non-BPS States Research Articles

The fate of the type I non-BPS D7-brane

We describe the fate of the Type I non-BPS D7-brane, which is tachyonic but carries a non-trivial K-theory Z 2 charge. It decays to topologically non-trivial gauge field configurations on the background D9-branes. In the uncompactified theory the decay proceeds to infinity, while with a transverse torus the decay reaches a final state, a toron gauge configuration with vanishing Chern classes but non-trivial Z 2 charge. A similar behaviour is obtained for the type I non-BPS D8-brane, and other related systems. We construct explicit examples of type IIB orientifolds with non-BPS D7-branes, which are hence non-supersymmetric, but for which supersymmetry is restored upon condensation of the tachyon. We also report on the interesting structure of non-BPS states of type IIA theory in the presence of an O6-plane, their M-theory lifts, the relation between string theory K-theory and M-theory cohomology, and its interplay with NS–NS charged objects. We discuss several new effects, including: (i) transmutation between NS–NS and RR torsion charges, (ii) non-BPS states classified by K-theory but not by cohomology in string theory, but whose lift to M-theory is cohomological.

Branes from Unstable Systems of Branes

We discuss various aspects of the description of branes as topological solitons in unstable brane systems of higher dimensions. We first describe a classification of all the possible realisations of branes of M and type II theories as topological solitons of a brane-antibrane system. We then present a description of type IIB NS-NS p-branes in terms of topological solitons in systems of spacetime-filling NS9, anti-NS9 pairs and discuss the implications of these constructions in the description of BPS and non-BPS states in the strongly coupled Heterotic SO(32) theory. We finally present briefly the construction of a conjectured spacetime-filling non-BPS M10-brane, starting point for a brane descent construction of the branes of M-theory.

D-Branes in Type I String Theory

We review the boundary state description of D-branes in type I string theory and show that the only stable non-BPS configurations are the D-particle and the D-instanton. We also compute the gauge and gravitational interactions of the non-BPS D-particles and compare them with the interactions of the dual non-BPS states of the heterotic string, finding complete agreement.

STABLE NON-BPS STATES AND THEIR HOLOGRAPHIC DUALS

Stable non-BPS states can be constructed and studied in a variety of contexts in string theory. Here we review some interesting constructions that arise from suspended and wrapped branes. We also exhibit some stable non-BPS states that have holographic duals.

Is a classical description of stable non-BPS D-branes possible?

We study the classical geometry produced by a stack of stable (i.e. tachyon free) non-BPS D-branes present in K3 compactifications of type II string theory. This classical representation is derived by solving the equations of motion describing the low-energy dynamics of the supergravity fields which couple to the non-BPS state. Differently from what expected, this configuration displays a singular behaviour: the space-time geometry has a repulson-like singularity. This fact suggests that the simplest setting, namely a set of coinciding non-interacting D-branes, is not acceptable. We finally discuss the possible existence of other acceptable configurations corresponding to more complicated bound states of these non-BPS branes.

Gauge and gravitational interactions of non-BPS D-particles

We study the gauge and gravitational interactions of the stable non-BPS D-particles of the type I string theory. The gravitational interactions are obtained using the boundary state formalism while the SO(32) gauge interactions are determined by evaluating disk diagrams with suitable insertions of boundary changing (or twist) operators. In particular the gauge coupling of a D-particle is obtained from a disk with two boundary components produced by the insertion of two twist operators. We also compare our results with the amplitudes among the non-BPS states of the heterotic string which are dual to the D-particles. After taking into account the known duality and renormalization effects, we find perfect agreement, thus confirming at a non-BPS level the expectations based on the heterotic/type I duality.

Lectures on non-BPSDirichlet branes

A comprehensive introduction to the boundary state approach toDirichlet branes is given. Various examples of BPS and non-BPSDirichlet branes are discussed. In particular, the non-BPS states inthe duality of type IIA on K3 and the heterotic string on T4 areanalysed in detail.

Bags, junctions, and networks of BPS and non-BPS defects

We investigate several models of coupled scalar fields that present discrete Z_2, Z_2 x Z_2, Z_3 and other symmetries. These models support topological domain wall solutions of the BPS and non-BPS type. The BPS solutions are stable, but the stability of the non-BPS solutions may depend on the parameters that specify the models. The BPS and non-BPS states give rise to bags, and also to three-junctions that may allow the presence of networks of topological defects. In particular, we show that the non-BPS defects of a specific model that engenders the Z_3 symmetry give rise to a stable regular hexagonal network of domain walls.

Non-BPS states and heterotic – type I ′ duality

There are two families of non-BPS bi-spinors in the perturbative spectrum of the nine-dimensional heterotic string charged under the gauge group SO(16)× SO(16). The relation between these perturbative non-BPS states and certain non-perturbative non-BPS D-brane states of the dual type I ′ theory is exhibited. The relevant branes include a Z 2 charged non-BPS D-string, and a bound state of such a D-string with a fundamental string. The domains of stability of these states as well as their decay products in both theories are determined and shown to agree with the duality map.

Stable non-BPS states in F-theory

F-theory on K3 admits non-BPS states that are represented as string junctions extending between 7-branes. We classify the non-BPS states which are guaranteed to be stable on account of charge conservation and the existence of a region of moduli space where the 7-branes supporting the junction can be isolated from the rest of the branes. We find three possibilities; the 7-brane configurations carrying: (i) the D_1 algebra representing a D7-brane near an orientifold O7-plane, whose stable non-BPS state was identified before, (ii) the exotic affine E_1 algebra, whose stable non-BPS state seems to be genuinely non-perturbative, and, (iii) the affine E_2 algebra representing a D7-brane near a pair of O7-planes. As a byproduct of our work we construct explicitly all 7-brane configurations that can be isolated in a K3. These include non-collapsible configurations of affine type.

S-duality and brane descent relations

We present a description of the type IIB NS-NS p-branes in terms of topological solitons in systems of spacetime-filling brane-antibrane pairs. S-duality implies that these spacetime-filling branes are NS9-branes, S-dual to the D9-branes of the type IIB theory. The possible vortex-like solutions in an NS9,anti-NS9 configuration are identified by looking at its worldvolume effective action. Finally we discuss the implications of these constructions in the description of BPS and non-BPS states in the strongly coupled Heterotic SO(32) theory.

Brane-antibrane constructions

In type II string theories, we examine intersecting brane constructions containing brane-antibrane pairs suspended between 5-branes, and more general non-BPS constructions. The tree-level spectra are obtained in each case. We identify various models with distinct physics: parallel brane-antibrane pairs, adjacent pairs, non-adjacent pairs, and configurations which break all supersymmetry even though any pair of branes preserves some supersymmetry. In each case we examine the possible decay modes. Some of these configurations turn out to be tachyon-free, stable non-BPS states. We use T-duality to map some of our brane constructions to brane-antibrane pairs at ALE singularities. This enables us to explicitly derive the spectra by the analogue of the quiver construction, and to compute the sign of the brane-antibrane force in each case.

STABLE NON-BPS STATES IN STRING THEORY: A PEDAGOGICAL REVIEW

We present a pedagogical review of the stable non-BPS states in string theory which have recently attracted some attention in the literature. In particular, following the analysis of A. Sen, we discuss in detail the case of the stable non-BPS D-particle of Type I theory whose existence is predicted (and required) by the heterotic/Type I duality. We show that this D-particle originates from an unstable bound state formed by a D1anti-D1 pair of Type IIB in which the tachyon field acquires a solitonic kink configuration. The mechanism of tachyon condensation is discussed first at a qualitative level and then with an exact conformal field theory analysis.

Stable non-BPS states on a 3-brane probe

As a novel application of string junctions, we provide evidence for the existence of stable non-BPS dyons with magnetic charge greater than 1 in (the semiclassical regime of) N=2 SU(2) Super-Yang-Mills theory. In addition, we find a new curve of marginal stability. Moduli space is therefore divided into four regions, each containing a different stable particle spectrum.

Brane transfer operations and T-duality of non-BPS states

Using the relation between D-brane charges and K-theory, we study non-BPS D-branes and their behavior under T-duality. We point out that in general compactifications, D-brane charges are classified by relative K-theory groups. T-duality is found to act as a symmetry between the relative K-theory groups in Type II and Type I/IA theories. We also study Type \tilde\IA theory (which contains an O8^- plane and an O8^+ plane), using K-theory and T-duality to identify its stable D-branes. Comparison with string theory constructions reveals two interesting effects. One of them involves the transfer of branes between O-planes, while in the other, a D-brane charge which seems conserved near one O-plane in fact decays due to the presence of another type of O-plane.

Non-BPS states in heterotic-type IIA duality

The relation between some perturbative non-BPS states of the heterotic theory on T^4 and non-perturbative non-BPS states of the orbifold limit of type IIA on K3 is exhibited. The relevant states include a non-BPS D-string, and a non-BPS bound state of BPS D-particles (`D-molecule'). The domains of stability of these states in the two theories are determined and compared.

String webs and [formula omitted] BPS monopoles

We argue for the existence of many new 1 4 BPS states in N = 4 SU( N c ) Super-Yang-Mills theory with N c ⩾ 3, by constructing them from supersymmetric string webs whose external strings terminate on parallel D3-branes. The masses of the string webs are shown to agree with the BPS bound for the corresponding states in SYM. We identify the curves of marginal stability, at which these states decay into other BPS states. We find the bosonic and fermionic zero-modes of the string webs, and thereby the degeneracy and spin content of some of the BPS states. States of arbitrarily high spin are predicted in this manner, all of which become massless at the conformal point. For N c ⩾ 4 we find BPS states which transform in long multiplets, and are therefore not protected against becoming stable non-BPS states as moduli are varied. The mass of these extremal non-BPS states is constrained as they are connected to BPS states. Analogous geometric phenomena are anticipated.

Stable non-BPS D-particles

It is shown that the orbifold of type IIB string theory by (−1) F L I 4 admits a stable non-BPS Dirichlet particle that is stuck on the orbifold fixed plane. It is charged under the SO(2) gauge group coming from the twisted sector, and transforms as a long multiplet of the D=6 supersymmetry algebra. This suggests that it is the strong coupling dual of the perturbative stable non-BPS state that appears in the orientifold of type IIB by Ω I 4 .

Stable non-BPS bound states of BPS D-branes

S-duality symmetry of type IIB string theory predicts the existence of a stable non-BPS state on an orbifold five plane of the type IIB theory if the orbifold group is generated by the simultaneous action of (-1)^{F_L} and the reversal of sign of the four coordinates transverse to the orbifold plane. We calculate the mass of this state by starting from a pair of D-strings carrying the same charge as this state, and then identifying the point in the moduli space where this pair develops a tachyonic mode, signalling the appearance of a bound state of this configuration into the non-BPS state.

Stable non-BPS states in string theory

Many string theories contain states which are not BPS, but are stable due to charge conservation. In many cases the description of these states in the strong coupling limit remains unknown despite the existence of a weakly coupled dual theory. However, we show that in some cases duality symmetries in string theory do enable us to identify these states in the strong coupling limit and calculate their masses. We also speculate that in some of the other cases the missing states might arise from non-supersymmetric analog of D0-branes.