Crosscap States Research Articles

Notes on Orientifolds of Rational Conformal Field Theories

We review and develop the construction of crosscap states associated with parity symmetries in rational conformal field theories. A general method to construct crosscap states in abelian orbifold models is presented. It is then applied to rational U(1) and parafermion systems, where in addition we study the geometrical interpretation of the corresponding parities.

Crosscaps in Gepner Models and Type IIA Orientifolds

As a first step to a detailed study of orientifolds of Gepner models associated with Calabi-Yau manifolds, we construct crosscap states associated with anti-holomorphic involutions (with fixed points) of Calabi-Yau manifolds. We argue that these orientifolds are dual to M-theory compactifications on (singular) seven-manifolds with $G_2$ holonomy. Using the spacetime picture as well as the M-theory dual, we discuss aspects of the orientifold that should be obtained in the Gepner model. This is illustrated for the case of the quintic.

BPS orientifold planes from crosscap states in Calabi-Yau compactifications

We use the results of hep-th/0007174 on the simple current classification of open unoriented CFTs to construct half supersymmetry preserving crosscap states for rational Calabi-Yau compactifications. We show that the corresponding orientifold fixed planes obey the BPS-like relation M=exp(i*phi)Q. To prove this relation, it is essential that the worldsheet CFT properly includes the degrees of freedom from the uncompactified space-time component. The BPS-phase phi can be identified with the automorphism type of the crosscap states. To illustrate the method we compute crosscap states in Gepner models with each k_i odd.

Orientifolds of type IIA strings on Calabi-Yau manifolds

We identify type IIA orientifolds that are dual toM-theory compactifications on manifolds withG 2-holonomy. We then discuss the construction of cross-cap states in Gepner models.

Off-shell crosscap state and orientifold planes with background dilatons

We show that a non-trivial dilaton condensation alters the dimensions of orientifold planes. An off-shell crosscap state which naturally interpolates between the usual on-shell crosscap states and their T-duals plays an important role in the analysis. We present an explicit representation of the off-shell crosscap state on an RP 2 worldsheet in the gauge in which the worldsheet curvature in the bulk of the fundamental region of the RP 2 vanishes. We show that the non-trivial dilaton condensation reproduces the correct descent relation among orientifold plane tensions.

Extension of boundary string field theory on disc andRP2worldsheet geometries

We present an extension of boundary string field theory on disc and ${\mathrm{RP}}^{2}$ worldsheet geometries. Finding an appropriate Becchi-Rouet-Stora (BRS) operator in the case of the ${\mathrm{RP}}^{2}$ geometry, we generalize the background independent open string field theory (or boundary string field theory) of Witten on a unit disc. The space of two-dimensional field theories on ${\mathrm{RP}}^{2}$ is spanned by the scalar operator inserted at the nontrivial loop of ${\mathrm{RP}}^{2}.$ We discuss the off-shell extension of the crosscap states, which provides an interpolation of orientifold planes of various dimensions.

Orientifolds of string theory Melvin backgrounds

We study the dynamics of type I strings on Melvin backgrounds, with a single or multiple twisted two-planes. We construct two inequivalent types of orientifold models that correspond to (non-compact) irrational versions of Scherk–Schwarz type breaking of supersymmetry. In the first class of vacua, D-branes and O-planes are no longer localized in space–time but are smeared along the compact Melvin coordinate with a characteristic profile. On the other hand, the second class of orientifolds involves O-planes and D-branes that are both rotated by an angle proportional to the twist. In case of “multiple Melvin spaces”, some amount of supersymmetry is recovered if the planes are twisted appropriately and part of the original O-planes are transmuted into new ones. The corresponding boundary and crosscap states are determined.

Crosscap States for Orientifolds of Euclidean AdS3

Crosscap states for orientifolds of Euclidean AdS_3 are constructed. We show that our crosscap states describe the same orientifolds which were obtained by the classical analysis. The spectral density of open strings in the system with orientifold can be read from the M"obius strip amplitudes and it is compared to that of the open strings stretched between branes and their mirrors. We also compute the Klein bottle amplitudes.

Geometry of WZW orientifolds

We analyze unoriented Wess–Zumino–Witten models from a geometrical point of view. We show that the geometric interpretation of simple current crosscap states is as centre orientifold planes localized on conjugacy classes of the group manifold. We determine the locations and dimensions of these planes for arbitrary simply-connected groups and orbifolds thereof. The dimensions of the O-planes turn out to be given by the dimensions of symmetric coset manifolds based on regular embeddings. Furthermore, we give a geometrical interpretation of boundary conjugation in open unoriented WZW models; it yields D-branes together with their images under the orientifold projection. To find the agreement between O-planes and crosscap states, we find explicit answers for lattice extensions of Gaussian sums. These results allow us to express the modular P-matrix, which is directly related to the crosscap coefficient, in terms of characters of the horizontal subgroup of the affine Lie algebra. A corollary of this relation is that there exists a formal linear relation between the modular P- and the modular S-matrix.

On Orientifolds of WZW Models and their Relation to Geometry

We investigate D-branes in orientifolds of WZW models. A connection between the conformal field theory approach to orientifolds and the target space motivated analysis is established. In particular, we associate previously constructed crosscap states to involutions of the group manifold and their fixed point sets. Whereas our analysis of D-branes in orientifolds of general WZW models is restricted to special D0-branes, we investigate all symmetry preserving branes of SU(2)-orientifolds in detail. For that case, the location of the orientifold fixed point set is independently determined by scattering localized graviton wave packets.

Off-shell Crosscap State and Orientifold Planes with Background Dilatons

Off-shell Crosscap State and Orientifold Planes with Background Dilatons

OPEN STRING ON SYMMETRIC PRODUCT

We discuss some basic properties of the open string on the symmetric product which is supposed to describe the open string field theory in discrete light-cone quantization (DLCQ). We first derive the consistent twisted boundary conditions for Annulus/Möbius/Klein Bottle diagrams and give the explicit form of the corresponding amplitude. They have the interpretation as the long open (or closed) string amplitude but the world sheet topology viewed from the short string and from the long string is in general different. Boundary (cross-cap) states of the short string are classified into three categories, the boundary (cross-cap) states of the long string and the "joint" state which connects two strings. The partition function has the typical structure of the string field theory in DLCQ. Tadpole condition is also analyzed and gives a reasonable gauge group SO(213).

The Critical Ising Model on a Mobius Strip

We study the two-dimensional critical Ising model on a M\"obius strip based on a duality relation between conformally invariant boundary conditions. By using a Majorana fermion field theory, we obtain explicit representations of crosscap states corresponding to the boundary states. We also discuss the duality structure of the partition functions.

BOUNDARY AND CROSSCAP STATES IN COMPACTIFICATIONS OF OPEN AND CLOSED BOSONIC STRINGS

Orbifold compactifications of open and closed bosonic strings are examined and constrained by unitarity requirements. In particular, the role of crosscap and boundary states in evaluating amplitudes is investigated.

THE BOUNDARY AND CROSSCAP STATES IN CONFORMAL FIELD THEORIES

A method to obtain the boundary states and the crosscap states explicitly in various conformal field theories, is presented. This makes it possible to construct and analyse open string theories in several closed string backgrounds. We discuss the construction of such theories in the case of the backgrounds corresponding to the conformal field theories with SU(2) current algebra symmetry.