Buscher duality is a sigma-model duality, implemented by transformation of the target space. Not only in the case of a flat target space, but in a general background, should the Buscher duality reduce to the $T$-duality familiar in the flat-space string context. We exhibit this reduction explicitly using a pp-wave background as a tractable example. String theory is solved in a compactified Nappi-Witten background and the Buscher-dual theory is likewise solved. The Hamiltonian is computed in both cases, and the results are verified to be $T$-dual.

In a toy model with gases of membranes and strings wrapping over a two-dimensional internal torus, we study the stabilization problem for the shape modulus. It is observed that winding modes of partially wrapped strings and momentum modes give rise to stress in the energy-momentum tensor. We show that this stress dynamically stabilizes the shape modulus of the two torus.

The one-loop fermionic contribution to the probability of an instanton transition with fermion number violation is calculated in the chiral Abelian Higgs model in $1+1$ dimensions, where the fermions have a Yukawa coupling to the scalar field. The dependence of the determinant on fermionic, scalar, and vector mass is determined. We show in detail how to renormalize the fermionic determinant in partial wave analysis, which is convenient for computations.

We consider the vacuum structure of two-dimensional ${\varphi }^4$ theory on $S^1/Z_2$ both in the bosonic and the supersymmetric cases. When the size of the orbifold is varied, a phase transition occurs at $L_c=2\pi /m$, where $m$ is the mass of $\varphi$. For $L<L_c$, there is a unique vacuum, while for $L>L_c$, there are two degenerate vacua. We also obtain the 1-loop quantum corrections around these vacuum solutions, exactly in the case of $L<L_c$ and perturbatively for $L$ greater than but close to $L_c$. Including the fermions we find that the “chiral” zero modes around the fixed points are different for $L<L_c$ and $L>L_c$. As for the quantum corrections, the fermionic contributions cancel the singular part of the bosonic contributions at $L=0$. Then the total quantum correction has a minimum at the critical length $L_c$.

The possibility of a modification of special relativity with an invariant energy scale playing the role of a minimum energy is explored. Consistency with the equivalence of different inertial frames is obtained by an appropriate choice of a nonlinear action of the Lorentz group on momentum space. Limits on the low energy cutoff from tests of Einstein’s theory and possible ways to measure the new energy scale are discussed.

We consider a six-dimensional braneworld model and we study the cosmological evolution of a $(4+1)$ brane-universe. Introducing matter on the brane we show that the scale factor of the physical three-dimensional brane-universe is related to the scale factor of the fourth dimension on the brane, and the suppression of the extra dimension compared to the three dimensions requires the presence of dark energy.

We have studied spacetime structures of static solutions in the $n$-dimensional Einstein-Gauss-Bonnet-Maxwell-$\Lambda$ system. Especially we focus on effects of the Maxwell charge. We assume that the Gauss-Bonnet coefficient $\alpha$ is non-negative and $4\tilde{\alpha }/{\ell }^2\le 1$ in order to define the relevant vacuum state. Solutions have the $(n-2)$-dimensional Euclidean submanifold whose curvature is $k=1$, 0, or $-1$. In Gauss-Bonnet gravity, solutions are classified into plus and minus branches. In the plus branch all solutions have the same asymptotic structure as those in general relativity with a negative cosmological constant. The charge affects a central region of a spacetime. A branch singularity appears at the finite radius $r=r_b>0$ for any mass parameter. There the Kretschmann invariant behaves as $O((r-r_b{)}^{-3})$, which is much milder than the divergent behavior of the central singularity in general relativity $O(r^{-4(n-2)})$. In the $k=1$ and 0 cases plus-branch solutions have no horizon. In the $k=-1$ case, the radius of a horizon is restricted as $r_h<\sqrt{2\tilde{\alpha }}$ ($r_h>\sqrt{2\tilde{\alpha }}$) in the plus (minus) branch. Some charged black hole solutions have no inner horizon in Gauss-Bonnet gravity. There are topological black hole solutions with zero and negative mass in the plus branch regardless of the sign of the cosmological constant. Although there is a maximum mass for black hole solutions in the plus branch for $k=-1$ in the neutral case, no such maximum exists in the charged case. The solutions in the plus branch with $k=-1$ and $n\ge 6$ have an inner black hole and inner and outer black hole horizons. In the $4\tilde{\alpha }/{\ell }^2=1$ case, only a positive mass solution is allowed, otherwise the metric function takes a complex value. Considering the evolution of black holes, we briefly discuss a classical discontinuous transition from one black hole spacetime to another.

We show that a quantum-mechanical $N=2$ supersymmetry is hidden in 4d mass spectrum of any gauge invariant theories with extra dimensions. The $N=2$ supercharges are explicitly constructed in terms of differential forms. The analysis can be extended to extra dimensions with boundaries, and for a single extra dimension we clarify a possible set of boundary conditions consistent with 5d gauge invariance, although some of the boundary conditions break 4d gauge symmetries.

In light of recent positive results from the DAMA experiment, as well as new null results from CDMS Soudan, Edelweiss, ZEPLIN-I and CRESST, we reexamine the framework of inelastic dark matter with a standard halo. In this framework, which was originally introduced to reconcile tensions between CDMS and DAMA, dark matter particles can scatter off of nuclei only by making a transition to a nearly degenerate state that is roughly $100\mathrm{keV}$ heavier. We find that recent data significantly constrains the parameter space of the framework, but that there are still regions consistent with all experimental results. Because of the enhanced annual modulation and dramatically different energy dependence in this scenario, we emphasize the need for greater information on the dates of data taking, and on the energy distribution of signal and background. We also study the specific case of “mixed-sneutrino” dark matter, and isolate regions of parameter space which are cosmologically interesting for that particular model. A significant improvement in limits by heavy target experiments such as ZEPLIN or CRESST should be able to confirm or exclude the inelastic dark matter scenario in the near future. Within the mixed-sneutrino model, an elastic scattering signature should be seen at upcoming germanium experiments, including future results from CDMS Soudan.

We derive the low energy effective theory for a two brane system with bulk complex scalar fields. Then we find that higher order corrections to the effective equation for scalar fields on the brane lead us to the baryon number ($B$) violating process if the complex scalar field is regarded as a particle carrying the baryon number current. We see that the motion of the brane leads us to the baryon number violation via the current-curvature coupling even if the potential for scalar fields does not exist. We also estimate the net baryon number assuming a $C/CP$ violating interaction.

We examine contributions from Majorana phases to lepton flavor violating processes in the framework of the minimal supersymmetric standard model with heavy right-handed neutrinos. All phases in the complex neutrino Yukawa matrix are taken into account in our study. We find that in the scenario with universal soft-breaking terms sizable phase effects can appear on the lepton flavor violating processes such as $\mu \to e\gamma$, $\tau \to e\gamma$, and $\tau \to \mu \gamma$. In particular, the branching ratio of $\mu \to e\gamma$ can be considerably enhanced due to the Majorana phases, so that it can be much greater than that of $\tau \to \mu \gamma$.

It is pointed out that the sine law for the $k-$string tension emerges as the critical threshold below which the spatial $Z_N$ symmetry of the static baryon potential is spontaneously broken. This result applies not only to $SU(N)$ gauge theories, but to any gauge system with stable $k-$strings admitting a baryon vertex made with $N$ sources in the fundamental representation. Some simple examples are worked out.

We study the possibilities for the indirect detection of dark matter in split supersymmetry from $\gamma$ rays, positrons, and antiprotons. The most promising signal is the $\gamma$-ray line, which may be observable at the next generation of detectors. For certain halo profiles and a high mass neutralino, the line can even be visible in current experiments. The continuous $\gamma$-ray signal may be observable, if there is a central spike in the galactic halo density. The signals are found to be similar to those in the minimal supersymmetric standard models. These indirect signals complement other experiments, being most easily observable for regions of parameter space, such as heavy $W$-ino and Higgsino dominated neutralinos, which are least accessible with direct detection and accelerator searches.

The two-flavor color-superconducting (2SC) phase in small strangelets is studied. In order to describe the 2SC phase we use the three-flavor Nambu–Jona-Lasinio model. We explicitly take into account finite-size effects by making use of the approximation for the density of states in spherical cavities called multiple reflection expansion (MRE). The thermodynamic potential for the 2SC strangelets is derived in the mean-field approximation with the help of the MRE. We found that 2SC phase survives in small strangelets with a sizable gap. Consequences for the 2SC phases are also discussed.

We derive a $\Lambda \Lambda$ potential from a chiral constituent quark model that has been successful in describing one, two, and three nonstrange baryon systems. The resulting interaction at low energy is attractive at all distances due to the $\sigma$ exchange term. The attraction allows for a slightly bound state just below the $\Lambda \Lambda$ threshold. No short-range repulsive core is found. We extract the diquark-diquark contribution that turns out to be the most attractive and probable at small distances. At large distances the asymptotic behavior of the $\Lambda \Lambda$ interaction provides a prediction for the $\sigma \Lambda \Lambda$ coupling constant.

We investigate the sources of neutrino mass generation in little Higgs theories, by confining ourselves to the “littlest Higgs” scenario. Our conclusion is that the most satisfactory way of incorporating neutrino masses is to include a lepton-number violating interaction between the scalar triplet and lepton doublets. The tree-level neutrino masses generated by the vacuum expectation value of the triplet are found to dominate over contributions from dimension-five operators so long as no additional large lepton-number violating physics exists at the cutoff scale of the effective theory. We also calculate the various decay branching ratios of the charged and neutral scalar triplet states, in regions of the parameter space consistent with the observed neutrino masses, hoping to search for signals of lepton-number violating interactions in collider experiments.

It is known that flavor democracy favors the existence of the fourth standard model (SM) family. In order to give nonzero masses for the first three-family fermions flavor democracy has to be slightly broken. A parametrization for democracy breaking, which gives the correct values for fundamental fermion masses and, at the same time, predicts quark and lepton Cabibbo-Kobayashi-Maskawa (CKM) matrices in a good agreement with the experimental data, is proposed. The pair productions of the fourth SM family Dirac $({\nu }_4)$ and Majorana $(N_1)$ neutrinos at future linear colliders with $\sqrt{s}=500\mathrm{GeV}$, 1 TeV, and 3 TeV are considered. The cross section for the process $e^{+}{e}^{-}\to {\nu }_4{\overline{\nu }}_4(N_1{N}_1)$ and the branching ratios for possible decay modes of the both neutrinos are determined. The decays of the fourth family neutrinos into muon channels $({\nu }_4(N_1)\to {\mu }^{\pm }{W}^{\mp })$ provide cleanest signature at $e^{+}{e}^{-}$ colliders. Meanwhile, in our parametrization this channel is dominant. $W$ bosons produced in decays of the fourth family neutrinos will be seen in detector as either di-jets or isolated leptons. As an example, we consider the production of 200 GeV mass fourth family neutrinos at $\sqrt{s}=500\mathrm{GeV}$ linear colliders by taking into account di-muon plus four jet events as signatures.

Using 88.9 million $B\overline{B}$ events collected by the BABAR detector at the $\mathit{{\rm Y}}(4S)$, we measure the branching fraction for the radiative penguin process $B\to X_s\gamma$ from the sum of 38 exclusive final states. The inclusive branching fraction above a minimum photon energy $E_{\gamma }>1.9\mathrm{GeV}$ is $\mathcal{B}(b\to s\gamma )=(3.27\pm 0.18(\mathrm{stat}{)}_{-0.40}^{+0.55}(\mathrm{syst}{)}_{-0.09}^{+0.04}(\mathrm{theory}))\times {10}^{-4}$. We also measure the isospin asymmetry between $B^{-}\to X_{s\overline{u}}\gamma$ and ${\overline{B}}^0\to X_{s\overline{d}}\gamma$ to be ${\Delta }_{0-}=-0.006\pm 0.058(\mathrm{stat})\pm 0.009(\mathrm{syst})\pm 0.024({\overline{B}}^0/B^{-})$. The photon energy spectrum is measured in the $B$ rest frame, from which moments are derived for different values of the minimum photon energy. We present fits to the photon spectrum and moments which give the heavy-quark parameters $m_b$ and ${\mu }_{\pi }^2$. The fitted parameters are consistent with those obtained from semileptonic $B\to X_c\ell \nu$ decays, and are useful inputs for the extraction of $|V_{ub}|$ from measurements of semileptonic $B\to X_u\ell \nu$ decays.

We show that with proper accounting of convention-dependent phases the mass spectra evaluated by us in an earlier paper satisfy the trace, $SU(5)$ reassembly and Goldstone counting consistency checks. Phase accounting shows that the transposition symmetry called Hermiticity will be manifest only if signs arising from the product of six phase factors are reinserted. This uncovers the errors in the claims of others (retracted in subsequent work) concerning the inconsistency of our results. The chiral multiplet spectra of the two calculations are equivalent. However our method also gives all gauge and gauge chiral spectra as well as a decomposition of all $SO(10)$ minimal supersymmetric grand unified theory couplings, for both tensors and spinors, which are unavailable, even in principle, using the methods of the above papers.

We explicitly show that minimal supersymmetric $SO(10)$ Higgs-Higgsino mass matrices evaluated by various groups are mutually consistent and correct. We comment on the corresponding results of other authors. We construct one-to-one mappings of our approach to the approaches of other authors.