Supersymmetry Conditions Research Articles

Standardlike models as type IIB flux vacua

We construct new semirealistic type IIB flux vacua on ${Z}_{2}\ifmmode\times\else\texttimes\fi{}{Z}_{2}$ orientifolds with three- and four-standard model families and up to three units of quantized flux. The open string sector is comprised of magnetized D-branes and is T-dual to supersymmetric intersecting D6-brane constructions. The standard model sector contains magnetized D9-branes with negative D3-brane charge contribution. There are large classes of such models and we present explicit constructions for representative ones. In addition to models with one and two units of quantized flux, we also construct the first three- and four-family standard-like models with supersymmetric fluxes, i.e. comprising three units of quantized flux. Supergravity fluxes are due to the self-dual Neveu-Schwarz-Neveu-Schwarz and Ramond-Ramond three-form field strength and they fix the toroidal complex structure moduli and the dilaton. The supersymmetry conditions for the D-brane sector fix in some models all three toroidal K\"ahler moduli. We also provide examples where toroidal K\"ahler moduli are fixed by strong gauge dynamics on the ``hidden sector'' D7-brane. Most of the models possess Higgs doublet pairs with Yukawa couplings that can generate masses for quarks and leptons. The models have (mainly right-) chiral exotics.

The Baryonic Branch of Klebanov-Strassler Solution: a Supersymmetric Family of SU(3) Structure Backgrounds

We exhibit a one-parameter family of regular supersymmetric solutions of type IIB theory that interpolates between Klebanov-Strassler (KS) and Maldacena-Nunez (MN). The solution is obtained by applying the supersymmetry conditions for SU(3)-structure manifolds to an interpolating ansatz proposed by Papadopoulos and Tseytlin. Other than at the KS point, the family does not have a conformally-Ricci-flat metric, neither it has self-dual three-form flux. Nevertheless, the asymptotic IR and UV are that of KS troughout the family, except for the extremal value of the interpolating parameter where the UV solution drastically changes to MN. This one-parameter family of solutions is interpreted as the dual of the baryonic branch of gauge theory, confirming the expecation that the KS solution corresponds to a particular symmetric point in the branch.

M-theory compactification, fluxes, andAdS4

We analyze supersymmetric solutions of M-theory based an a seven-dimensional internal space with $\mathrm{S}\mathrm{U}(3)$ structure and a four-dimensional maximally symmetric space. The most general supersymmetry conditions are derived and we show that a nonvanishing cosmological constant requires the norms of the two internal spinors to differ. We find explicit local solutions with singlet flux and the space being a warped product of a circle, a nearly K\"ahler manifold and ${\mathrm{A}\mathrm{d}\mathrm{S}}_{4}$. The embedding of solutions into heterotic M-theory is also discussed.

Type IIA Killing spinors and calibrations

We consider the dimensional reduction of eleven dimensional supergravity to type IIA in ten dimensions, and study the conditions for supersymmetry in terms of p-form spinor bi-linears of the supersymmetry parameter. For a bosonic solution to be supersymmetric these p-forms must satisfy a set of differential relations, which we derive in full; the supersymmetry variations of the dilatino give a set of algebraic relations which are also derived. These results are then used to provide the generalized calibration conditions for some of the basic brane solutions, we also follow up a suggestion of Hackett-Jones and Smith and present a calibration condition for IIA supertubes. We find that a probe supertube satisfies this bound but does not saturate it, with the bound successfully accounting for the D0 charge of the supertube but not the string charge; we speculate that there should be a stronger calibration inequality than the one given.

Gaugino Condensation and Generation of Supersymmetric 3-Form Flux

We extend the linearised solution of Polchinski and Strassler describing the supergravity dual of the N=1* gauge theory. By analysing the equations of motion of type IIB supergravity at cubic order in the mass perturbation parameter, we demonstrate the emergence of a 3-form flux of type (3,0) with respect to the natural complex structure. The generation of this flux can be associated to the dynamical formation of a gaugino condensate in the confining phase of the N=1* gauge theory. We also check that the supersymmetry conditions are satisfied, and we discuss how this (3,0)-form flux is tied to the existence of a supersymmetric background with SU(2)-structure.

Superstring orientifolds with torsion: O5 orientifolds of torus fibrations and their massless spectra

AbstractUsing a “Superstrings with Torsion” type description, we study a class of IIB orientifolds in which spacefilling O5 planes and D5 branes wrap the T2 fiber in a warped modification of the product of 4D Minkowski space and a T2 fibration. For the case that the base is T4, we provide examples that preserve 4D 𝒩 = 1, 2, and 3 supersymmetry, both with internal RR flux, and with a combination of internal RR and NS flux. In these examples, the internal geometries admit integrable complex structure; however, the almost complex structure selected by the supersymmetry conditions is nonintegrable in the case that there is NS flux. We indicate explicitly the massless spectrum of gauge fields and moduli in each example. In a previous investigation, this class of orientifolds was studied using T‐duality. Here, we extend the previous analysis, first by providing an intrinsic description that does not rely on duality, and then by elaborating on details of the T‐duality map, which we use to check our results.

Supersymmetry and the AdS Higgs Phenomenon

We examine the AdS Higgs phenomenon for spin-1 fields, and demonstrate that graviphotons pick up a dynamically generated mass in AdS_4, once matter boundary conditions are relaxed. We perform an explicit one-loop calculation of the graviphoton mass, and compare this result with the mass generated for the graviton in AdS. In this manner, we obtain a condition for unbroken supersymmetry. With this condition, we examine both N=2 and N=4 gauged supergravities coupled to matter multiplets, and find that for both cases the ratio between dynamically generated graviton and graviphoton masses is consistent with unbroken supersymmetry.

M5-brane geometries, T-duality and fluxes

We describe a duality relation between configurations of M5-branes in M-theory and type IIB theory on Taub-NUT geometries with NSNS and RR 3-form field strength fluxes. The flux parameters are controlled by the angles between the M5-brane and the (T)duality directions. For one M5-brane, the duality leads to a family of supersymmetric flux configurations which interpolates between imaginary self-dual fluxes and fluxes similar to the Polchinski-Strassler kind. For multiple M5-branes, the IIB configurations are related to fluxes for twisted sector fields in orbifolds. The dual M5-brane picture also provides a geometric interpretation for several properties of flux configurations (like the supersymmetry conditions, their contribution to tadpoles, etc), and for many non-trivial effects in the IIB side. Among the latter, the dielectric effect for probe D3-branes is dual to the recombination of probe M5-branes with background ones; also, a picture of a decay channel for non-supersymmetric fluxes is suggested.

Dynamical and invariant supersymmetry in the fermion pairing problem

We argue that fermion-boson mapping techniques represent a natural tool for studying many-body supersymmetry in fermionic systems with pairing. In particular, using the generalized Dyson mapping of a many-level fermion superalgebra with the SU(2) type of pairing we investigate two kinds of supersymmetry connecting excitations in the systems with even and odd particle numbers: dynamical supersymmetry, which ensures a unified classification of states for both even and odd populations, and invariant supersymmetry with actual degeneracies of states within the same supermultiplet. Dynamical supersymmetries based on the dynamical algebra of the type U(K/2\Omega) (where K and 2\Omega denote the number of fermion-pair and single-fermion states, respectively) naturally arise in the bosonized description of the system. Conditions for invariant supersymmetry are determined in a restricted case of bilinear supercharge operators.

Supersymmetric intersecting D6-branes and fluxes in massive Type IIA string theory

We study N=1 supersymmetric four-dimensional solutions of massive Type IIA supergravity with intersecting D6-branes in the presence NS–NS three-form fluxes. We derive N=1 supersymmetry conditions for the D6-brane and flux configurations in an internal manifold X 6 and derive the intrinsic torsion (or SU(3)-structure) related to the fluxes. In the absence of fluxes, N=1 supersymmetry implies that D6-branes wrap supersymmetric three-cycles of X 6 that intersect at angles of SU(3) rotations and the geometry is deformed by SU(3)-structures. The presence of fluxes breaks the SU(3) structures to SU(2) and the D6-branes intersect at angles of SU(2) rotations; non-zero mass parameter corresponds to D8-branes which are orthogonal to the common cycle of all D6-branes. The anomaly inflow indicates that the gauge theory on intersecting (massive) D6-branes is not chiral.

Gstructures, fluxes, and calibrations in M theory

We study the most general supersymmetric warped M-theory backgrounds with a non-trivial G flux of the type ${R}^{1,2}\ifmmode\times\else\texttimes\fi{}{\mathrm{M}}_{8}$ and ${\mathrm{AdS}}_{3}\ifmmode\times\else\texttimes\fi{}{\mathrm{M}}_{8}.$ We give a set of necessary and sufficient conditions for preservation of supersymmetry which are phrased in terms of G structures and their intrinsic torsion. These equations may be interpreted as calibration conditions for a static ``dyonic'' M-brane, that is, an M5-brane with a self-dual three-form turned on. When the electric flux is turned off we obtain the supersymmetry conditions and non-linear PDEs describing M5-branes wrapped on associative and special Lagrangian three-cycles in manifolds with ${G}_{2}$ and $\mathrm{SU}(3)$ structures, respectively. As an illustration of our formalism, we recover the 1/2 BPS dyonic M-brane, and also construct some new examples.

BPS action and superpotential for heterotic string compactifications with fluxes

We consider N =1 compactifications to four dimensions of heterotic string theory in the presence of fluxes. We show that up to order O(\alpha'^2) the associated action can be written as a sum of squares of BPS-like quantities. In this way we prove that the equations of motion are solved by backgrounds which fulfill the supersymmetry conditions and the Bianchi identities. We also argue for the expression of the related superpotential and discuss the radial modulus stabilization for a class of examples.

Supergravity null scissors and super-crosses

In this paper we construct the supergravity solutions for the orthogonally intersecting null scissors and the fluxed D-strings. We name the latter as the super-crosses according to their shape. It turns out that the smeared solutions are U-dual related to the intersecting $(p,q)$-strings. Their open string properties are also studied. As a by-product, we clarify the supersymmetry conditions of D2-D2 pairs with most generic fluxes.

D3-branes in NS5-brane backgrounds

We study D3-branes in an NS5-branes background defined by an arbitrary 4d harmonic function. Using a gauge-invariant formulation of Born-Infeld dynamics as well as the supersymmetry condition, we find the general solution for the $\omega$-field. We propose an interpretation in terms of the Myers effect.

Non-Kähler string backgrounds and their five torsion classes

We discuss the mathematical properties of six-dimensional non-Kähler manifolds which occur in the context of N=1 supersymmetric heterotic and type IIA string compactifications with non-vanishing background H-field. The intrinsic torsion of the associated SU(3) structures falls into five different classes. For heterotic compactifications we present an explicit dictionary between the supersymmetry conditions and these five torsion classes. We show that the non-Ricci-flat Iwasawa manifold solves the supersymmetry conditions with non-zero H-field, so that it is a consistent heterotic supersymmetric groundstate.

Permeable conformal walls and holography

We study conformal field theories in two dimensions separated by domain walls, which preserve at least one Virasoro algebra. We develop tools to study such domain walls, extending and clarifying the concept of `folding' discussed in the condensed-matter literature. We analyze the conditions for unbroken supersymmetry, and discuss the holographic duals in AdS3 when they exist. One of the interesting observables is the Casimir energy between a wall and an anti-wall. When these separate free scalar field theories with different target-space radii, the Casimir energy is given by the dilogarithm function of the reflection probability. The walls with holographic duals in AdS3 separate two sigma models, whose target spaces are moduli spaces of Yang-Mills instantons on T4 or K3. In the supergravity limit, the Casimir energy is computable as classical energy of a brane that connects the walls through AdS3. We compare this result with expectations from the sigma-model point of view.

Inflationary scenarios from branes at angles

We describe a simple mechanism that can lead to inflation within string-based brane-world scenarios. The idea is to start from a supersymmetric configuration with two parallel static Dp-branes, and slightly break the supersymmetry conditions to produce a very flat potential for the field that parametrises the distance between the branes, i.e. the inflaton field. This breaking can be achieved in various ways: by slight relative rotations of the branes with small angles, by considering small relative velocities between the branes, etc. If the breaking parameter is sufficiently small, a large number of e-folds can be produced within the D-brane, for small changes of the configuration in the compactified directions. Such a process is local, i.e. it does not depend very strongly on the compactification space nor on the initial conditions. Moreover, the breaking induces a very small velocity and acceleration, which ensures very small slow-roll parameters and thus an almost scale invariant spectrum of metric fluctuations, responsible for the observed temperature anisotropies in the microwave background. Inflation ends as in hybrid inflation, triggered by the negative curvature of the string tachyon potential. In this paper we elaborate on one of the simplest examples: two almost parallel D4-branes in a flat compactified space.

Supersymmetry of identical bands in 171,172Yb supported by lifetime data

Abstract Precision lifetimes of six states in the ground-state bands of 171Yb have been measured using the recoil distance method following Coulomb excitation with a detector of the Euroball Cluster type at the FN-Tandem accelerator in Cologne. From these and previous data on branching and mixing ratios from Canberra, we found, that the transition quadrupole moments for corresponding E2 transitions in 171,172Yb are almost equal. This gives strong support for a weakly broken supersymmetry in 171,172Yb. On the other hand, the neighbor pair of nuclei 171Tm and 172Yb shows no supersymmetry demonstrating the importance of an even pseudoorbital angular momentum as condition for supersymmetry.

Branes at angles, torons, stability and supersymmetry

We elucidate some properties of the relation between two T-dual systems in tori, branes at angles and branes wrapping the whole torus carrying fluxes. We analyze different features of these systems: charges, low energy spectrum, tadpole cancellation, symmetry groups,…, and the correspondence between the two viewpoints. Particular attention is paid to supersymmetry and stability conditions. While on the branes at angles side stability and supersymmetry can be expressed as conditions on the angles between the two branes at the intersection, on the dual side supersymmetry has to do with a correction to Hermite Yang–Mills and a modified notion of stability should be considered.

1/4 BPS Solutions in Massive IIA Supergravity

We study four kinds of 1/4 BPS solutions in massive IIA supergravity corresponding to D8-D0-F1, D8-D2, D8-D4 and D8-D6-NS5 systems. We show that these solutions are reproduced without making nontrivial assumptions by using supersymmetry conditions. D8-D2 and D8-D4 solutions are represented by harmonic functions, as usual, while the other two are represented by solutions of non-linear differential equations. Because these four solutions can be treated in almost identical ways, we mainly focus on the D8-D6-NS5 systems. We first discuss D6-NS5 solutions with uniform mass parameters. then, we introduce D8-branes as domain walls by connecting two solutions with different values of the mass parameter. We also discuss boundary conditions and supersymmetry on domain walls.