We consider the Bekenstein-Hawking entropy-area formula in four dimensional extended ungauged supergravity and its electric-magnetic duality property. Symmetries of both "large" and "small" extremal black holes are considered, as well as the ADM mass formula for N=4 and N=8 supergravity, preserving different fraction of supersymmetry. The interplay between BPS conditions and duality properties is an important aspect of this investigation.
Strong/weak coupling duality in Chern-Simons supergravity is studied. It is argued that this duality can be regarded as an example of superduality. The use of supergroup techniques for the description of Chern-Simons supergravity greatly facilitates the analysis.
This Ph.D. thesis was submitted to the Catholic University of Leuven. We discuss two main topics: various formulations of duality-symmetric theories and D=5 supergravity (both construction and supersymmetric solutions). The thesis is structured as follows: Ch. 1 Introduction; Ch. 2 String theory toolkit; Ch. 3 Free duality-symmetric theories; Ch. 4 Interacting duality-symmetric theories; Ch. 5 Conformal supergravity in D=5: Weyl multiplets; Ch. 6 Conformal supergravity in D=5: matter and gauge-fixing; Ch. 7 Supersymmetric solutions in D=5 gauged supergravity.
Starting from the bosonic sector of the M-theory super-five-brane we obtain the action for duality-symmetric three-brane and construct the consistent coupling of the proposed action with the bosonic sector of type IIB supergravity.
We discuss toroidal compactifications of maximal supergravity coupled to an extended configuration of BPS states which transform consistently under the U-duality group. Under certain conditions this leads to theories that live in more than eleven spacetime dimensions, with maximal supersymmetry but only partial Lorentz invariance. We demonstrate certain features of this construction for the case of nine-dimensional N=2 supergravity.
For nonlinear models of an Abelian vector supermultiplet coupled to N = 2 supergravity in four dimensions, we formulate the self-duality equation which expresses invariance under U(1) duality rotations. In the flat space limit, this equation reduces to the N = 2 self-duality equation proposed in hep-th/0001068. We also give an example of a self-dual locally supersymmetric model containing a higher-derivative extension of the Born-Infeld action at the component level.
The standard eleven-dimensional supergravity action depends on a three-form gauge field and does not allow direct coupling to five-branes. Using previously developed methods, we construct a covariant eleven-dimensional supergravity action depending on a three-form and six-form gauge field in a duality-symmetric manner. This action is coupled to both the M-theory two-brane and five-brane, and corresponding equations of motion are obtained. Consistent coupling relates D=11 duality properties with self-duality properties of the M-5-brane. From this duality-symmetric formulation, one can derive an…
We perform explicitly the toroidal compactification of eleven dimensional supergravity to six dimensions and present its action in a manifestly $SO(5,5)\over SO(5)\times SO(5)$ invariant form using the recently proposed covariant formulation of theories involving chiral fields.
We will report on recent advances in the understanding of non-perturbative interconnections between different string dualities. Weak-strong coupling duality (S-duality) and T-duality (symmetry under compactification on dual tori) allows one to compare and explore the strong coupling regime of seemingly unrelated theories. These theories naturally merge in a quantum version of supergravity called M-theory. The dynamical role of `branes' of different nature and the new dynamical tool of (M)atrix formulation of M-theory will be briefly mentioned.
This thesis deals with the two duality symmetries of N=2 D=10 supergravity theories that are descendant from the full superstring theory: fermionic T-duality and U-duality. The fermionic T-duality transformation is applied to the D-brane and pp-wave solutions of type IIB supergravity. New supersymmetric solutions of complexified supergravity are generated. We show that the pp-wave yields a purely imaginary background after two dualities, undergoes a geometric transformation after four dualities, and is self-dual after eight dualities. Next we apply six bosonic and six fermionic T-dualities to …
We examine the known Riemann curvature corrections to the supergravity action at order $α'^3$ under the T-duality transformations. Using the compatibility of the action with the linear T-duality and with the S-matrix calculations as guiding principles, we have found the couplings of four $B$-field strengths and the couplings of two Riemann curvatures and two $B$-field strengths at order $α'^3$. Using the S-matrix calculations we have also found new dilaton couplings in the string frame at this order.
We study 2+1D toroidal compactifications of M-theory with twists in the U-duality group. These compactifications realize many symmetric-manifolds from the classification of 2+1D extended supergravity moduli-spaces. We then focus on the moduli-space $SU(2,1)/U(2)$ obtained by dimensional reduction of pure N=2 supergravity in 3+1D. This space is realized with an explicit example. Assuming that there are no quantum corrections, we conjecture that the classical discrete duality group has to be augmented with an extra strong/weak coupling duality. This implies the existence of new phases of the the…
It is shown in a quantum-mechanically exact manner that a supersymmetric and $κ$-symmetric D-string action in a general type IIB supergravity background is transformed to a form of the type IIB Green-Schwarz superstring action with the SL(2,Z) covariant tension through an S-duality transformation. This result precisely proves a conjecture mentioned previously that the SL(2,Z) S-duality of a super D-string action in a flat background is also valid even in a curved IIB background geometry. We point further out the validity of the more generalized conjecture that various duality relations of supe…
Chiral/self-dual restrictions of various super Yang-Mills and supergravity theories in (2,2) dimensions are described. These include the N=1 supergravity with a cosmological term and the N=1 new minimal supergravity theory. In the latter case, a self-duality condition on a torsionful Riemann curvature is possible, and it implies the equations of motion that follow from an $R^2$ type supergravity action.
We review the current status of the construction of unitary representations of U-duality groups of supergravity theories in five, four and three dimensions. We focus mainly on the maximal supergravity theories and on the N=2 Maxwell-Einstein supergravity (MESGT) theories defined by Jordan algebras of degree three in five dimensions and their descendants in four and three dimensions. Entropies of the extremal black hole solutions of these theories in five and four dimensions are given by certain invariants of their U-duality groups. The five dimensional U-duality groups admit extensions to spec…
In this review we show that a Clifford algebra possesses a unique irreducible representation; the spinor representation. We discuss what types of spinors can exist in Minkowski space-times and we explain how to construct all the supersymmetry algebras that contain a given space-time Lie algebra. After deriving the irreducible representations of the superymmetry algebras, we explain how to use them to systematically construct supergravity theories. We give the maximally supersymmetric supergravity theories in ten and eleven dimensions and discuss their properties. We find which superbranes can …
We show that supersymmetric and $κ$-symmetric Dp-brane actions in type II supergravity background have the same duality transformation properties as those in a flat Minkowskian background. Specially, it is shown that the super D-string transforms in a covariant way while the super D3-brane is self-dual under the $SL(2,Z)$ duality. Also, the D2-brane and the D4-brane transform in ways expected from the relation between type IIA superstring theory and M-theory. The present study proves that various duality symmetries, which were originally found in the flat background field, are precisely valid …
Fermionic T-duality transformation is studied for the N=1 supersymmetric solutions of massive type IIA supergravity with the metric AdS_{10-k} x M_k for k=3 and 5. We derive the Killing spinors of these backgrounds and use them as an input for the fermionic T-duality transformation. The resulting dual solutions form a large family of supersymmetric deformations of the original solutions by complex valued RR fluxes. We observe that the Romans mass parameter does not change under fermionic T-duaity, and prove its invariance in the k=3 case.
In this paper which is based on the results obtained in collaboration with Igor Bandos and Dmitri Sorokin I present the extention of the "doubled fields" formalism by Cremmer, Julia, Lu and Pope to the supersymmetric case and lifting this construction onto the level of the proper duality-symmetric action for D=11 supergravity. Further extension of the doubled field formulation to include dynamical sources is also discussed.
Drawing an analogy between gravity dynamical equation of motion and that of Maxwell electrodynamics with an electric source we outline a way of appearance of a dual to graviton field. We propose a dimensional reduction ansatz for the field strength of this field which reproduces the correct duality relations between fields arising in the dimensional reduction of D-dimensional gravity action to D-1 dimensions. Modifying the PST approach we construct a new term entering the action of D=11 duality-symmetric gravity and by use of the proposed ansatz we confirm the relevance of such a term to repro…
We construct the heterotic dual theory in four dimensions of eleven dimensional supergravity compactified on a particular Joyce manifold, $J$. In particular, $J$ is constructed from resolving fixed point singularities of orbifolds of the seven torus in such a way that one is forced to consider a generalised orbifold on the heterotic side. We conjecture that a heterotic dual exists for all the compact 7-manifolds of $G_{2}$ holonomy constructed by Joyce.
We examine duality transformations of supersymmetric and $κ$-symmetric Dp-brane actions in a general type II supergravity background where in particular the dilaton and the axion are supposed to not be zero or a constant but a general superfield. Due to non-constant dilaton and axion, we can explicitly show that the dilaton and the axion as well as the two 2-form gauge potentials transform as doublets under the $SL(2,R)$ transformation from the point of view of the world-volume field theory.
N=4 Poincare supergravity has a global SU(1,1) duality symmetry that acts manifestly only on shell as it involves duality rotations of vector fields. A U(1) subgroup of this symmetry is known to be anomalous at the quantum level in the presence of a non-trivial gravitational background. We first derive this anomaly from a novel perspective, by relating it to a similar anomaly in conformal supergravity where SU(1,1) acts off shell, using the fact that N=4 Poincare supergravity has a superconformal formulation. We explicitly construct the corresponding local and nonlocal anomalous terms in the o…
The role of duality symmetries in the construction of counterterms for maximal supergravity theories is discussed in a field-theoretic context from different points of view. These are: dimensional reduction, the question of whether appropriate superspace measures exist and information about non-linear invariants that can be gleaned from linearised ones. The former allows us to prove that F-term counterterms cannot be E7(7)-invariant in D=4, N=8 supergravity or E6(6)-invariant in D=5 maximal supergravity. This is confirmed by the two other methods which can also be applied to D=4 theories with …
We consider duality transformations in N=2, d=4 Yang--Mills theory coupled to N=2 supergravity. A symplectic and coordinate covariant framework is established, which allows one to discuss stringy `classical and quantum duality symmetries' (monodromies), incorporating T and S dualities. In particular, we shall be able to study theories (like N=2 heterotic strings) which are formulated in symplectic basis where a `holomorphic prepotential' F does not exist, and yet give general expressions for all relevant physical quantities. Duality transformations and symmetries for the N=1 matter coupled Yan…
Recently, it has been shown that the NS-NS corrections to the type II supergravity given by Gross and Sloan are invariant under the linear T-duality. In this paper, we study the invariance of this action under sequence of S-duality and linear T-duality to find the R-R corrections to the supergravity at order $α'^3$, up to field redefinition.
We present an alternative formulation of duality-symmetric eleven-dimensional supergravity with both three-form and six-form gauge fields. Instead of the recently-proposed scalar auxiliary field, we use a simpler lagrangian with a non-propagating auxiliary multiplier tensor field with eight-indices. We also complete the superspace formulation in a duality-symmetric manner. An alternative super M-5-brane action coupled to this eleven-dimensional background is also presented. This formulation bypasses the usual obstruction for an invariant lagrangian for a self-dual three-form field strength, by…
We present a formulation of $N=1,D=10$ Supergravity--Super--Maxwell theory in superspace in which the graviphoton can be described by a 2--form $B_2$ or a 6--form $B_6$, the photon by a 1--form $A_1$ or a 7--form $A_7$ and the dilaton by a scalar $φ$ or an 8--form $φ_8$, the supercurvatures of these fields being related by duality. Duality interchanges Bianchi identities and equations of motion for each of the three couples of fields. This construction envisages the reformulation of $D=10$ Supergravity, involving 7--forms as gauge fields, conjectured by Schwarz and Sen, which, upon toroidal co…
We study the effect of T-duality on supersymmetry in the context of type II supergravity. For both U(1) Abelian and SU(2) non-Abelian T-duality, we demonstrate that the supersymmetry variations after T-duality are related to the variations before T-duality through the Kosmann spinorial Lie derivative, which vanishes when the Killing spinors are independent of the T-duality directions. As a byproduct of our analysis, we present closed expressions for SU(2) T-duality in a class of spacetimes with diagonal Bianchi IX symmetry and comment on specific examples of T-dual geometries, including a nove…
The concept of self-dual supersymmetric nonlinear electrodynamics is generalized to a curved superspace of N = 1 supergravity, for both the old minimal and the new minimal versions of N = 1 supergravity. We derive the self-duality equation, which has to be satisfied by the action functional of any U(1) duality invariant model of a massless vector multiplet, and construct a family of self-dual nonlinear models. This family includes a curved superspace extension of the N = 1 super Born-Infeld action. The supercurrent and supertrace in such models are proved to be duality invariant. The most inte…
For a general class of SO(4) symmetric backgrounds in type II-supergravity, we show that the action of non-Abelian T-duality can be described via consistent truncation to seven dimensional theories with seemingly massive modes. As such, any solution to these theories uplifts to both massive type IIA and IIB supergravities presenting an invertible map between the two. For supersymmetric backgrounds, we show that for spinors transforming under SO(4) the non-Abelian T-duality transformation breaks the original supersymmetry by half. We use these mappings to generate the non-Abelian T-duals of the…
Field transformation rules of the standard fermionic T-duality require fermionic isometries to anticommute, which leads to complexification of the Killing spinors and results in complex valued dual backgrounds. We generalize the field transformations to the setting with non-anticommuting fermionic isometries and show that the resulting backgrounds are solutions of double field theory. Explicit examples of non-abelian fermionic T-dualities that produce real backgrounds are given. Some of our examples can be bosonic T-dualized into usual supergravity solutions, while the others are genuinely non…
We examine the NS-NS corrections to the type II supergravity given by Gross and Sloan, under the linear T-duality transformations. We show that the gravity and the B-field couplings are invariant under off-shell T-duality, whereas the dilaton couplings are invariant under on-shell T-duality. Requiring the compatibility of the dilaton couplings with off-shell T-duality as a guiding principle, we extend them to include the appropriate Ricci curvature and the divergence of the B-field strength.
Montonen and Olive's conjecture in 1977 that some theories possess a duality symmetry that interchanges the electrically charged particle with that of negatively charged t' Hooft-Polyakov monopoles which relates strong coupling to weak coupling. This will be nearly the same as Shapere et al, who showed that the equation of motion of the coupled Einstein-Maxwell-axion dilaton system, occurs in low energy in String theory, is invariant under electromagnetic duality transformation; that also interchanges the strong and weak coupling limit of the theory. These ideas have been persued in the $SO(6)…
The equations of motion (e.m.'s) of the N=1, D=10 anomaly free supergravity, obtained in the framework of the superspace approach, are analyzed. The formal equivalence of the usual and dual supergravities is discussed at the level of e.m.'s. The great simplicity of the dual formulation is established. The possibillity of the lagrangian formulation of the dual supergravity is pointed out. The bosonic part of the lagrangian is constructed including anomaly compensating superstring corrections.
We review the underlying algebraic structures of supergravity theories with symmetric scalar manifolds in five and four dimensions, orbits of their extremal black hole solutions and the spectrum generating extensions of their U-duality groups. For 5D, N=2 Maxwell-Einstein supergravity theories (MESGT) defined by Euclidean Jordan algebras, J, the spectrum generating symmetry groups are the conformal groups Conf(J) of J which are isomorphic to their U-duality groups in four dimensions. Similarly, the spectrum generating symmetry groups of 4D, N=2 MESGTs are the quasiconformal groups QConf(J) ass…
Candidate counterterms break E7 type U-duality symmetry of $N \geq 5$ supergravity theories in four dimensions \cite{Kallosh:2011dp}. A proposal was made in \cite{Bossard:2011ij} to restore it, starting with a double set of vector fields and argued that a supersymmetric extension of their proposal should exist. We show that the extra vectors, needed for the deformation, can not be auxiliary fields in an eventual off-shell formulation $N \geq 5$ supergravity, assuming that such a formulation exists. Furthermore we show that these extra vector fields can not be dynamical either since that change…
The dimensional reduction of the bosonic sector of five-dimensional minimal supergravity to a Lorentzian four-dimensional spacetime leads to a theory with a massless axion and a dilaton coupled to gravity and two U(1) gauge fields and the dimensionally reduced equations of motion have SL(2,R)/SO(2)-duality invariance. In our previous work, utilizing the duality invariance, we formulated solution-generation techniques within five-dimensional minimal supergravity. In this work, by choosing a timelike Killing vector, we consider dimensional reduction to a four-dimensional Euclidean space, in whic…
We present a unified treatment in superspace of the two dual formulations of $D=10$, $N=1$ {\it pure} supergravity based on a strictly super-geometrical framework: the only fundamental objects are the super Riemann curvature and torsion, and the related Bianchi identities are sufficient to set the theory on shell; there is no need to introduce, from the beginning, closed three- or seven-superforms. This formulation extends also to {\it non minimal} models. Moreover, in this framework the algebraic analogy between pure super Yang--Mills theories and pure supergravity in $D=10$ is manifest. As a…
The equations that follow from kappa symmetry of the type II Green-Schwarz string are a certain deformation, by a Killing vector field $K$, of the type II supergravity equations. We analyze under what conditions solutions of these `generalized' supergravity equations are trivial in the sense that they solve also the standard supergravity equations. We argue that for this to happen $K$ must be null and satisfy $dK=i_KH$ with $H=dB$ the NSNS three-form field strength. Non-trivial examples are provided by symmetric pp-wave solutions. We then analyze the consequences for non-abelian T-duality and …
In this note, we study a simplified variant of the familiar holographic duality between supergravity on AdS$_3\times S^3\times T^4$ and the SCFT (on the moduli space of) the symmetric orbifold theory $Sym^N(T^4)$ as $N \rightarrow \infty$. This variant arises conjecturally from a twist proposed by the first author and Si Li. We recover a number of results concerning protected subsectors of the original duality working directly in the twisted bulk theory. Moreover, we identify the symmetry algebra arising in the $N\rightarrow \infty$ limit of the twisted gravitational theory. We emphasize the r…
We study and utilize duality transformations in a particular STU-model of four dimensional gauged supergravity. This model is a truncation of the de Wit-Nicolai N=8 theory and as such has a lift to eleven-dimensional supergravity on the seven-sphere. Our duality group is $U(1)^3$ and while it can be applied to any solution of this theory, we consider the known asymptotically AdS$_4$, supersymmetric black holes and focus on duality transformations which preserve supersymmetry. For static black holes we generalize the supersymmetric solutions of Cacciatori and Klemm from three magnetic charges t…
We show that the string backgrounds AdS2 x S2 x T6 and AdSd x Sd x Sd x T{10 - 3d} (d = 2, 3) are self-dual under a series of bosonic and fermionic T-dualities. We do this using the fermionic Buscher rules derived by Berkovits and Maldacena, thus working at the level of the supergravity fields. This allows us to explicitly track the behaviour of the RR fields, from which we see that we need T-duality along some torus directions. For the AdS x S x S cases, which contain cosets of D(2,1;alpha), it is necessary to perform bosonic T-duality along some complexified Killing spinors in one of the sph…
A geometric treatment of T-duality as an operation which acts on differential forms in superspace allows us to derive the complete set of T-duality transformation rules which relate the superfield potentials of D=10 type IIA supergravity with those of type IIB supergravity including Ramond-Ramond superfield potentials and fermionic supervielbeins. We show that these rules are consistent with the superspace supergravity constraints.
We propose a twelve-dimensional supergravity action, which describes low energy dynamics of F-theory. Dimensional reduction leads the theory to eleven-dimensional, IIA, and IIB supergravities. Self-duality of the four-form field in IIB supergravity is understood. It is necessary to abandon twelve-dimensional Poincare symmetry by making one dimension compact, which is to be decompactified in some region of parameter space, such that the physical degrees of freedom are the same as those of eleven-dimensional supergravity. This makes T-duality explicit as a relation between different compactifica…
We quickly review the current status of gravitational duality in General Relativity. We summarize and comment some recent work on constructing dual (topological) charges and understanding how this duality acts in supergravity theories.
We establish a relation between time-like, light-like and space-like orbits of the non-compact E{7(7)}(R)symmetry and discrete E{7(7)}(Z) invariants. We discuss the U-duality invariant formula for the degeneracy of states d(Q) which in the approximation of large occupation numbers reproduces the Bekenstein-Hawking entropy formula for regular black holes with AdS_2 horizon. We explain why the states belonging to light-like orbits, corresponding to classical solutions of "light black holes with null singularity", decouple from the corresponding index. We also present a separate U-duality invaria…
The dimensional reduction of (the bosonic sector of) five-dimensional minimal supergravity to four dimensions leads to a theory with a massless axion and a dilaton coupled to gravity and two U(1) gauge fields (one of which has Chern-Simons coupling), whose field equations have SL(2,R)-invariance. Utilizing this SL(2,R)-duality, we provide a new formalism for solution generation. As an example, applying it to the Rasheed solution, which are known to describe dyonic rotating black holes (from the four-dimensional point of view) of five-dimensional pure gravity, we obtain rotating Kaluza-Klein bl…
The background underlying the $η$-deformed $AdS_5\times S^5$ sigma-model is known to satisfy a generalization of the IIB supergravity equations. Their solutions are related by T-duality to solutions of type IIA supergravity with non-isometric linear dilaton. We show how the generalized IIB supergravity equations can be naturally obtained from exceptional field theory. Within this manifestly duality covariant formulation of maximal supergravity, the generalized IIB supergravity equations emerge upon imposing on the fields a simple Scherk-Schwarz ansatz which respects the section constraint.
In this note, we construct explicit Type IIA uplifts of $D=5$ minimal gauged supergravity, by T-dualising known Type IIB uplifts on $N_5 = S^5$, $T^{1,1}$ and $Y^{p,q}$ along their $SU(2)$ isometries. When the $D=5$ gauge field is set to zero, our uplifts recover precisely the known non-Abelian T-duals of the $AdS_5\times N_5$ solutions. As an application, we obtain new supersymmetric $AdS_3\timesΣ\times M_5$ solutions in Type IIA, where $Σ= \mathbb{WCP}^1_{[n_-,n_+]}$ is a weighted projective space. Existing holographic results of T-dualised AdS solutions suggest that our solutions capture fe…
We present a manifestly Lorentz invariant and supersymmetric component field action for $D = 10$, type $IIB$ supergravity, using a newly developed method for the construction of actions with chiral bosons, which implies only a single scalar non propagating auxiliary field. With the same method we construct also an action in which the complex two-form gauge potential and its Hodge-dual, a complex six-form gauge potential, appear in a symmetric way in compatibility with supersymmetry and Lorentz invariance. The duals of the two physical scalars of the theory turn out to be described by a $SL(2,R…
We derive a duality-symmetric action for type IIA D=10 supergravity by the Kaluza-Klein dimensional reduction of the duality-symmetric action for D=11 supergravity with the 3-form and 6-form gauge field. We then double the bosonic fields arising as a result of the Kaluza-Klein dimensional reduction and add mass terms to embrace the Romans's version, so that in its final form the bosonic part of the action contains the dilaton, NS-NS and RR potentials of the standard type IIA supergravity as well as their duals, the corresponding duality relations are deduced directly from the action. We discus…
Black hole solutions of supergravity theories form families that realizing the deep nonlinear "duality" symmetries of these theories. They form orbits under the action of these symmetry groups, with extremal (i.e. BPS) solutions at the limits of such orbits. An important technique in the analysis of such solution families employs timelike dimensional reduction and exchanges the stationary black-hole problem for a nonlinear sigma-model problem. Families of extremal or BPS solutions are characterized by nilpotent orbits under the duality symmetries, based upon a tri-graded or penta-graded decomp…
It is known that for N=8 supergravity, the double-soft-scalar limit of a n-point amplitude is given by a sum of local SU(8) rotations acting on a (n-2)-point amplitude. For N<8 supergravity theories, complication arises due to the presence of a U(1) in the U(N) isotropy group, which introduces a soft-graviton singularity that obscures the action of the duality symmetry. In this paper, we introduce an anti-symmetrised extraction procedure that exposes the full duality group. We illustrate this procedure for tree-level amplitudes in 4<=N<8 supergravity in four dimensions, as well as N=16 supergr…
It is shown that the super Higgs mechanism that occurs in a wide class of models with vanishing cosmological constant (at the classical level) is obtained by the gauging of a flat group which must be an electric subgroup of the duality group. If the residual massive gravitinos which occur in the partial supersymmetry breaking are BPS saturated, then the flat group is non abelian. This is so for all the models obtained by a Scherk-Schwarz supersymmetry breaking mechanism. If gravitinos occur in long multiplets, then the flat groups may be abelian. This is the case of supersymmetry breaking by s…
We calculate the dimensions of operators in three and six dimensional superconformal field theories by using the duality between these theories at large N and D=11 supergravity on $AdS_{4/7} \times S^{7/4}$. We find that for the duality relations to work the Kaluza--Klein masses given in the supergravity literature must be rescaled and/or shifted.
We present a duality procedure that relates conventional four-dimensional matter-coupled N=1 supergravities to dual formulations in which auxiliary fields are replaced by field-strengths of gauge three-forms. The duality promotes specific coupling constants appearing in the superpotential to vacuum expectation values of the field-strengths. We then apply this general duality to type IIA string compactifications on Calabi-Yau orientifolds with RR fluxes. This gives a new supersymmetric formulation of the corresponding effective four-dimensional theories which includes gauge three-forms.
