We introduce an ansatz which allows us to solve the supersymmetry equations for warped N=1 AdS4 type II supergravity compactifications of general SU(3)xSU(3) structure. As a byproduct we obtain a set of necessary conditions which every supersymmetric AdS4 vacuum should obey. The case of AdS4 compactifications of IIB on manifolds of static SU(2) structure is examined in detail. Several examples of solutions are presented. In the limit of four-dimensional Minkowski space, we present examples of supersymmetric IIB warped compactifications with partially localized NS5- and D5-branes. We also present `massive' non-supersymmetric AdS4xM6 solutions of IIA, where M6 can be any six-dimensional Einstein-Kaehler manifold.
We give the full supersymmetric and kappa-symmetric actions for the Dirichlet p-branes, including their coupling to background superfields of ten-dimensional type IIA and IIB supergravity.
In this paper we will construct all BPS and non-BPS D-branes in Type IIA and Type IIB theories from tachyon condensation. We also propose form of Wess-Zumino term for non-BPS D-brane and we will show that tachyon condensation in this term leads to standard Wess-Zumino term for BPS D-brane.
We examine T-duality transformations for supersymmetric strings with target space geometry with compact abelian isometries. We consider the partition function of these models and we show that although T-duality is not a symmetry, due to an anomaly, it relates type IIA to type IIB strings. In this way we extend the corresponding result for toroidal compactification to the general case of non-trivial backgrounds with abelian isometries and for world sheets of any genera.
We discuss the T-duality between the solutions of type IIA versus IIB superstrings compactified on Calabi-Yau threefolds. Within the context of the N=2, D=4 supergravity effective Lagrangian, the T-duality transformation is equivalently described by the c-map, which relates the special Kahler moduli space of the IIA N=2 vector multiplets to the quaternionic moduli space of the N=2 hyper multiplets on the type IIB side (and vice versa). Hence the T-duality, or c-map respectively, transforms the IIA black hole solutions, originating from even dimensional IIA branes, of the special Kahler effecti…
We analyze the decomposition of recently constructed unfaithful spinor representations of K(E10) under its SO(9) x SO(9), and SO(9) x SO(2) subgroups, respectively, where K(E10) is the `maximal compact' subgroup of the hyperbolic Kac--Moody group E(10). We show that under these decompositions, respectively, one and the same K(E10) spinor gives rise to both the fermionic fields of IIA supergravity, and to the (chiral) fermionic fields of IIB supergravity. This result is thus the fermionic analogue of the decomposition of E(10) under its SO(9,9) and SL(9) x SL(2) subgroups, respectively, which y…
We consider the present absence of 31 out of 32 supersymmetric solutions in supergravity i.e., of solutions describing BPS preons. A recent result indicates that (bosonic) BPS preonic solutions do not exist in type IIB supergravity. We reconsider this analysis by using the G-frame method, extend it to the IIA supergravity case, and show that there are no (bosonic) preonic solutions for type IIA either. For the classical D=11 supergravity no conclusion can be drawn yet, although the negative IIA results permit establishing the conditions that preonic solutions would have to satisfy. For supergr…
We perform a careful investigation of which p-form fields can be introduced consistently with the supersymmetry algebra of IIA and/or IIB ten-dimensional supergravity. In particular the ten-forms, also known as "top-forms", require a careful analysis since in this case, as we will show, closure of the supersymmetry algebra at the linear level does not imply closure at the non-linear level. Consequently, some of the (IIA and IIB) ten-form potentials introduced in earlier work of some of us are discarded. At the same time we show that new ten-form potentials, consistent with the full non-linear …
Starting from the (q,p) 5-brane solution of type IIB string theory, we here construct the low energy configuration corresponding to (NS5,Dp)-brane bound states (for $0\leq p\leq 4$) using the T-duality map between type IIB and type IIA string theories. We use the SL(2,Z) symmetry on the type IIB bound state (NS5,D3) to construct (NS5,D5,D3) bound state. We then apply T-duality transformation again on this state to construct the bound states of the form (NS5,D(p+2),Dp) (for $0\leq p\leq 2$) of both type IIB and type IIA string theories. We give the tension formula for these states and show that…
We show that the commonly considered half BPS solutions of eleven dimensional supergravity and the ten dimensional type II theories, when expressed in terms of $E_{11}$ group elements, take the universal form $\exp(-{1\over 2}ln N β\cdot H)\exp((1-N)E_β)$. Using this formula we find new potential solutions to the $E_{11}$ non-linearly realisations corresponding to active fields which are beyond those in the supergravity approximations. These include the space filling nine brane of the IIB theory. We use $E_{11}$ to give a correspondence between the fields of the eleven dimensional and the IIA …
We present a new Type IIB supergravity background of the warped form AdS$_4\times \mathcal{M}_6$ with dilaton, $B$-field and all Ramond-Ramond fluxes turned on. We obtain the solution by applying non-Abelian T-duality to a certain representative of a class of AdS$_4$ backgrounds in massive IIA supergravity. By explicitly constructing the Killing spinor of the seed solution and using an argument involving Kosmann spinorial Lie derivative we demonstrate that the background is supersymmetric.
We analyse different N=4 supergravities coupled to six vector multiplets corresponding to low-energy descriptions of the bulk sector of T6/Z2 orientifolds with p-brane in IIB (p odd) and in IIA (p even) superstrings. When fluxes are turned on, a gauging emerges corresponding to some non-semisimple Lie algebra related to nilpotent algebras N_p inside so(6,6), with dimension 15 + (p-3)(9-p). The non-metric axions have Stueckelberg couplings that induce a spontaneous breaking of gauge symmetries. In four cases the gauge algebra is non-abelian with a non-commutative structure of the compactificati…
The gauge transformations of p-form fields in supergravity theories acquire a non-commuting character when one introduces potentials both for the theory's original field strengths and for their duals. This has previously been shown in the ``doubled'' formalism for maximal supergravities, where a generalised duality relation between original and dual field strengths replaces the equations of motion. In the doubled formalism, the gauge transformations generate a superalgebra, and the corresponding symmetries have accordingly been called ``superdualities.'' The corresponding Noether charges form …
We show that the M-theory/IIA and IIA/IIB superstring dualities together with the diffeomorphism invariance of the underlying theories require the presence of certain p-brane bound states in IIA and IIB superstring theories preserving 1/2 of the spacetime supersymmetry. We then confirm the existence of IIA and IIB supergravity solutions having the appropriate p-brane bound states interpretation.
We summarize and extend our work on flux vacua attractors in generalized compactifications. After reviewing the attractor equations for the heterotic string on SU(3) structure manifolds, we study attractors for N=1 vacua in type IIA/B on SU(3)xSU(3) structure spaces. In the case of vanishing RR flux, we find attractor equations that encode Minkowski vacua only (and which correct a previous normalization error). In addition to our previous considerations, here we also discuss the case of nonzero RR flux and the possibility of attractors for AdS vacua.
We study some applications of solvable Lie algebras in type IIA, type IIB and M theories. RR and NS generators find a natural geometric interpretation in this framework. Special emphasis is given to the counting of the abelian nilpotent ideals (translational symmetries of the scalar manifolds) in arbitrary D dimensions. These are seen to be related, using Dynkin diagram techniques, to one-form counting in D+1 dimensions. A recipy for gauging isometries in this framework is also presented. In particular, we list the gauge groups both for compact and translational isometries. The former agree wi…
We discuss the four-dimensional N=1 effective actions of single space-time filling Dp-branes in general Type IIA and Type IIB Calabi-Yau orientifold compactifications. The effective actions depend on an infinite number of normal deformations and gauge connection modes. For D6-branes the N=1 Kaehler potential, the gauge-coupling function, the superpotential and the D-terms are determined as functions of these fields. They can be expressed as integrals over chains which end on the D-brane cycle and a reference cycle. The infinite deformation space will reduce to a finite-dimensional moduli space…
We use exceptional field theory to establish a duality between certain consistent 7-dimensional truncations with maximal SUSY from IIA to IIB. We use this technique to obtain new consistent truncations of IIB on $S^3$ and $H^{p,q}$ and work out the explicit reduction formulas in the internal sector. We also present uplifts for other gaugings of 7-d maximal SUGRA, including theories with a trombone gauging. Some of the latter can only be obtained by a non-geometric compactification.
We present a matrix model which interpolates between type IIA and type IIB NS five-branes. The matrix description involves a three-dimensional bulk quantum field theory interacting with impurities localized in one spatial direction. We obtain a dual matrix formulation for the exotic six-dimensional theory on coincident type IIB NS five-branes by studying the T-dual description in terms of Kaluza-Klein monopoles in type IIA string theory. After decoupling the bulk physics, the matrix description reduces to the conformal field theory of the Coulomb branch for the type IIA matrix string propagati…
Using U-duality transformations we map perturbative Type IIA string theory compactified on a class of Joyce 7-manifolds to a D-strings on D-manifold description in Type IIB theory. For perturbative Type IIB theory on the same class of Joyce manifolds we use duality transformations to map to an M-theory, M-manifold description, which is an orientifold with fivebrane twisted sectors. D and M-manifold descriptions of discrete torsion are found. For the same class of compactifications we show that Type IIA/IIB theory on a Joyce orbifold without (with) discrete torsion is T-dual to Type IIB/IIA the…
To the full order in fermions, we construct D=10 type II supersymmetric double field theory. We spell the precise N=2 supersymmetry transformation rules as for 32 supercharges. The constructed action unifies type IIA and IIB supergravities in a manifestly covariant manner with respect to O(10,10) T-duality and a pair of local Lorentz groups, or Spin(1,9) \times Spin(9,1), besides the usual general covariance of supergravities or the generalized diffeomorphism. While the theory is unique, the solutions are twofold. Type IIA and IIB supergravities are identified as two different types of solutio…
We consider four-dimensional N=1 field theories realized by type IIA brane configurations of NS-branes and D4-branes, in the presence of orientifold six-planes and D6-branes. These configurations are known to present interesting effects associated to the appearance of chiral symmetries and chiral matter in the four-dimensional field theory. We center on models with one compact direction (elliptic models) and show that, under T-duality, the configurations are mapped to a set of type IIB D3-branes probing N=1 orientifolds of C^2/Z_N singularities. We explicitly construct these orientifolds, and …
The matrix model formulation of M-theory can be generalized by compactification to ten-dimensional type II string theory, formulated in the infinite momentum frame. Both the type IIA and IIB string theories can be formulated in this way. In the M-theory and type IIA cases, the transverse rotational invariance is manifest, but in the IIB case, one of the transverse dimensions materializes in a completely different way from the other seven. The full O(8) rotational symmetry then follows in a surprising way from the electric-magnetic duality of supersymmetric Yang-Mills field theory.
The usual T-duality that relates the type IIA and IIB theories compactified on circles of inversely-related radii does not operate if the dimensional reduction is performed on the time direction rather than a spatial one. This observation led to the recent proposal that there might exist two further ten-dimensional theories, namely type IIA^* and type IIB^*, related to type IIB and type IIA respectively by a timelike dimensional reduction. In this paper we explore such dimensional reductions in cases where time is the coordinate of a non-trivial U(1) fibre bundle. We focus in particular on sit…
In this paper we study aspects of geometries in Type IIA and Type IIB String theory and elaborate on their field theory dual pairs. The backgrounds are associated with reductions to Type IIA of solutions with $G_2$ holonomy in eleven dimensions. We classify these backgrounds according to their G-structure, perform a non-Abelian T-duality on them and find new Type IIB configurations presenting {\it dynamical} $SU(2)$-structure. We study some aspects of the associated field theories defined by these new backgrounds. Various technical details are clearly spelled out.
Building on our recent results on dynamic SU(3)xSU(3) structures we present a set of sufficient conditions for supersymmetric AdS4xM6 backgrounds of type IIA/IIB supergravity. These conditions ensure that the background solves, besides the supersymmetry equations, all the equations of motion of type II supergravity. The conditions state that the internal manifold is locally a codimension-one foliation such that the five dimensional leaves admit a Sasaki-Einstein structure. In type IIA the supersymmetry is N=2, and the total six-dimensional internal space is locally an S^2 bundle over a four-di…
0-brane of type IIA string theory can be interpreted as a dimensional reduction of a gravitational wave in 11 dimensions. We observe that a similar interpretation applies also to the D-instanton background of type IIB theory: it can be viewed as a reduction (along one spatial and one time-like direction) of a wave in a 12-dimensional theory. The instanton charge is thus related to a linear momentum in 12 dimensions. This suggests that the instanton should play as important role in type IIB theory as the 0-brane is supposed to play in type IIA theory.
We address the implementation of non-Abelian Wilson lines in D=4 N=1 Type IIB orientifold constructions. We present an explicit three-family example with the gauge group (U(4)xU(2)xSU(2)xSU(2))^2x(U(6)xSp(4))^2 and give the particle spectrum and the trilinear superpotential. Emphasizing the new subtleties associated with the introduction of non-Abelian Wilson lines, we show that the Abelian gauge anomalies are cancelled by the Green-Schwarz-type mechanism, and calculate the Fayet-Iliopoulos terms and gauge coupling corrections. The analysis thus sets a stage for further investigations of the p…
We study the N=1 supersymmetric cascading gauge theory found in type IIB string theory on p regular and M fractional D3-branes at the tip of the conifold, using the T-dual type IIA description. We reproduce the supersymmetric vacuum structure of this theory, and show that the IIA analog of the non-supersymmetric state found by Kachru, Pearson and Verlinde in the IIB description is metastable in string theory, but the barrier for tunneling to the supersymmetric vacuum goes to infinity in the field theory limit. We also comment on the N=2 supersymmetric gauge theory corresponding to regular and …
We consider Type II string theories on ${\bf T^n}/{{\bf Z_2}^m}$ Joyce orbifolds. This class contains orbifolds which can be desingularised to give manifolds of $G_2$ $({\bf n}$$=$$7)$ and $Spin(7)$ holonomy $({\bf n}$$=$$8)$. In the $G_2$ holonomy case we present two types of $T$-duality transformation which are clearly generalisations of the $T$-duality/mirror transformation in Calabi-Yau spaces. The first maps Type IIA theory on one such space from this class to Type IIB theory on another such space. The second maps Type IIA (IIB) to Type IIA (IIB). In the case of $Spin(7)$ holonomy we pres…
We present a geometric formulation of type-IIA and -IIB superstring theories in which the Wess-Zumino term is second order in the supersymmetric currents. The currents are constructed using supergroup manifolds corresponding to superalgebras: the IIA superalgebra derived from M-algebra and the IIB superalgebra obtained by a T-duality transformation of the IIA superalgebra. We find that a slight modification of the IIB superalgebra is needed to describe D-string theories, in which the U(1) gauge field on the worldsheet is explicitly constructed in terms of D-string charges. A unification of the…
We re-examine the classification of supersymmetric extended objects in the light of the recently discovered Type II p-branes, previously thought not to exist for p> 1. We find new points on the brane-scan only in D = 10 and then only for p = 3(Type IIB), p = 4 (Type IIA), p = 5 (Type IIA and IIB) and p = 6 (Type IIA). The case D = 10, p = 2 (Type IIA) also exists but is equivalent to the previously classified D = 11 supermembrane.
It has not been clarified whether a matrix model can describe various vacua of string theory. In this paper, we show that the IIB matrix model includes type IIA string theory. In the naive large N limit of the IIB matrix model, configurations consisting of simultaneously diagonalizable matrices form a moduli space, although the unique vacuum would be determined by complicated dynamics. This moduli space should correspond to a part of perturbatively stable vacua of string theory. Actually, one point on the moduli space represents type IIA string theory. Instead of integrating over the moduli sp…
We show that the branes of ten-dimensional IIA/IIB string theory must satisfy, upon toroidal compactification, specific wrapping rules in order to reproduce the number of supersymmetric branes that follows from a supergravity analysis. The realization of these wrapping rules suggests that IIA/IIB string theory contains a whole class of generalized Kaluza-Klein monopoles.
We explore the entire form of S-Matrix elements of a potential $C_{n-1}$ Ramond-Ramond (RR) form field, a tachyon and two transverse scalar fields on both world volume and transverse directions of type IIB and IIA superstring theories. Apart from $<V_{C^{-2}}V_{ϕ^{0}}V_{ϕ^{0}}V_{T ^{0}}>$ the other scattering amplitude, namely $<V_{C^{-1}}V_{ϕ^{-1}}V_{ϕ^{0}}V_{T ^{0}}>$ is also revealed. We then start to compare all singularity structures of symmetric and asymmetric analysis, generating all infinite singularity structures as well as all order $α'$ contact interactions on the whole directions. …
The connection between IIA superstring theory compactified on a circle of radius R and IIB theory compactified on a circle of radius 1/R is reexamined from the perspective of N=2, D=9 space-time supersymmetry. We argue that the consistency of IIA/B duality requires the BPS states corresponding to momentum and winding of either of the type-II superstrings to transform as inequivalent supermultiplets. We show that this is indeed the case for any finite compactification radius, thus providing a nontrivial confirmation of IIA/B duality. From the point of view of N=2, D=9 supergravity, one is natur…
We review the actions of the supergravity theory in eleven dimensions as well as the type IIA and IIB supergravities in ten dimensions and derive the bosonic equations of motion in a coordinate-free notation. We also consider the existence of supersymmetries and the associated generalized Killing spinor equations. The aim of this note is to serve as a formulary and make the equations of supergravity more easily accessible to mathematicians.
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 $α'$ corrections. The closed form of S-matrices of two closed string RR in both IIB, IIA, including their all order $α'$ corrections have also been addressed. Our results confirm that, not only the structures…
5-branes of nontrivial topology are associated in the Diaconescu-Hanany-Witten-Witten (DHWW) approach with the Seiberg-Witten (SW) theory of low-energy effective actions. There are two different "pictures", related to the IIA and IIB phases of M-theory. They differ by the choice of $6d$ theory on the 5-brane world volume. In the IIB picture it is just the 6d SUSY Yang-Mills, while in the IIA picture it is a theory of SUSY self-dual 2-form. These two pictures appear capable to describe the (non-abelian) Lax operator and (abelian) low-energy effective action respectively. Thus IIB-IIA duality is…
We construct an N=1 superconformal field theory using branes of type IIA string theory. The IIA construction is related via T-duality to a IIB configuration with 3-branes in a background generated by two intersecting O7-planes and 7-branes. The IIB background can be viewed as a local piece of an F-theory compactification previously studied by Sen in connection with the Gimon-Polchinski orientifold. We discuss the deformations of the IIA and IIB constructions and describe a new supersymmetric configuration with curving D6-branes. Starting from the IIB description we find the supergravity dual o…
We investigate whether 4-dimensional static and cosmological Lifshitz solutions can be found from deforming the existing (A)dS_4 compactifications in IIA and IIA* supergravity. Using a well motivated compactification Ansatz on SU(3)-structure manifolds with 19 undetermined parameters we demonstrate that this is not the case in ordinary IIA supergravity, thereby generalising previous nogo results in different ways. On the other hand, for IIA* we construct explicit cosmological Lifshitz solutions. We also consider solutions with non-constant scalars and are able to find simple static and cosmolo…
We examine the T-duality relation between 1+1 NCOS and the DLCQ limit of type IIA string theory. We show that, as long as there is a compact dimension, one can meaningfully define an `NCOS' limit of IIB/A string theory even in the absence of D-branes (and even if there is no B-field). This yields a theory of closed strings with strictly positive winding, which is T-dual to DLCQ IIA/B without any D-branes. We call this the Type IIB/A Wound String Theory. The existence of decoupled sectors can be seen directly from the energy spectrum, and mirrors that of the DLCQ theory. It becomes clear then t…
We conduct an exhaustive search for solutions of IIA and IIB supergravity with augmented supersymmetry. We find a two-parameter family of IIB solutions preserving 28 supercharges, as well as several other IIA and IIB families of solutions with 24 supercharges. Given the simplicity of the pp-wave solution, the algorithm described here represents a systematic way of classifying all such solutions with augmented supersymmetry. By T-dualizing some of these solutions we obtain exact non-pp wave supergravity solutions (with 8 or 16 supercharges), which can be interpreted as perturbations of the AdS-…
We compute Yukawa couplings in type IIB string theory compactified on a non factorisable six-torus in the presence of D9 branes and fluxes. The setting studied in detail, is obtained by T-dualising an intersecting brane configuration of type IIA theory compactified on a torus generated by the SO(12) root lattice. Particular deformations of such torus are taken into account and provide moduli dependent couplings. Agreement with the type IIA result is found in a non trivial way. The classical type IIB calculation gives also information on a factor accessible only by quantum computations on the t…
In this paper we discuss the construction of non-geometric Q- and R-branes as sources of non-geometric Q- and R-fluxes in string compactifications. The non-geometric Q-branes, being obtained via T-duality from the NS 5-brane or respectively from the KK-monopole, are still local solutions of the standard NS action, where however the background fields G and B possess non-geometric global monodromy properties. We show that using double field theory, redefined background fields tilde G and beta as well as their corresponding effective action, the Q-branes are locally and globally well behaved solu…
We study the 2d N = 4 gauge theory descriptions of little strings on type II NS5- branes. The IIB strings on N NS5-branes are described by the N = (4,4) gauge theories, whose Higgs branch CFTs on U(N) instanton moduli spaces are relevant. The IIA strings are described by N = (4,4) circular A_{N-1} quiver theories, whose Coulomb branch CFTs are relevant. We study new N = (0,4) quiver gauge theories for the IIA strings, which make it easier to study some infrared observables. In particular, we show that the elliptic genera of the IIA / IIB strings precisely map to each other by T-duality.
We compute the non-abelian couplings in the Chern-Simons action for a set of coinciding fundamental strings in both the type IIA and type IIB Matrix string theories. Starting from Matrix theory in a weakly curved background, we construct the linear couplings of closed string fields to type IIA Matrix strings. Further dualities give a type IIB Matrix string theory and a type IIA theory of Matrix strings with winding.
We study the flux parameter spaces for semi-realistic supersymmetric Pati-Salam models in the AdS vacua on Type IIA orientifold and realistic supersymmetric Pati-Salam models in the Minkowski vacua on Type IIB orientifold. Because the fluxes can be very large, we show explicitly that there indeed exists a huge number of semi-realistic Type IIA and realistic Type IIB flux models. In the Type IIA flux models, in the very large flux limit, the theory can become weakly coupled and the AdS vacua can approach to the Minkowski vacua. In a series of realistic Type IIB flux models, at the string scale,…
Employing uplift formulae, we uplift supersymmetric $AdS_6$ black holes from $F(4)$ gauged supergravity to massive type IIA and type IIB supergravity. In massive type IIA supergravity, we obtain supersymmetric $AdS_6$ black holes asymptotic to the Brandhuber-Oz solution. In type IIB supergravity, we obtain supersymmetric $AdS_6$ black holes asymptotic to the non-Abelian T-dual of the Brandhuber-Oz solution. For the uplifted black hole solutions, we calculate the holographic entanglement entropy. In massive type IIA supergravity, it precisely matches the Bekenstein-Hawking entropy of the black …
We describe brane configurations that interpolate between the N=6 AdS4xCP3 background of Type IIA supergravity and the N=0 AdS4xCP3 background of massive Type IIA supergravity. Using the T-dual Type IIB configurations we prove that this leads to unequal Chern-Simons levels in the dual gauge theory, and find the precise relation between the parameters of the gauge theory and the RR fluxes of the background. This provides further evidence for the conjecture of Gaiotto and Tomasiello about the CFT dual of the massive Type IIA background.
The four-dimensional N=1 supergravity theories arising in compactifications of type IIA and type IIB on generalized orientifold backgrounds with background fluxes are discussed. The Kahler potentials are derived for reductions on SU(3) structure orientifolds and shown to consist of the logarithm of the two Hitchin functionals. These are functions of even and odd forms parameterizing the geometry of the internal manifold, the B-field and the dilaton. The superpotentials induced by background fluxes and the non-Calabi-Yau geometry are determined by a reduction of the type IIA and type IIB fermio…
In this paper, we are looking for $\mathcal{N}=1$, AdS$_4$ sourceless vacua in type IIB. While several examples exist in type IIA , there exists only one example of such vacua in type IIB . Thanks to the framework of generalized geometry we were able to devise a semi-algorithmical method to look for sourceless vacua. We present this method, which can easily be generalized to more complex cases, and give two new vacua in type IIB.
We consider near horizon geometries of extremal black holes in six-dimensional type IIB supergravity. In particular, we use the entropy function formalism to compute the charges and thermodynamic entropy of these solutions. We also comment on the role of attractor mechanism in understanding the entropy of the Hopf T-dual solutions in type IIA supergravity.
The explicit form of the fermionic zero-modes in the fivebrane backgrounds of type IIA and IIB supergravity theories is investigated. In type IIA fivebrane background there are four zero-modes of gravitinos and dilatinos. In type IIB fivebrane background four zero-modes of dilatinos and no zero-modes of gravitinos are found. These zero-modes indicate the four-fermion condensates which have been suggested in a calculation of the tension of the D-brane in fivebrane backgrounds.
We generalize the recent proposal that invariance under T-duality leads to additional non-geometric fluxes required so that superpotentials in type IIA and type IIB orientifolds match. We show that invariance under type IIB S-duality requires the introduction of a new set of fluxes leading to further superpotential terms. We find new classes of N=1 supersymmetric Minkowski vacua based on type IIB toroidal orientifolds in which not only dilaton and complex moduli but also Kahler moduli are fixed. The chains of dualities relating type II orientifolds to heterotic and M-theory compactifications s…
