BPS Branes Research Articles

Non-geometric BPS branes on T-folds

We give a detailed (microscopic) description of the geometric and non-geometric fundamental branes and their bound states in Type II superstring compactifications preserving N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 6 supersymmetry. We consider general boundary states that couple to the twisted sector and compute the relevant annulus amplitudes. We check consistency of the construction by relating the ‘transverse’ channel, corresponding to closed-string ‘tree-level’ exchange, with the ‘direct’ open-string loop channel. Focussing on the Type IIA frame, we show that D0-D4 have the expected tension for a geometric brane, while the non-geometric D2-D6 boundary states have a tension equal to 1/K\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ 1/\\sqrt{K} $$\\end{document} the one of a geometric brane for the ZK orbifold. This is consistent with Fricke T-duality of the N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 6 model.

On BPS World Volume, RR Couplings, and Their α′ Corrections in Type IIB

We compute the asymmetric and symmetric correlation functions of a four-point amplitude of a gauge field, a scalar field, and a closed string Ramond-Ramond (RR) for different nonvanishing BPS branes. All world volume, the Taylor and pull-back couplings, and their all-order α′ corrections have also been explored. Due to various symmetry structures, different restricted BPS Bianchi identities have also been constructed. The prescription of exploring all the corrections of two closed string RR couplings in type IIB is given. We obtain the closed form of the entire S-matrix elements of two closed string RRs and a gauge field on the world volume of BPS branes in type IIB. All the correlation functions of VA0x1VC−1z1,z¯1VC−1z2,z¯2 are also revealed accordingly. The algebraic forms for the most general case of the integrations ∫d2zz−iaz+ibz−z¯cz+z¯d on the upper half plane are derived in terms of Pochhammer and some analytic functions. Lastly, we generate various singularity structures in both effective field theory and IIB string theory, producing different contact interactions as well as their α′ higher derivative corrections.

Exotic branes from del Pezzo surfaces

We revisit a correspondence between toroidal compactifications of M-theory and del Pezzo surfaces, in which rational curves on the del Pezzo are related to $\frac{1}{2}$-BPS branes of the corresponding compactification. We argue that curves of higher genus correspond to nongeometric backgrounds of the M-theory compactifications, which are related to exotic branes. In particular, the number of ``special directions'' of the exotic brane is equal to the genus of the corresponding curve. In addition to predicting three new nongeometric backgrounds, we discuss a relation between addition of curves in the del Pezzo and the brane polarization effect.

On WZ and RR couplings of BPS branes and their all order α ′ corrections in IIB, IIA

We compute all three and four point couplings of BPS $D_{p}$-branes for all different nonzero $p$-values on the entire world volume and transverse directions. We start finding out all four point function supersymmetric Wess-Zumino (WZ) actions of one closed string Ramond-Ramond (RR) field with two fermions, either with the same (IIB) or different chirality (IIA) as well as their all order $\alpha'$ corrections. The closed form of S-matrices of two closed string RR in both IIB, IIA, including their all order $\alpha'$ corrections have also been addressed. Our results confirm that, not only the structures of $\alpha'$ corrections but also their coefficients of IIB are quite different from their IIA ones. The S-matrix of an RR and two gauge (scalar) fields and their all order corrections in antisymmetric picture of RR have been carried out as well. Various remarks on the restricted Bianchi identities as well as all order $\alpha'$ corrections to all different supersymmetric WZ couplings in both type IIA and IIB superstring theory are also released. Lastly, different singularity structures as well as all order contact terms for all non-vanishing traces in type II have also been constructed.

Decoupling of gravity on non-susy Dp branes

We study the graviton scattering in the background of non-susy D$p$ branes of type II string theories consisting of a metric, a dilaton and a $(p+1)$ form gauge field. We show numerically that in these backgrounds graviton experiences a scattering potential which takes the form of an infinite barrier in the low energy (near brane) limit for $p\leq 5$ and therefore is never able to reach the branes. This shows, contrary to what is known in the literature, that gravity indeed decouples from the non-susy D$p$ branes for $p \leq 5$. For non-susy D6 brane, gravity couples as there is no such barrier for the potential. To give further credence to our claim we solve the scattering equation in some situation analytically and calculate the graviton absorption cross-sections on the non-susy branes and show that they vanish for $p \leq 4$ in the low energy limit. This shows, as in the case of BPS branes, that gravity does decouple for non-susy D$p$ branes for $p\leq 4$ but it does not decouple for D6 brane as the potential here is always attractive. We argue for the non-susy D5 brane that depending on one of the parameters of the solution gravity either always decouples (unlike the BPS D5 brane) or it decouples when the energy of the graviton is below certain critical value, otherwise it couples, very similar to BPS D5 brane.

Remarks on the mixed Ramond–Ramond, open string scattering amplitudes of BPS, non-BPS and brane–anti-brane

From the world-sheet point of view we compute three, four and five point BPS and non-BPS scattering amplitudes of type IIA and IIB superstring theory. All these the mixed S-matrix elements including a closed string Ramond-Ramond (RR) in the bulk and a scalar/gauge or tachyons with their all different pictures ( including RR in asymmetric and symmetric pictures) have been carried out. We have also shown that in asymmetric pictures various equations must be kept fixed. More importantly, by direct calculations on upper half plane, it is realized that some of the equations (that must be true) for BPS branes can not be necessarily applied to non-BPS amplitudes. We also derive the S-Matrix elements of $<V_C^{-2} V_{\phi}^{0}V _A^{0} V_T^{0} >$ and clarify the fact that in the presence of the scalar field and RR, the terms carrying momentum of RR in transverse directions play important role in the entire form of the S-matrix and their presence is needed in order to have gauge invariance for the entire S-matrix elements of type IIA (IIB) superstring theory.

Universality in all-[formula omitted] order corrections to BPS/non-BPS brane world volume theories

Knowledge of all-α′ higher derivative corrections to leading order BPS and non-BPS brane actions would serve in future endeavor of determining the complete form of the non-abelian BPS and tachyonic effective actions. In this paper, we note that there is a universality in the all-α′ order corrections to BPS and non-BPS branes. We compute amplitudes between one Ramond–Ramond C-field vertex operator and several SYM gauge/scalar vertex operators. Specifically, we evaluate in closed form string correlators of two-point amplitudes ACϕ, ACA, a three-point amplitude ACϕϕ, and a four-point amplitude ACϕϕϕ. We carry out pole and contact term analysis. In particular we reproduce some of the contact terms and the infinite massless poles of ACϕϕϕ by SYM vertices obtained through the universality.

Geometry and stability of spinning branes in AdS gravity

The geometry of spinning codimension-two branes in AdS spacetime is analyzed in three and higher dimensions. The construction of non-extremal solutions is based on identifications in the covering of AdS space by isometries that have fixed points. The discussion focuses on the cases where the parameters of spinning states can be related to the velocity of a boosted static codimension-two brane. The resulting configuration describes a single spinning brane, or a set of intersecting branes, each one produced by an independent identification. The nature of the singularity is also examined, establishing that the AdS curvature acquires one in the form of a Dirac delta distribution. The stability of the branes is studied in the framework of Chern-Simons AdS supergravity. A class of branes, characterized by one free parameter, are shown to be stable when the BPS conditions are satisfied. In 3D, these stable branes are extremal, while in higher dimensions, the BPS branes are not the extremal ones.

Three Point Tree Level Amplitude in Superstring Theory

In order to check the definite amplitude and the exact zero result of the amplitude of three massless points $(CAA)$ in both string theory and field theory side for $p=n$ case and to find all gauge field couplings to R-R closed string, we investigate the disk level S-matrix element of one Ramond-Ramond field and two gauge field vertex operators in the world volume of BPS branes.

MULTIPLE Dp-BRANES AS A Dp+2-BRANE

From BFSS matrix theory considerations, it is expected that a single D p+2-brane action can be obtained from N D p-brane action in large N limit. We examine and confirm this expectation by working out the details of DBI and Chern–Simons terms of D p+2-brane action from D p-brane action. We show that the same relation works for non-BPS, as well as BPS branes.

A universal lower bound on the specific temperatures of AdS-Reissner–Nordström black holes with flat event horizons

We show that, in a gravitational theory [in any number of dimensions greater than 3] which admits BPS branes and AdS-Reissner–Nordström black holes with flat event horizons, the specific [dimensionless] temperature of such a black hole is bounded below by ≈0.156875. This confirms the recent suggestion by Hartnoll and Tavanfar, to the effect that no such black hole can be arbitrarily cold, since from the AdS/CFT dual point of view the low-temperature degrees of freedom should not be concealed by the equivalent of an event horizon.

On effective actions of BPS branes and their higher derivative corrections

We calculate in detail the disk level S-matrix element of one Ramond-Ramond field and three gauge field vertex operators in the world volume of BPS branes, to find four gauge field couplings to all orders of $\alpha'$ up to on-shell ambiguity. Then using these infinite couplings we find that the massless pole of the field theory amplitude is exactly equal to the massless pole S-matrix element of this amplitude for the $p=n$ case to all orders of $\alpha'$. Finally we show that the infinite massless poles and the contact terms of this amplitude for the $p=n+2$ case can be reproduced by the Born-Infeld action and the Wess-Zumino actions and by their higher derivative corrections.

Topological BPS charges in 10- and 11-dimensional supergravity

In this thesis we construct closed expressions that correspond to the topological charges of the various BPS branes of the IIA, IIB and $D=11$ supergravity theories. These expressions are related to the structure of the SUSY algebras in curved spacetimes. We consider charges for all the M-, NS- and D-branes as well as the Kaluza-Klein monopoles. Additionally we consider the $SL(2,\mathbb{R})$ symmetry that exists in the IIB theory and $D=11$ theory in a double M9-brane background, and determine the charges for the remaining branes that fill up the $SL(2,\mathbb{R})$ multiplets. These include the charges corresponding to the multiplets of 7 and 9-branes in IIB as well as several new types of branes in $D=11$. We find that examining the possible multiplet structures of the charges provides another tool for exploring the spectrum of BPS branes that appear in these theories. Furthermore, we demonstrate how these charges map between theories. As a prerequisite to constructing some of the charges we determine the field equations and multiplet structure of the $D=11$ gauge potentials, extending previous results on the subject. The massive gauge transformations of the fields are also discussed, and we demonstrate how they are compatible with the construction of an $SL(2,\mathbb{R})$ covariant kinetic term in the $D=11$ Kaluza-Klein monopole worldvolume action.

Strings and D-branes in a supersymmetric magnetic flux background

We investigate how the presence of RR magnetic Fp+2 fluxes affects the energy of classical Dp branes, for specific string theory supersymmetric backgrounds which are solutions to the leading order in α' including back-reaction effects. The Dp brane dynamics is found to be similar to the well known dynamics of particles and strings moving in magnetic fields. We find a class of BPS solutions which generalize the BPS fundamental strings or BPS branes with momentum and winding to the case of non-zero magnetic fields. Remarkably, the interaction with the magnetic fields does not spoil the supersymmetry of the solution, which turns out to be invariant under four supersymmetry transformations. We find that magnetic fields can significantly reduce the energy of some BPS strings and Dp branes, in particular, some macroscopic Dp branes become light for sufficiently large magnetic fields.

Fuzzy sphere dynamics and non-abelian DBI in curved backgrounds

We consider the non-Abelian action for the dynamics of $N Dp'$-branes in the background of $M Dp$-branes, which parameterises a fuzzy sphere using the SU(2) algebra. We find that the curved background leads to collapsing solutions for the fuzzy sphere except when we have $D0$ branes in the $D6$ background, which is a realisation of the gravitational Myers effect. Furthermore we find the equations of motion in the Abelian and non-Abelian theories are identical in the large $N$ limit. By picking a specific ansatz we find that we can incorporate angular momentum into the action, although this imposes restriction upon the dimensionality of the background solutions. We also consider the case of non-Abelian non-BPS branes, and examine the resultant dynamics using world-volume symmetry transformations. We find that the fuzzy sphere always collapses but the solutions are sensitive to the combination of the two conserved charges and we can find expanding solutions with turning points. We go on to consider the coincident $NS$5-brane background, and again construct the non-Abelian theory for both BPS and non-BPS branes. In the latter case we must use symmetry arguments to find additional conserved charges on the world-volumes to solve the equations of motion. We find that in the Non-BPS case there is a turning solution for specific regions of the tachyon and radion fields. Finally we investigate the more general dynamics of fuzzy $\mathbb{S}^{2k}$ in the $Dp$-brane background, and find collapsing solutions in all cases.

Fermion localization on thick branes

We consider chiral fermion confinement in scalar thick branes, which are known to localize gravity, coupled through a Yukawa term. The conditions for the confinement and their behavior in the thin-wall limit are found for various different BPS branes, including double walls and branes interpolating between different $\mathrm{Ad}{\mathrm{S}}_{5}$ spacetimes. We show that only one massless chiral mode is localized in all these walls, whenever the wall thickness is keep finite. We also show that, independently of wall's thickness, chiral fermionic modes cannot be localized in $\mathrm{d}{\mathrm{S}}_{4}$ walls embedded in a ${M}_{5}$ spacetime. Finally, massive fermions in double wall spacetimes are also investigated. We find that, besides the massless chiral mode localization, these double walls support quasilocalized massive modes of both chiralities.

The spectrum of BPS branes on a noncompact Calabi-Yau

We begin the study of the spectrum of BPS branes and its variation on lines of marginal stability on O_P^2(-3), a Calabi-Yau ALE space asymptotic to C^3/Z_3. We show how to get the complete spectrum near the large volume limit and near the orbifold point, and find a striking similarity between the descriptions of holomorphic bundles and BPS branes in these two limits. We use these results to develop a general picture of the spectrum. We also suggest a generalization of some of the ideas to the quintic Calabi-Yau.

Stability and BPS branes

We define the concept of Pi-stability, a generalization of mu-stability of vector bundles, and argue that it characterizes N=1 supersymmetric brane configurations and BPS states in very general string theory compactifications with N=2 supersymmetry in four dimensions.

Stability in asymptotically AdS spaces

We discuss two types of instabilities which may arise in string theory compactified to asymptotically AdS spaces: perturbative, due to discrete modes in the spectrum of the Laplacian, and non-perturbative, due to brane nucleation. In the case of three dimensional Einstein manifolds, we completely characterize the presence of these instabilities, and in higher dimensions we provide a partial classification. The analysis may be viewed as an extension of the Breitenlohner-Freedman bound. One interesting result is that, apart from a very special class of exceptions, all Euclidean asymptotically AdS spaces with more than one conformal boundary component are unstable, if the compactification admits BPS branes or scalars saturating the Breitenlohner-Freedman bound. As examples, we analyze quotients of AdS in any dimension and AdS Taub-NUT spaces, and show a space which was previously discussed in the context of AdS/CFT is unstable both perturbatively and non-perturbatively.

BPS branes in discrete torsion orbifolds

We investigate D-branes in a Z_3xZ_3 orbifold with discrete torsion. For this class of orbifolds the only known objects which couple to twisted RR potentials have been non-BPS branes. By using more general gluing conditions we construct here a D-brane which is BPS and couples to RR potentials in the twisted and in the untwisted sectors.