Yasuaki Hikida

Superstrings on PP-Wave Backgrounds and Symmetric Orbifolds

We study the superstring theory on pp-wave background with NSNS-flux that is realized as the Penrose limit of AdS3 ? S3 ? M4, where M4 is T4 or T4/2 (K3). Quantizing this system in the covariant gauge, we explicitly construct the space-time supersymmetry algebra and the complete set of DDF operators. We analyse the spectrum of physical states by using the spectrally flowed representations of current algebra. This spectrum is classified by the ``short string sectors and the ``long string sectors as in AdS3 string theory. The states of the latter propagate freely along the transverse plane of pp-wave background, but the states of the former do not. We compare the short string spectrum with the BPS and almost BPS states which have large R-charges in the symmetric orbifold conformal theory, which is known as the candidate of dual theory of superstrings on AdS3 ? S3 ? M4. We show that every short string states can be embedded successfully in the single particle Hilbert space of symmetric orbifold conformal theory.

D-branes in PP-Waves and Massive Theories on Worldsheet with Boundary

We investigate the supersymmetric D-brane configurations in the pp-wave backgrounds proposed by Maldacena and Maoz. We study the surviving supersymmetry in a D-brane configuration from the worldvolume point of view. When we restrict ourselves to the background with = (2,2) supersymmetry and no holomorphic Killing vector term, there are two types of supersymmetric D-branes: A-type and B-type. An A-type brane is wrapped on a special lagrangian submanifold, and the imaginary part of the superpotential should be constant on its worldvolume. On the other hand, a B-type brane is wrapped on a complex submanifold, and the superpotential should be constant on its worldvolume. The results are almost consistent with the worldsheet theory in the lightcone gauge. The inclusion of gauge fields is also discussed and found BPS D-branes with the gauge field excitations. Furthermore, we consider the backgrounds with holomorphic Killing vector terms and = (1,1) supersymmetric backgrounds.

Formation of spherical D2-brane from multiple D0-branes

Abstract We study D-branes in SU (2) WZW model by means of the boundary state techniques. We realize the “fuzzy sphere” configuration of multiple D0-branes as the boundary state with the insertion of suitable Wilson line. By making use of the path-integral representation we show that this boundary state preserves the appropriate boundary conditions and leads to the Cardy state describing a spherical D2-brane under the semi-classical approximation. This result directly implies that the spherical D2-brane in SU (2) WZW model can be well described as the bound state of D0-branes. After presenting the supersymmetric extension, we also investigate the BPS and the non-BPS configurations of D-branes in the NS5 background. We demonstrate that the non-BPS configurations are actually unstable, since they always possess the open string tachyons. We further notice that the stable BPS bound state constructed by the tachyon condensation is naturally interpreted as the brane configuration of fuzzy sphere.

Boundary States of D-Branes in AdS3 Based on Discrete Series

We study D-branes in the Lorentzian AdS 3 background from the viewpoint of boundary states, emphasizing the role of open-closed duality in string theory. Employing the world sheet with Lorentzian signature, we construct the Cardy states with the discrete series. We show that they are compatible with (1) unitarity and normalizability, and (2) the spectral flow symmetry, in the open string spectrum. We also discuss their brane interpretation. We further show that in the case of superstrings on AdS 3 × S 3 × T 4 , our Cardy states yield an infinite number of physical BPS states in the open string channel, on which the spectral flows act consistently.

String theory on AdS3 as discrete light-cone Liouville theory

We investigate (super) string theory on AdS3 background based on an approach of free field realization. We demonstrate that this string theory can be reformulated as a string theory defined on a linear dilaton background along the transverse direction (“Liouville mode”) and compactified onto S1 along a light-like direction. n nUnder this reformulation we analyze the physical spectrum as that of a free field system, and discuss the consequences when we turn on the Liouville potential. The discrete light-cone momentum in our framework is naturally interpreted as the “winding number” of the long string configuration and is identified with the spectral flow parameter that is introduced in the recent work by Maldacena and Ooguri (hep-th/0001053). n nMoreover we show that there exist infinite number of the on-shell chiral primary states possessing the different light-cone momenta and the spectral flow consistently acts on the space of chiral primaries. We observe that they are also chiral primaries in the sense of space–time (or the conformal theory of long string) and the spectrum of space–time U(1)R charge is consistent with the expectation from the AdS3/CFT2-duality. We also clarify the correspondence between our framework and the symmetric orbifold theory of multiple long string system (K. Hosomichi, Y. Sugawara, JHEP 9907 (1999) 027, hep-th/9905004).

Tachyon condensation on fuzzy sphere and noncommutative solitons

Abstract We study a brane–antibrane system and a non-BPS D-brane in SU(2) WZW model. We first discuss the tachyon condensation using the vertex operator formalism and find the generation of codimension two D-branes after the condensation. Our result is consistent with the recent interpretation that a D2-brane is a bound state of D0-branes. Then we investigate the world-volume effective theory on a non-BPS D-brane. It becomes a field theory on the “fuzzy sphere” when the level is sent to infinity. The most interesting feature is that there exist the noncommutative tachyonic solitons and we can identify them with D0-branes. We also discuss the brane–antibrane system from the world-volume point of view and comment on the relation to the noncommutative version of the index theorem.

Boundary states for D-branes with traveling waves

We construct boundary states for D-branes which carry traveling waves in the covariant formalism. We compute their vacuum amplitudes to investigate their interactions. In non-compact space, the vacuum amplitudes become trivial as is common in plane wave geometries. However, we found that if they are compactified in the traveling direction, then the amplitudes are affected by non-trivial time dependent effects. The interaction between D-branes with waves traveling in the opposite directions (`pulse-antipulse scattering) are also computed. Furthermore, we apply these ideas to open string tachyon condensation with traveling waves.

Superstring Vacua of 4-dimensional PP-Waves with Enhanced Supersymmetry

We study the superstring vacua constructed from the conformal field theories of the type H4 ? , where H4 denotes the super Nappi-Witten model (super WZW model on the 4-dimensional Heisenberg group H4) and denotes an arbitrary = 2 rational superconformal field theory with c = 9. We define (type-II) superstring vacua with 8 supercharges, which are twice as many as those on the backgrounds of H4 ? CY3. We explicitly construct as physical vertices the space-time SUSY algebra that is a natural extension of H4 Lie algebra. The spectrum of physical states is classified into two sectors: (1) strings freely propagating along the transverse plane of pp-wave geometry and possessing the integral U(1)R-charges in sector, and (2) strings that do not freely propagate along the transverse plane and possess the fractional U(1)R-charges in . The former behaves like the string excitations in the usual Calabi-Yau compactification, but the latter defines new sectors without changing the physics in ``bulk space. We also analyze the thermal partition functions of these systems, emphasizing the similarity to the DLCQ string theory. As a byproduct we prove the supersymmetric cancellation of conformal blocks in an arbitrary unitary = 2 SCFT of c = 12 with the suitable GSO projection.

Liouville field theory on an unoriented surface

Liouville field theory on an unoriented surface is investigated, in particular, the one point function on a 2 is calculated. The constraint of the one point function is obtained by using the crossing symmetry of the two point function. There are many solutions of the constraint and we can choose one of them by considering the modular bootstrap.

Orientifolds of SU(2)/U(1) WZW Models

The orientifolds of SU(2)/U(1) gauged WZW models are investigated. In particular, we construct the new type orientifolds and identify their geometries. We closely follow the analysis of D-branes in the SU(2)/U(1) WZW models, which was given by Maldacena, Moore and Seiberg.