Exotic Branes Research Articles

3d 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} = 2 theories from M-theory on CY4 and IIB brane box

We study 3D 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} = 2 supersymmetric field theories geometrically engineered from M-theory on non-compact Calabi-Yau fourfolds (CY4). We establish a detailed dictionary between the geometry and topology of non-compact CY4 and the physics of 3D 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} = 2 theories in three different regimes. The first one is the Coulomb branch description when the CY4 is smooth. The second one is non-abelian gauge theory when the CY4 has a degenerate ℙ1-fibration structure. The third one is the strongly coupled SCFT from a CY4 singularity. We find interesting flavor symmetry enhancements in the singular limit of CY4, as well as an interesting and previously unexplored phenomenon in 3D, termed “flavor symmetry duality”. Many examples are analyzed with an emphasis on toric CY4s and ℂ4 orbifolds with crepant resolutions. We develop a new brane box method to study the physics of Coulomb branch of 3D 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} = 2 theory that admits a toric construction. Via IIB/M-theory duality we find that the brane box diagram living in ℝ3 can be physically realized as a configuration of intersecting 4-branes which are extended objects in 8D maximal supersymmetric theory, which is shown to be consistent via various chains of dualities. The rank, effective gauge coupling and certain hints to flavor symmetry enhancement of the 3D 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} = 2 theory are read off from the brane box and cross-checked against the results obtained from geometric engineering. The exotic branes in 8D maximal supersymmetric theory and the 4-string junctions thereof are shown to play a crucial role in the construction of the brane box.

Resolving spacetime singularities in flux compactifications & KKLT

In flux compactifications of type IIB string theory with D3 and seven-branes, the negative induced D3 charge localized on seven-branes leads to an apparently pathological profile of the metric sufficiently close to the source. With the volume modulus stabilized in a KKLT de Sitter vacuum this pathological region takes over a significant part of the entire compactification, threatening to spoil the KKLT effective field theory. In this paper we employ the Seiberg-Witten solution of pure SU(N) super Yang-Mills theory to argue that wrapped seven-branes can be thought of as bound states of more microscopic exotic branes. We argue that the low-energy worldvolume dynamics of a stack of n such exotic branes is given by the (A1, An−1) Argyres-Douglas theory. Moreover, the splitting of the perturbative (in α′) seven-brane into its constituent branes at the non-perturbative level resolves the apparently pathological region close to the seven-brane and replaces it with a region of mathcal{O} (1) Einstein frame volume. While this region generically takes up an mathcal{O} (1) fraction of the compactification in a KKLT de Sitter vacuum we argue that a small flux superpotential dynamically ensures that the 4d effective field theory of KKLT remains valid nevertheless.

The geometry, branes and applications of exceptional field theory

This is a review of exceptional field theory: a generalisation of Kaluza–Klein theory that unifies the metric and [Formula: see text]-form gauge field degrees of freedom of supergravity into a generalised or extended geometry, whose additional coordinates may be viewed as conjugate to brane winding modes. This unifies the maximal supergravities, treating their previously hidden exceptional Lie symmetries as a fundamental geometric symmetry. Duality orbits of solutions simplify into single objects, that in many cases have simple geometric interpretations, for instance as wave or monopole-type solutions. It also provides a route to explore exotic or nongeometric aspects of M-theory, such as exotic branes, [Formula: see text]-folds, and more novel sorts of non-Riemannian spaces.

Exotic branes and mixed-symmetry potentials II: Duality rules and exceptional p-form gauge fields

Abstract In $U$-duality-manifest formulations, supergravity fields are packaged into covariant objects such as the generalized metric and $p$-form fields $\mathcal A_p^{I_p}$. While a parameterization of the generalized metric in terms of supergravity fields is known for $U$-duality groups $E_n$ with $n\leq 8$, a parameterization of $\mathcal A_p^{I_p}$ has not been fully determined. In this paper, we propose a systematic method to determine the parameterization of $\mathcal A_p^{I_p}$, which necessarily involves mixed-symmetry potentials. We also show how to systematically obtain the $T$- and $S$-duality transformation rules of the mixed-symmetry potentials entering the multiplet. As the simplest non-trivial application, we find the parameterization and the duality rules associated with the dual graviton. Additionally, we show that the 1-form field $\mathcal A_1^{I_1}$ can be regarded as the generalized graviphoton in the exceptional spacetime.

Special holonomy manifolds, domain walls, intersecting branes and T-folds

We discuss the special holonomy metrics of Gibbons, Lu, Pope and Stelle, which were constructed as nilmanifold bundles over a line by uplifting supersymmetric domain wall solutions of supergravity to 11 dimensions. We show that these are dual to intersecting brane solutions, and considering these leads us to a more general class of special holonomy metrics. Further dualities relate these to non-geometric backgrounds involving intersections of branes and exotic branes. We discuss the possibility of resolving these spaces to give smooth special holonomy manifolds.

The doubled geometry of nilmanifold reductions

A class of special holonomy spaces arise as nilmanifolds fibred over a line interval and are dual to intersecting brane solutions of string theory. Further dualities relate these to T-folds, exotic branes, essentially doubled spaces and spaces with R-flux. We develop the doubled geometry of these spaces, with the various duals arising as different slices of the doubled space.

Degenerations of K3, orientifolds and exotic branes

A recently constructed limit of K3 has a long neck consisting of segments, each of which is a nilfold fibred over a line, that are joined together with Kaluza-Klein monopoles. The neck is capped at either end by a Tian-Yau space, which is non-compact, hyperkähler and asymptotic to a nilfold fibred over a line. We show that the type IIA string on this degeneration of K3 is dual to the type I′ string, with the Kaluza-Klein monopoles dual to the D8-branes and the Tian-Yau spaces providing a geometric dual to the O8 orientifold planes. At strong coupling, each O8-plane can emit a D8-brane to give an O8∗ plane, so that there can be up to 18 D8-branes in the type I′ string. In the IIA dual, this phenomenon occurs at weak coupling and there can be up to 18 Kaluza-Klein monopoles in the dual geometry. We consider further duals in which the Kaluza-Klein monopoles are dualised to NS5-branes or exotic branes. A 3-torus with H -flux can be realised in string theory as an NS5-brane wrapped on T3, with the 3-torus fibred over a line. T-dualising gives a 4-dimensional hyperk¨ahler manifold which is a nilfold fibred over a line, which can be viewed as a Kaluza-Klein monopole wrapped on T2. Further T-dualities then give non-geometric spaces fibred over a line and can be regarded as wrapped exotic branes. These are all domain wall configurations, dual to the D8-brane. Type I′ string theory is the natural home for D8-branes, and we dualise this to find string theory homes for each of these branes. The Kaluza-Klein monopoles arise in the IIA string on the degenerate K3. T-duals of this give exotic branes on non-geometric spaces.

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.

The different faces of branes in double field theory

We show how the Wess-Zumino terms of the different branes in string theory can be embedded within double field theory. Crucial ingredients in our construction are the identification of the correct brane charge tensors and the use of the double field theory potentials that arise from dualizing the standard double field theory fields. This leads to a picture where under T-duality the brane does not change its worldvolume directions but where, instead, it shows different faces depending on whether some of the worldvolume and/or transverse directions invade the winding space. As a non-trivial by-product we show how the different Wess-Zumino terms are modified when the brane propagates in a background with a non-zero Romans mass parameter. Furthermore, we show that for non-zero mass parameter the brane creation process, when one brane passes through another brane, gets generalized to brane configurations that involve exotic branes as well.

Gauge Field Fluxes and Bianchi Identities in Extended Field Theories

Tensor hierarchy of Exceptional Field Theories contains gauge fields satisfying certain Bianchi identities with source part governing interaction with standard and exotic branes. These are responsible for tadpole cancellation in compactification schemes and provide consistency constraints for cosmological model building. Analysis of reduction of (10+10)-dimensional DFT into (D+d+d)-dimensional split DFT allows to consider all Bianchi identities of the theory in the form analogous to the ExFT approach. Here we review in details and elaborate on these ideas.

Symmetries of M-theory and free Lie superalgebras

We study systematically various extensions of the Poincaré superalgebra. The most general structure starting from a set of spinorial supercharges Qα is a free Lie superalgebra that we discuss in detail. We explain how this universal extension of the Poincaré superalgebra gives rise to many other algebras as quotients, some of which have appeared previously in various places in the literature. In particular, we show how some quotients can be very neatly related to Borcherds superalgebras. The ideas put forward also offer some new angles on exotic branes and extended symmetry structures in M-theory.

Exotic branes in Exceptional Field Theory: E7(7) and beyond

In recent years, it has been widely argued that the duality transformations of string and M-theory naturally imply the existence of so-called ‘exotic branes’ — low codimension objects with highly non-perturbative tensions, scaling as gsα for α ≤ −3. We argue that their intimate link with these duality transformations make them an ideal object of study using the general framework of Double Field Theory (DFT) and Exceptional Field Theory (EFT) — collectively referred to as ExFT. Parallel to the theme of dualities, we also stress that these theories unify known solutions in string- and M-theory into a single solution under ExFT. We argue that not only is there a natural unifying description of the lowest codimension objects, many of these exotic states require this formalism as a consistent supergravity description does not exist.

Weaving the exotic web

String and M-theory contain a family of branes forming U -duality multiplets. In particular, standard branes with codimension higher than or equal to two, can be explicitly found as supergravity solutions. However, whether domain-wall branes and space-filling branes can be found as supergravity solutions is still unclear. In this paper, we firstly provide a full list of exotic branes in type II string theory or M-theory compactified to three or higher dimensions. We show how to systematically obtain backgrounds of exotic domain-wall branes and space-filling branes as solutions of the double field theory or the exceptional field theory. Such solutions explicitly depend on the winding coordinates and cannot be given as solutions of the conventional supergravity theories. However, as the domain-wall solutions depend linearly on the winding coordinates, we describe them as solutions of deformed supergravities such as the Romans massive IIA supergravity or lower-dimensional gauged supergravities. We establish explicit relations among the domain-wall branes, the mixed-symmetry potentials, the locally non-geometric fluxes, and deformed supergravities.

Exotic branes in Exceptional Field Theory: the SL(5) duality group

We study how exotic branes, i.e. branes whose tensions are proportional to gs− α, with α > 2, are realised in Exceptional Field Theory (EFT). The generalised torsion of the Weitzenböck connection of the SL(5) EFT which, in the language of gauged supergravity describes the embedding tensor, is shown to classify the exotic branes whose magnetic fluxes can fit into four internal dimensions. By analysing the weight diagrams of the corresponding representations of SL(5) we determine the U-duality orbits relating geometric and non-geometric fluxes. As a further application of the formalism we consider the Kaluza-Klein monopole of 11D supergravity and rotate it into the exotic 6(3,1)-brane.

Space-filling branes & gaugings

We consider in any dimension the supersymmetric ℤ2 truncations of the maximal supergravity theories. In each dimension and for each truncation we determine all the sets of 1/2-BPS space-filling branes, i.e. branes whose world-volume invades the whole of space-time, that preserve the supersymmetry of the truncated theory and the representations of the symmetry of such theory to which they belong. We show that in any dimension below eight these sets always contain exotic branes, that are objects that do not have a ten-dimensional origin. We repeat the same analysis for half-maximal theories and for the quarter-maximal theories in four and three dimensions. We then discuss all the possible gaugings of these theories as described in terms of the embedding tensor. In general, the truncation acts on the quadratic constraints of the embedding tensor in such a way that some representations survive the truncation although they are not required by the supersymmetry of the truncated theory. We show that for any theory, among these representations, the highest-dimensional ones are precisely those of the 1/2-BPS space-filling branes that preserve the same supersymmetry of the truncated theory, and we interpret this result as the fact that these quadratic constraints after the truncation become tadpole conditions for such branes.

Wrapping rules (in) string theory

In this paper we show that the number of all 1/2-BPS branes in string theory compactified on a torus can be derived by universal wrapping rules whose formulation we present. These rules even apply to branes in less than ten dimensions whose ten-dimensional origin is an exotic brane. In that case the wrapping rules contain an additional combinatorial factor that is related to the highest dimension in which the ten-dimensional exotic brane, after compactification, can be realized as a standard brane. We show that the wrapping rules also apply to cases with less supersymmetry. As a specific example, we discuss the compactification of IIA/IIB string theory on (T4/ℤ2) × Tn.

Non-geometric fluxes & tadpole conditions for exotic branes

We extend the mathcal{P} -flux analysis carried out recently on the T6/[ℤ2 × ℤ2] type-II orientifold model to include all the possible non-geometric fluxes. By deriving universal T-duality rules for all the fluxes, we are able to write down a complete expression for the superpotential for both the IIB and IIA theories. By exploiting the universal T-duality rules that apply to all the branes in string theory, we then identify all the exotic branes that can be consistently included to cancel the tadpoles induced by the fluxes. Finally, we derive the representations of these branes with respect to the SL(2, ℤ)7 duality symmetry of the model.

Effective action for non-geometric fluxes duality covariant actions

The (heterotic) double field theories and the exceptional field theories are manifestly duality covariant formulations, describing low-energy limit of various super-string and M-theory compactifications. These field theories are known to be reduced to the standard descriptions by introducing appropriately parameterized generalized metric and by applying suitably chosen section conditions. In this paper, we apply these formulations to non-geometric backgrounds. We introduce different parameterizations for the generalized metric in terms of the dual fields which are pertinent to non-geometric fluxes. Under certain simplifying assumptions, we construct new effective action for non-geometric backgrounds. We then study the non-geometric backgrounds sourced by exotic branes and find their U -duality monodromy matrices. The charge of exotic branes obtained from these monodromy matrices agrees with the charge obtained from the non-geometric flux integral.

P fluxes and exotic branes

We consider the ${\cal N}=1$ superpotential generated in type-II orientifold models by non-geometric fluxes. In particular, we focus on the family of $P$ fluxes, that are related by T-duality transformations to the S-dual of the $Q$ flux. We determine the general rule that transforms a given flux in this family under a single T-duality transformation. This rule allows to derive a complete expression for the superpotential for both the IIA and the IIB theory for the particular case of a $T^6/[\mathbb{Z}_2 \times \mathbb{Z}_2 ]$ orientifold. We then consider how these fluxes modify the generalised Bianchi identities. In particular, we derive a fully consistent set of quadratic constraints coming from the NS-NS Bianchi identities. On the other hand, the $P$ flux Bianchi identities induce tadpoles, and we determine a set of exotic branes that can be consistently included in order to cancel them. This is achieved by determining a universal transformation rule under T-duality satisfied by all the branes in string theory.

Branes in Extended Spacetime: Brane Worldvolume Theory Based on Duality Symmetry.

We propose a novel approach to the brane worldvolume theory based on the geometry of extended field theories: double field theory and exceptional field theory. We demonstrate the effectiveness of this approach by showing that one can reproduce the conventional bosonic string and membrane actions, and the M5-brane action in the weak-field approximation. At a glance, the proposed 5-brane action without approximation looks different from the known M5-brane actions, but it is consistent with the known nonlinear self-duality relation, and it may provide a new formulation of a single M5-brane action. Actions for exotic branes are also discussed.