Types Of Branes Research Articles

GEOMETRY OF ORIENTIFOLDS WITH NS–NS B FLUX

We discuss geometry underlying orientifolds with nontrivial NS–NS B flux. If D-branes wrap a torus with B flux the rank of the gauge group is reduced due to noncommuting Wilson lines whose presence is implied by the B flux. In the case of c-branes transverse to a torus with B flux the rank reduction is due to a smaller number of D-branes required by tadpole cancellation conditions in the presence of B flux as some of the orientifold planes now have the opposite orientifold projection. We point out that T duality in the presence of B flux is more subtle than in the case with trivial B flux, and it is precisely consistent with the qualitative difference between the aforementioned two setups. In the case where both types of branes are present, the states in the mixed (e.g. 59) open string sectors come with a nontrivial multiplicity, which we relate to a discrete gauge symmetry due to nonzero B flux, and construct vertex operators for the mixed sector states. Using these results we revisit K3 orientifolds with B flux (where K3 is a T4/ZM orbifold) and point out various subtleties arising in some of these models. For instance, in the Z2 case the conformal field theory orbifold does not appear to be the consistent background for the corresponding orientifolds with B flux. This is related to the fact that nonzero B flux requires the presence of both O5-- as well as O5+-planes at various Z2 orbifold fixed points, which appears to be inconsistent with the presence of the twistedB flux in the conformal field theory orbifold. We also consider four-dimensional [Formula: see text] and [Formula: see text] supersymmetric orientifolds. We construct consistent four-dimensional models with B flux which do not suffer from difficulties encountered in the K3 cases.

Baldness/delocalization in intersecting brane systems

Marginally bound systems of two types of branes are considered, such as the prototypical case of (Dp + 4)-branes and Dp-branes. As the transverse separation between the two types of branes goes to zero, different behaviour occurs in the supergravity solutions depending on p; no-hair theorems result for p1 only. Within the framework of the AdS-CFT correspondence, these supergravity no-hair results are understood as dual manifestations of the Coleman-Mermin-Wagner theorem. Furthermore, the rates of delocalization for p1 are matched in a scaling analysis.

Geometry of Orientifolds with NS-NS B-flux

We discuss geometry underlying orientifolds with non-trivial NS-NS B-flux. If D-branes wrap a torus with B-flux the rank of the gauge group is reduced due to non-commuting Wilson lines whose presence is implied by the B-flux. In the case of D-branes transverse to a torus with B-flux the rank reduction is due to a smaller number of D-branes required by tadpole cancellation conditions in the presence of B-flux as some of the orientifold planes now have the opposite orientifold projection. We point out that T-duality in the presence of B-flux is more subtle than in the case with trivial B-flux, and it is precisely consistent with the qualitative difference between the aforementioned two setups. In the case where both types of branes are present, the states in the mixed (e.g., 59) open string sectors come with a non-trivial multiplicity, which we relate to a discrete gauge symmetry due to non-zero B-flux, and construct vertex operators for the the mixed sector states. Using these results we revisit K3 orientifolds with B-flux (where K3 is a T^4/Z_M orbifold) and point out various subtleties arising in some of these models. For instance, in the Z_2 case the conformal field theory orbifold does not appear to be the consistent background for the corresponding orientifolds with B-flux. This is related to the fact that non-zero B-flux requires the presence of both O5^- as well as O5^+ planes at various Z_2 orbifold fixed points, which appears to be inconsistent with the presence of the twisted B-flux in the conformal field theory orbifold. We also consider four dimensional N=2 and N=1 supersymmetric orientifolds. We construct consistent four dimensional models with B-flux which do not suffer from difficulties encountered in the K3 cases.

Stable D8-branes and tachyon condensation in type 0 open string theory

We consider non-BPS D8 (and D7) branes in type 0 open string theory and describe under which circumstances these branes are stable. We find stable non-BPS D7 and D8 in type 0 with and without D9-branes in the background. By extending the descent relations between D-branes to type 0 theories, the non-BPS D8-brane is considered as the result of a tachyon condensation of a D9 anti-D9 pair in type 0. We study the condensation of the open string tachyons in type 0 with generic gauge groups giving rise to different configurations involving non-BPS D8-branes and discuss the stability in each case. The results agree with the topological analysis of the vacuum manifold of the tachyon potential for each case.

Branes in Type 0/Type II Duality

We derive relations between type 0 and type II D-brane configurations under the T-duality suggested by Bergman and Gaberdiel and confirm that the massless fields on D-branes are identical to those on the dual D-brane configurations. Furthermore, we discuss dualities of type 0 and type II NS5-branes and find that the dual of an unwrapped type 0 NS5-brane is a Kaluza-Klein monopole with non-supersymmetric blow up modes.

Baryons and string creation from the 5-brane world-volume action

We construct BPS-exact solutions of the world-volume Born-Infeld plus WZW action of a D5-brane in the background of N D3-branes. The non-trivial background metric and RR five-form field strength play a crucial role in the solution. When a D5-brane is dragged across a stack of N D3-branes a bundle of N fundamental strings joining the two types of branes is created, as in the Hanany-Witten effect. Our solutions give a detailed description of this bundle in terms of a D5-brane wrapped on a sphere. We discuss extensions of these solutions which have an interpretation in terms of gauge theory multi-quark states via the AdS/CFT correspondence.

Distributed systems of intersecting branes at arbitrary angles

A ‘reduced’ action formulation for a general class of the supergravity solutions, corresponding to the ‘marginally’ bound ‘distributed’ systems of various types of branes at arbitrary angles, is developed. It turns out that all the information regarding the classical features of such solutions is encoded in a first-order Lagrangian (the ‘reduced’ Lagrangian) corresponding to the desired geometry of branes. The marginal solution for a system of N such distributions (for various distribution functions) span an N-dimensional submanifold of the fields' configuration (target) space, parametrized by a set of N independent harmonic functions on the transverse space. This submanifold, which we call the ‘ H-surface’, is a null surface with respect to a metric on the configuration space, which is defined by the reduced Lagrangian. The equations of motion then transform to a set of equations describing the embedding of a null geodesic surface in this space, which is identified as the H-surface. Using these facts, we present a very simple derivation of the conventional orthogonal solutions together with their intersection rules. Then a new solution for a (distributed) pair of p-branes at SU(2) angles in D dimensions is derived.

On the supersymmetries of anti-de Sitter vacua

We present details of a geometric method to associate a Lie superalgebra with a large class of bosonic supergravity vacua of the type adS × X, corresponding to elementary branes in M-theory and type II string theory.

‘No-force’ condition and BPS combinations of p-branes in 11 and 10 dimensions

The condition of vanishing of the static force on a q-brane probe in the gravitational background produced by another p-brane is used to give a simple derivation of the pair-wise intersection rules which govern the construction of BPS combinations of branes. These rules, while implied also by supersymmetry considerations, thus have a purely bosonic origin. Imposing the nonforce requirement makes it possible to add branes ‘one by one’ to construct composite BPS configurations (with zero binding energy) of 2-branes and 5-branes in D = 11 and of various p-branes in D = 10. The advantage of this elementary approach is its universality, i.e. the cases of different dimensions and different types of branes (e.g., NS-NS, R-R and ‘mixed’ combinations of NS-NS and R-R branes in D = 10) are all treated in the same way.

Real structures on moduli spaces of Higgs bundles

We construct triples of commuting real structures on the moduli space of Higgs bundles, whose fixed loci are branes of type (B, A, A), (A, B, A) and (A, A, B). We study the real points through the associated spectral data and describe the topological invariants involved using KO, KR and equivariant K-theory.