General Operator Solutions and BRST Quantization of Superstrings in the pp-Wave with Torsion

We completely accomplish the canonically covariant quantization of Ramond-Neveu-Schwarz (RNS) superstrings in the pp-wave background with a non-zero flux of the NS-NS antisymmetric two-form field. Here this flux is equivalent to a nonvanishing torsion. In this quantization, general operator solutions, which satisfy the entire equation of motion and all the canonical (anti)commutation relations, play an important role. The whole of covariant string coordinates and fermions can be composed of free modes. Moreover, employing covariant free-mode representations, we calculate the anomaly in the super-Virasoro algebra and determine the number of dimensions of spacetime and the ordering constant from the nilpotency condition of the BRST charge in the pp-wave background with the flux.Comment: 31 page

Covariant BRST Quantization of Closed Strings in the PP-Wave Background

We canonically quantize closed string theory in the pp-wave background with a non-zero flux of the three-form field strength by using the covariant BRST operator formalism. In this canonical quantization, we completely construct new covariant free-mode representations, for which it is particularly important to take account of the commutation relations of the zero mode of the light-cone string coordinate X^{-} with other modes. All covariant string coordinates are composed of the free-modes. Moreover, employing these covariant string coordinates for the energy-momentum tensor, we calculate the anomaly in the Virasoro algebra and determine the number of dimensions of spacetime and the ordering constant from the nilpotency condition of the BRST charge in the pp-wave background.Comment: 30 page

String Field Theory in Rindler Space-Time and String Thermalization

Quantization of free string field theory in the Rindler space-time is studied by using the covariant formulation and taking the center-of-mass value of the Rindler string time-coordinate $\eta(\sigma)$ as the time variable for quantization. We construct the string Rindler modes which vanish in either of the Rindler wedges $\pm$ defined by the Minkowski center-of-mass coordinate of the string. We then evaluate the Bogoliubov coefficients between the Rindler string creation/annihilation operators and the Minkowski ones, and analyze the string thermalization. An approach to the construction of the string Rindler modes corresponding to different definitions of the wedges is also presented toward a thorough understanding of the structure of the Hilbert space of the string field theory on the Rindler space-time.Comment: 37 pages + 2 uuencoded eps figures, LaTeX, References adde

Comments on D-Instantons in c<1 Strings

We suggest that the boundary cosmological constant \zeta in c<1 unitary string theory be regarded as the one-dimensional complex coordinate of the target space on which the boundaries of world-sheets can live. From this viewpoint we explicitly construct analogues of D-instantons which satisfy Polchinski's ``combinatorics of boundaries.'' We further show that our operator formalism developed in the preceding articles is powerful in evaluating D-instanton effects, and also demonstrate for simple cases that these effects exactly coincide with the stringy nonperturbative effects found in the exact solutions of string equations.Comment: 12 pages with 1 figure, LaTex, Version to appear in PL

Low Energy Action of "Covariant" Superstring Field Theory in the NS-NS pp-Wave Background

Exact construction of superstring field theory in some background fields is very important. We construct the low energy NS-NS sector of superstring field action in the pp-wave background with the flux of NS-NS antisymmetric tensor field (NS-NS pp-wave) without gauge fixing up to the second-order where the action is world-sheet BRST invariant. Here we use the word "covariant" in a invariant theory for a symmetric transformation of the pp-wave background which is not the Lorentz transformation in the flat background. Moreover we prove the exact correspondence between this low energy action and the second-order perturbation of supergravity action in the same background. We also prove the correspondence of the gauge transformation in both the actions. This construction is based on the BRST first quantization of superstrings in the pp-wave background in our previous paper.Comment: 34 page

Combinatorics of Solitons in Noncritical String Theory

We study the combinatorics of solitons in $D<2$ (or $c<1$) string theory. The weights in the summation over multi-solitons are shown to be automatically determined if we further require that the partition function with soliton background be a $\tau$ function of the KP hierarchy, in addition to the $W_{1+\infty}$ constraint.Comment: 10 pages, LaTe

Nonperturbative Effects in Noncritical Strings with Soliton Backgrounds

We explicitly construct soliton operators in $D<2$ (or $c<1$) string theory, and show that the Schwinger-Dyson equations allow solutions with these solitons as backgrounds. The dominant contributions from 1-soliton background are explicitly evaluated in the weak coupling limit, and shown to agree with the nonperturbative analysis of string equations. We suggest that fermions should be treated as fundamental dynamical variables since both macroscopic loops and solitons are constructed in their bilinear forms.Comment: 15 pages + 1 eps figure, LaTeX, Minor Change

The excitation of a charged string passing through a shock wave in a charged Aichelburg-Sexl spacetime

We investigate how much a first-quantized charged bosonic test string gets excited after crossing a shock wave generated by a charged particle with mass $\tilde{M}$ and charge $\tilde{Q}$. On the basis of Kaluza-Klein theory, we pay attention to a closed string model where charge is given by a momentum along a compactified extra-dimension. The shock wave is given by a charged Aichelburg-Sexl (CAS) spacetime where $\tilde{Q}=0$ corresponds to the ordinary Aichelburg-Sexl one. We first show that the CAS spacetime is a solution to the equations of motion for the metric, the gauge field, and the axion field in the low-energy limit. Secondly, we compute the mass expectation value of the charged test string after passing through the shock wave in the CAS spacetime. In the case of small $\tilde{Q}$, gravitational and Coulomb forces are canceled out each other and hence the excitation of the string remains very small. This is independent of the particle mass $\tilde{M}$ or the strength of the shock wave. In the case of large $\tilde{Q}$, however, every charged string gets highly excited by quantum fluctuation in the extra-dimension caused by both the gauge and the axion fields. This is quite different from classical "molecule", which consists of two electrically charged particles connected by a classical spring.Comment: Latex, 20 pages, no figures, accepted for Nucl. Phys.

Information Metric on Instanton Moduli Spaces in Nonlinear Sigma Models

We study the information metric on instanton moduli spaces in two-dimensional nonlinear sigma models. In the CP^1 model, the information metric on the moduli space of one instanton with the topological charge Q=k which is any positive integer is a three-dimensional hyperbolic metric, which corresponds to Euclidean anti--de Sitter space-time metric in three dimensions, and the overall scale factor of the information metric is (4k^2)/3; this means that the sectional curvature is -3/(4k^2). We also calculate the information metric in the CP^2 model.Comment: 9 pages, LaTeX; added references for section 1; typos adde

The stability of the shell of D6-D2 branes in a N=2{\cal N}=2 supergravity solution

The stability of the shell of wrapped D6-branes on K3 is investigated from the point of view of supergravity. We first construct an effective energy-momentum tensor for the shell under the reasonable conditions and show that supersymmetric solutions satisfy Israel's junction conditions at arbitrary radius of the shell. Next we study the perturbation of the whole system including the self-gravity of the shell. It is found that in spite of the existence of wrapped D6-branes with negative tension, there is no eigenmode whose frequencies of the shell and the fields are imaginary numbers, at any radius of the shell. Furthermore, when the radius of the shell is less than the enhan\c{c}on radius, resonances are produced, and this indicates a kind of ``instability'' of the system. This can even classically explain why the shell is constructed at the enhan\c{c}on radius.Comment: 14 pages, 3 figures, corrected some calculation