Calculation of transition probabilities and ac Stark shifts in two-photon laser transitions of antiprotonic helium

Numerical ab initio variational calculations of the transition probabilities and ac Stark shifts in two-photon transitions of antiprotonic helium atoms driven by two counter-propagating laser beams are presented. We found that sub-Doppler spectroscopy is in principle possible by exciting transitions of the type (n,L)->(n-2,L-2) between antiprotonic states of principal and angular momentum quantum numbers n~L-1~35, first by using highly monochromatic, nanosecond laser beams of intensities 10^4-10^5 W/cm^2, and then by tuning the virtual intermediate state close (e.g., within 10-20 GHz) to the real state (n-1,L-1) to enhance the nonlinear transition probability. We expect that ac Stark shifts of a few MHz or more will become an important source of systematic error at fractional precisions of better than a few parts in 10^9. These shifts can in principle be minimized and even canceled by selecting an optimum combination of laser intensities and frequencies. We simulated the resonance profiles of some two-photon transitions in the regions n=30-40 of the \bar{p}^4He^+ and \bar{p} ^3He^+ isotopes to find the best conditions that would allow this.Comment: 18 pages 2 tables 12 figures, submitted to Phys. Rev.

Proposed method for laser spectroscopy of pionic helium atoms to determine the charged-pion mass

Metastable pionic helium ($\pi{\rm He}^+$) is a three-body atom composed of a helium nucleus, an electron occupying the $1s$ ground state, and a negatively charged pion $\pi^-$ in a Rydberg state with principal- and orbital angular momentum quantum numbers of $n\sim \ell+1\sim 16$. We calculate the spin-independent energies of the $\pi{\rm ^3He}^+$ and $\pi{\rm ^4He}^+$ isotopes in the region $n=15$--19. These include relativistic and quantum electrodynamics corrections of orders $R_{\infty}\alpha^2$ and $R_{\infty}\alpha^3$ in atomic units, where $R_{\infty}$ and $\alpha$ denote the Rydberg and fine structure constants. The fine-structure splitting due to the coupling between the electron spin and the orbital angular momentum of the $\pi^-$, and the radiative and Auger decay rates of the states are also calculated. Some states $(n,\ell)=(16,15)$ and $(17,16)$ retain nanosecond-scale lifetimes against $\pi^-$ absorption into the helium nucleus. We propose to use laser pulses to induce $\pi^-$ transitions from these metastable states, to states with large ($\sim 10^{11}$ s$^{-1}$) Auger rates. The $\pi{\rm He}^{2+}$ ion that remains after Auger emission of the $1s$ electron undergoes Stark mixing with the $s$, $p$, and $d$ states during collisions with the helium atoms in the experimental target. This leads to immediate nuclear absorption of the $\pi^-$. The resonance condition between the laser beam and the atom is thus revealed as a sharp spike in the rates of neutrons, protons, deuterons, and tritons that emerge....(continued)Comment: 25 pages, 3 tables, 11 figure

D-branes in Topological Minimal Models: the Landau-Ginzburg Approach

We study D-branes in topologically twisted N=2 minimal models using the Landau-Ginzburg realization. In the cases of A and D-type minimal models we provide what we believe is an exhaustive list of topological branes and compute the corresponding boundary OPE algebras as well as all disk correlators. We also construct examples of topological branes in E-type minimal models. We compare our results with the boundary state formalism, where possible, and find agreement.Comment: 29 pages, late

D-brane Categories for Orientifolds -- The Landau-Ginzburg Case

We construct and classify categories of D-branes in orientifolds based on Landau-Ginzburg models and their orbifolds. Consistency of the worldsheet parity action on the matrix factorizations plays the key role. This provides all the requisite data for an orientifold construction after embedding in string theory. One of our main results is a computation of topological field theory correlators on unoriented worldsheets, generalizing the formulas of Vafa and Kapustin-Li for oriented worldsheets, as well as the extension of these results to orbifolds. We also find a doubling of Knoerrer periodicity in the orientifold context.Comment: 45 pages, 6 figure

Permutation branes and linear matrix factorisations

All the known rational boundary states for Gepner models can be regarded as permutation branes. On general grounds, one expects that topological branes in Gepner models can be encoded as matrix factorisations of the corresponding Landau-Ginzburg potentials. In this paper we identify the matrix factorisations associated to arbitrary B-type permutation branes.Comment: 43 pages. v2: References adde

Orientifolds of Gepner Models

We systematically construct and study Type II Orientifolds based on Gepner models which have N=1 supersymmetry in 3+1 dimensions. We classify the parity symmetries and construct the crosscap states. We write down the conditions that a configuration of rational branes must satisfy for consistency (tadpole cancellation and rank constraints) and spacetime supersymmetry. For certain cases, including Type IIB orientifolds of the quintic and a two parameter model, one can find all solutions in this class. Depending on the parity, the number of vacua can be large, of the order of 10^{10}-10^{13}. For other models, it is hard to find all solutions but special solutions can be found -- some of them are chiral. We also make comparison with the large volume regime and obtain a perfect match. Through this study, we find a number of new features of Type II orientifolds, including the structure of moduli space and the change in the type of O-planes under navigation through non-geometric phases.Comment: 142 page

Orientifolds and Mirror Symmetry

We study parity symmetries and crosscap states in classes of N=2 supersymmetric quantum field theories in 1+1 dimensions, including non-linear sigma models, gauged WZW models, Landau-Ginzburg models, and linear sigma models. The parity anomaly and its cancellation play important roles in many of them. The case of the N=2 minimal model are studied in complete detail, from all three realizations -- gauged WZW model, abstract RCFT, and LG models. We also identify mirror pairs of orientifolds, extending the correspondence between symplectic geometry and algebraic geometry by including unorientable worldsheets. Through the analysis in various models and comparison in the overlapping regimes, we obtain a global picture of orientifolds and D-branes.Comment: 137 page

Bulk perturbations of N=2 branes

The evolution of supersymmetric A-type D-branes under the bulk renormalization group flow between two different N=2 minimal models is studied. Using the Landau-Ginzburg description we show that a specific set of branes decouples from the infrared theory, and we make detailed predictions for the behavior of the remaining branes. The Landau-Ginzburg picture is then checked against a direct conformal field theory analysis. In particular we construct a natural index pairing which is preserved by the RG flow, and show that the branes that decouple have vanishing index with the surviving branes.Comment: 35 pages (30 pages plus title and references), 8 figure

Integrability of the N=2 boundary sine-Gordon model

We construct a boundary Lagrangian for the N=2 supersymmetric sine-Gordon model which preserves (B-type) supersymmetry and integrability to all orders in the bulk coupling constant g. The supersymmetry constraint is expressed in terms of matrix factorisations.Comment: LaTeX, 19 pages, no figures; v2: title changed, minor improvements, refs added, to appear in J. Phys. A: Math. Ge

Worldsheet Matter Superfields on Half-Shell

In this paper we discuss some of the effects of using "unidexterous" worldsheet superfields, which satisfy worldsheet differential constraints and so are partly on-shell, i.e., on half-shell. Most notably, this results in a stratification of the field space that reminds of "brane-world" geometries. Linear dependence on such superfields provides a worldsheet generalization of the super-Zeeman effect. In turn, non-linear dependence yields additional left-right asymmetric dynamical constraints on the propagating fields, again in a stratified fashion.Comment: 15 pages, 2 figures; minor algebraic correction