at the point where the beta function defined from the gravity side becomes zero. In general, we can also identify the $c$ function of the dual two-dimensional field theory. We show that these flow equations are completely equivalent to not only BPS but also non-BPS attractor flow equations of the moduli fields. The attractor mechanism by which the values of the moduli fields are fixed at the event horizon of the extremal black hole can be understood equivalently to the fact that the RG flows are fixed at the critical points in the dual field theory.

We analyze the dynamics of a single scalar field in Friedmann-Robertson-Walker universes with spatial curvature. We obtain the fixed point solutions which are shown to be late time attractors. In particular, we determine the corresponding scalar field potentials which correspond to these stable solutions. The analysis is quite general and incorporates expanding and contracting universes with both positive and negative scalar potentials. We demonstrate that the known power law, exponential, and de Sitter solutions are certain limits of our general set of solutions.

We investigate color superconducting phase at high density in the extended Nambu–Jona-Lasinio model for two-flavor quarks. Because of the nonrenormalizability of the model, physical observables may depend on the regularization procedure; that is why we apply two types of regularization, the cutoff and the dimensional one to evaluate the phase structure, the equation of state, and the relationship between the mass and the radius of a dense star. To obtain the phase structure we evaluate the minimum of the effective potential at finite temperature and chemical potential. The stress tensor is calculated to derive the equation of state. Solving the Tolman-Oppenheimer-Volkoff equation, we show the relationship between the mass and the radius of a dense star. The dependence on the regularization is found not to be small, interestingly. The dimensional regularization predicts color superconductivity phase at rather large values of $\mu$ (in agreement with perturbative QCD in contrast to the cutoff regularization), in the larger temperature interval, the existence of heavier and larger quark stars.

We study the nonperturbative dynamics of nonsupersymmetric asymptotically free gauge theories with fermionic matter in distinct representations of the $SO(N)$ and $Sp(2N)$ gauge groups. We use different analytic methods to unveil the associated conformal windows for the relevant matter representations. We propose a direct test for confronting and establishing the validity of the analytic methods used to constrain the conformal windows. By comparing the resulting windows for $SU$, $Sp$, and $SO$ a pleasing universal picture emerges.

We unveil the temperature-dependent electroweak phase transition in new extensions of the standard model in which the electroweak symmetry is spontaneously broken via strongly coupled, nearly conformal dynamics achieved by the means of multiple matter representations. In particular, we focus on the low energy effective theory introduced to describe ultra minimal walking technicolor at the phase transition. Using the one-loop effective potential with ring improvement, we identify regions of parameter space, which yield a strong first-order transition. A striking feature of the model is the existence of a second phase transition associated to the electroweak-singlet sector. The interplay between these two transitions leads to an extremely rich phase diagram.

Considering Dirac neutrinos and Fritzsch-like texture six zero and five zero mass matrices, detailed predictions for cases pertaining to normal/inverted hierarchy as well as degenerate scenario of neutrino masses have been carried out. All the cases considered here pertaining to inverted hierarchy and degenerate scenario of neutrino masses are ruled out by the existing data. For the normal hierarchy cases, the lower limit of $m_{{\nu }_1}$ and of $s_{13}$ as well as the range of Dirac-like $CP$ violating phase ${\delta }_l$ would have implications for the texture specific cases considered here.

The maximal $CP$ violation hypothesis is applied to a simple lepton mixing matrix form $U=V^{†}{U}_{\mathrm{TB}}$, $V$and $U_{\mathrm{TB}}$ are the quark mixing matrix and the so-called tribimaximal mixing matrix, respectively, which has recently been speculated under an ansatz that $U$ becomes an exact tribimaximal mixing $U_{\mathrm{TB}}$ in the limit of the quark mixing matrix $V\to \mathbf{1}$. The prediction ${tan}^2{\theta }_{12}=1/2$ in the case of the exact tribimaximal mixing $U=U_{\mathrm{TB}}$ is considerably spoiled in the speculated mixing $U=V^{†}{U}_{\mathrm{TB}}$. However, the application of the hypothesis to the lepton sector can again recover the spoiled value to ${tan}^2{\theta }_{12}\simeq 1/2$ if the original Kobayashi-Maskawa phase convention for $V$ is adopted.

We reexamine relic abundance of a singlet fermion as a cold dark matter candidate, which contributes to the neutrino mass generation through radiative seesaw mechanism. We search solutions for Yukawa couplings and the mass spectrum of relevant fields to explain neutrino oscillation data. For such solutions, we show that an abundance of a lightest singlet fermion can be consistent with WMAP data without conflicting with both bounds of $\mu \to e\gamma$ and $\tau \to \mu \gamma$. This reconciliation does not need any modification of the original radiative seesaw model other than by specifying flavor structure of Yukawa couplings and taking account of coannihilation effects.

The $CP$ asymmetry in neutrino oscillations, assuming new physics at production and/or detection processes, is analyzed. We compute this $CP$ asymmetry using the standard quantum field theory within a general new physics scenario that may generate new sources of $CP$ and flavor violation. Well-known results for the $CP$ asymmetry are reproduced in the case of $V-A$ operators, and additional contributions from new physics operators are derived. We apply this formalism to SUSY extensions of the standard model where the contributions from new operators could produce a $CP$ asymmetry observable in the next generation of neutrino experiments.

We investigate the interactions of closed strings in a IIB matrix model. The basic interaction of the closed superstring is realized by the recombination of two intersecting strings. Such interaction is investigated in a IIB matrix model via two-dimensional noncommutative gauge theory in the IR limit. By estimating the probability of the recombination, we identify the string coupling $g_s$ in the IIB matrix model. We confirm that our identification is consistent with matrix string theory.

In models where there is a global chiral symmetry which spontaneously breaks to its vectorial subgroup, the introduction of an explicit symmetry breaking perturbation will define the true vacuum of the theory. This true vacuum is found via the minimization of the expectation value of the perturbing Hamiltonian between different vacua as prescribed by Dashen. The procedure of finding the correct vacuum of the theory may result in the spontaneous breaking of $CP$ symmetry even if one initially demands $CP$ invariance on the perturbation. In this work we study, in detail, models where the perturbation is provided by four-Fermi operators. We present the exact treatment for models with two fermion flavors and study the three flavor case in depth numerically. We show that after the Dashen procedure is applied the solutions for the true vacuum fall in three classes with different $CP$ breaking patterns. Critical transitions are possible between these classes as one varies the parameters of the perturbation. We rigorously show that at these transitions a pseudo-Goldstone boson mass vanishes. We also advocate, and substantiate with numerical statistical analysis for various types of models, that if one imposes $CP$ invariance on the perturbation before solving the vacuum alignment, the resulting vacuum structure will have a sizable probability for a light pseudo-Goldstone boson mass. That is a statistical variant of Peccei-Quinn mechanism can be speculated to operate.

Template-based searches for gravitational waves are often limited by the computational cost associated with searching large parameter spaces. The study of efficient template banks, in the sense of using the smallest number of templates, is therefore of great practical interest. The traditional approach to template-bank construction requires every point in parameter space to be covered by at least one template, which rapidly becomes inefficient at higher dimensions. Here we study an alternative approach, where any point in parameter space is covered only with a given probability $\eta <1$. We find that by giving up complete coverage in this way, large reductions in the number of templates are possible, especially at higher dimensions. The prime examples studied here are random template banks in which templates are placed randomly with uniform probability over the parameter space. In addition to its obvious simplicity, this method turns out to be surprisingly efficient. We analyze the statistical properties of such random template banks, and compare their efficiency to traditional lattice coverings. We further study relaxed lattice coverings (using ${\mathbb{Z}}_n$ and $A_n^{*}$ lattices), which similarly cover any signal location only with probability $\eta$. The relaxed $A_n^{*}$ lattice is found to yield the most efficient template banks at low dimensions ($n\lesssim 10$), while random template banks increasingly outperform any other method at higher dimensions.

Gravitational waves from test masses bound to geodesic orbits of rotating black holes are simulated, using Teukolsky’s black hole perturbation formalism, for about ten thousand generic orbital configurations. Each binary radiates power exclusively in modes with frequencies that are integer-linear combinations of the orbit’s three fundamental frequencies. General spectral properties are found with a survey of orbits about a black hole taken to be rotating at 80% of the maximal spin. The orbital eccentricity is varied from 0.1 to 0.9. Inclination ranges from 20° to 160° and comes to within 20° of polar. Semilatus rectum is varied from 1.2 to 3 times the value at the innermost stable circular orbits. The following general spectral properties are found: (i) 99% of the radiated power is typically carried by a few hundred modes, and at most by about a thousand modes, (ii) the dominant frequencies can be grouped into a small number of families defined by fixing two of the three integer frequency multipliers, and (iii) the specifics of these trends can be qualitatively inferred from the geometry of the orbit under consideration. Detections using triperiodic analytic templates modeled on these general properties would constitute a verification of radiation from an adiabatic sequence of black hole orbits and would recover the evolution of the fundamental orbital frequencies. In an analogy with ordinary spectroscopy, this would compare to observing the Bohr model’s atomic hydrogen spectrum without being able to rule out alternative atomic theories or nuclei. The suitability of such a detection technique is demonstrated using snapshots computed at 12-hour intervals throughout the last three years before merger of a kludged inspiral. The system chosen is typical of those thought to occur in galactic nuclei and to be observable with space-based gravitational wave detectors like LISA. Because of circularization, the number of excited modes decreases as the binary evolves. A hypothetical detection algorithm that tracks mode families dominating the first 12 hours of the inspiral would capture 98% of the total power over the remaining three years.

The possibility of generation of nonextensive statistics, in the sense of Tsallis, due to space-time foam is discussed within the context of a particular kind of foam in string/brane theory, the D-particle foam model. The latter involves pointlike brane defects (D-particles), which provide the topologically nontrivial foamy structures of space-time. A stochastic Langevin equation for the velocity recoil of D-particles can be derived from the pinched approximation for a sum over genera in the calculation of the partition function of a bosonic string in the presence of heavy D-particles. The string coupling in standard perturbation theory is related to the exponential of the expectation of the dilaton. Inclusion of fluctuations of the dilaton itself and uncertainties in the string background will then necessitate fluctuations in $g_s$. The fluctuation in the string coupling in the sum over genera typically leads to a generic structure of the Langevin equation where the coefficient of the noise term fluctuates owing to dependence on the string coupling $g_s$. The positivity of $g_s$ leads naturally to a stochastic modeling of its distribution with a $\chi$ distribution. This then rigorously implies a Tsallis-type nonextensive or, more generally, a superstatistics distribution for the recoil velocity of D-particles. As a concrete and physically interesting application, we provide a rigorous estimate of an $\omega$-like effect, pertinent to $CPT$ violating modifications of the Einstein-Podolsky-Rosen correlators in entangled states of neutral kaons. In the case of D-particle foam fluctuations, which respect the Lorentz symmetry of the vacuum on average, we find that the $\omega$ effect may be within the range of sensitivity of future meson factories.

We construct static and mass-shedding limit sequences of hybrid stars, composed of a color flavour locked (CFL) quark matter core, for a set of equations of state (EOSs). The EOS for the hadronic matter is obtained using an appropriately calibrated, extended field theoretical based, relativistic mean-field model. The MIT bag model is employed to compute the EOSs of the CFL quark matter for different values of the CFL gap parameter in the range of 50–150 MeV with the deconfinement phase transition density ranging from $4{\rho }_0$ to $6{\rho }_0$ (${\rho }_0=0.16{\mathrm{fm}}^{-3}$). We find that, depending on the values of the CFL gap parameter and the deconfinement phase transition density, the sequences of stable configurations of hybrid stars either form third families of the compact stars or bifurcate from the hadronic sequence. The hybrid stars have masses $1.0–2.1M_{\odot }$ with radii 9–13.5 km. The maximum values of the mass-shedding limit frequency for such hybrid stars are 1–2 kHz. For the smaller values of the CFL gap parameter and the deconfinement phase transition density, mass-radius relationships are in harmony with those deduced by applying an improved hydrogen atmosphere model to fit the high quality spectra from compact star X7 in the globular cluster 47 Tucanae. We observed, for some cases, that the third family of compact stars exist in the static sequence but disappear from the mass-shedding limit sequence. Our investigation suggests that the third family of compact stars in the mass-shedding limit sequence is more likely to appear, provided these stars have maximum mass in the static limit higher than their second-family counterpart composed of pure hadronic matter.

A stable Dirac fermion with four-fermion interactions to leptons suppressed by a scale $\Lambda \sim 1\mathrm{TeV}$ is shown to provide a viable candidate for dark matter. The thermal relic abundance matches cosmology, while nuclear recoil direct detection bounds are automatically avoided in the absence of (large) couplings to quarks. The annihilation cross section in the early Universe is the same as the annihilation in our Galactic neighborhood. This allows Dirac fermion dark matter to naturally explain the positron ratio excess observed by PAMELA with a minimal boost factor, given present astrophysical uncertainties. We use the Galprop program for propagation of signal and background; we discuss in detail the uncertainties resulting from the propagation parameters and, more importantly, the injected spectra. Fermi/GLAST has an opportunity to see a feature in the gamma-ray spectrum at the mass of the Dirac fermion. The excess observed by ATIC/PPB-BETS may also be explained with Dirac dark matter that is heavy. A supersymmetric model with a Dirac bino provides a viable UV model of the effective theory. The dominance of the leptonic operators, and thus the observation of an excess in positrons and not in antiprotons, is naturally explained by the large hypercharge and low mass of sleptons as compared with squarks. Minimizing the boost factor implies the right-handed selectron is the lightest slepton, which is characteristic of our model. Selectrons (or sleptons) with mass less than a few hundred GeV are an inescapable consequence awaiting discovery at the LHC.

We present results from a numerical study of $\mathcal{N}=1$ supersymmetric Yang-Mills theory using domain wall fermions. In this particular lattice formulation of the theory, supersymmetry is expected to emerge accidentally in the continuum and chiral limits without any fine-tuning of operators. Dynamical simulations were performed for the gauge group $SU(2)$ on $8^3\times 8$ and ${16}^3\times 32$ lattice space-time volumes and at three different values of the coupling: $\beta =2.3$, $2.35\overline{3}$, and 2.4. Results from this study include measurements of the static potential, residual mass, and a chirally extrapolated value for the gluino condensate at $\beta =2.3$. In addition to these, we study the low-lying eigenvalues and eigenvectors of the five-dimensional Hermitian domain-wall fermion Dirac operator and present evidence that, for the choice of parameters under investigation, features of the spectrum appear qualitatively consistent with strong coupling and the presence of a large residual mass. From the five-dimensional eigenvalues we explore the possibility of using the Banks-Casher relation to determine an independent value for the gluino condensate in the chiral limit.