Consistent embeddings are found of the minimal $\mathcal{N} = 2$ and $\mathcal{N} = 3$ gauged supergravities in four dimensions into its maximally supersymmetric, $\mathcal{N} = 8$, counterpart with a dyonic ISO(7) gauging. These minimal truncations retain the metric along with relevant U(1) and SO(3) R-symmetry gauge fields selected from the ISO(7) ones. The remaining ISO(7) gauge fields are turned off, with subtleties introduced by the dyonic gauging, and the scalars are fixed to their expectation values at the $\mathcal{N} = 2$ and $\mathcal{N} = 3$ vacua of the $\mathcal{N} = 8$ theory. Using the truncation formulae for massive type IIA supergravity on the six-sphere to $D=4$ $\mathcal{N} = 8$ ISO(7) supergravity, the minimal $D=4$ $\mathcal{N} = 2$ and $\mathcal{N} = 3$ gauged supergravities are then uplifted consistently to ten dimensions.
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.
Massive type IIA supergravity is shown to admit a consistent truncation on the six-sphere to maximal supergravity in four dimensions with a dyonic ISO(7) gauging. We obtain the complete, non-linear embedding of all the $D=4$ fields into the IIA metric and form potentials, and show its consistency. We first rewrite the IIA theory in an $\textrm{SO}(1,3) \times \textrm{SL}(7)$--covariant way. Then, we employ an ${\cal N}=8$ SL(7)--covariant restriction of the $D=4$ tensor hierarchy in order to find the full embedding. The redundant $D=4$ degrees of freedom introduced by the tensor hierarchy can …
We show how to construct supersymmetric warped AdS$_7$ vacua of massive IIA and AdS$_6$ vacua of IIB supergravity, using "half-maximal structures" of exceptional field theory. We use this formalism to obtain the minimal consistent truncations around these AdS vacua.
Using exceptional field theory we construct supersymmetric warped AdS$_7$ vacua of massive IIA and AdS$_6$ vacua of IIB, as well as their consistent truncations including vector multiplets. We show there are no consistent truncations of massive IIA supergravity around its supersymmetric AdS$_7$ vacua with vector multiplets when the Roman's mass is non-vanishing. For AdS$_6$ vacua of IIB supergravity, we find that in addition to the consistent truncation to pure $\mathrm{F}(4)$ gauged SUGRA, the only other half-maximal truncations that are consistent result in $\mathrm{F}(4)$ gauged SUGRA coupl…
Recently, AdS_7 solutions of IIA supergravity have been classified; there are infinitely many of them, whose expression is known analytically, and with internal space of S^3 topology. Their field theory duals are six-dimensional (1,0) SCFT's. In this paper we show that for each of these AdS_7 solutions there exists a consistent truncation from massive IIA supergravity to minimal gauged supergravity in seven dimensions. This theory has an SU(2) gauge group, and a single scalar, whose value is related to a certain distortion of the internal S^3. This explains the universality observed in recent …
Explicit formulae are given for the consistent truncation of massive type IIA supergravity on the six-sphere to the SU(3)--invariant sector of $D=4$ ${\cal N}=8$ supergravity with dyonic ISO(7) gauging. These formulae are then used to construct AdS$_4$ solutions of massive type IIA via uplift on $S^6$ of the critical points of the $D=4$ supergravity with at least SU(3) symmetry. We find a new ${\cal N}=1$ solution with SU(3) symmetry, a new non-supersymmetric solution with SO(6) symmetry, and recover previously known solutions. We quantise the fluxes, calculate the gravitational free energies …
We show how to construct consistent truncations of 10-/11-dimensional supergravity to 3-dimensional gauged supergravity, preserving various amounts of supersymmetry. We show, that as in higher dimensions, consistent truncations can be defined in terms of generalised $G$-structures in Exceptional Field Theory, with $G \subset E_{8(8)}$ for the 3-dimensional case. Differently from higher dimensions, the generalised Lie derivative of $E_{8(8)}$ Exceptional Field Theory requires a set of "covariantly constrained" fields to be well-defined, and we show how these can be constructed from the $G$-stru…
We complete and extend the analysis of arXiv:1903.10504 in several directions: we put the 4d theory, arising from the IIA consistent truncation of the universal sector of Calabi-Yau compactification, in a form manifestly consistent with 4d $\mathcal{N}=2$ supergravity. We go beyond the universal sector and construct the 4d effective action of IIA compactified on Calabi-Yau's with $h^{1,1}=1$, $h^{2,1}\geq1$, in the presence of background flux and fermionic condensates. For ALE gravitational instantons, we show that the putative quartic gravitino condensate is non-negative, as required for the …
In this talk we investigate the symmetry under E10 of Romans' massive type IIA supergravity. We show that the dynamics of a spinning particle in a non-linear sigma model on the coset space E10/K(E10) reproduces the bosonic and fermionic dynamics of massive IIA supergravity, in the standard truncation. In particular, we identify Romans' mass with a generator of E10 that is beyond the realm of the generators of E10 considered in the eleven-dimensional analysis, but using the same, underformed sigma model. As a consequence, this work provides a dynamical unification of the massless and massive ve…
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 construct multiple embeddings of all solutions of $d=5$ minimal (un)gauged supergravity into massive Type IIA supergravity. The internal spaces and warpings of such embeddings are the same as those of the $\mathcal{N}=1$ supersymmetric (Mink$_5$) AdS$_5$ vacua, with the slight modification that the U(1) R-symmetry direction becomes fibered over the external space by the $d=5$ gauge field. In addition the fluxes are appropriately modified. There are many distinct types of the aforementioned internal spaces and as such many different embeddings of the $d=5$ supergravity. As examples of our se…
We derive the Bekenstein-Hawking entropy for a class of BPS black holes in the massive type IIA supergravity background AdS$_4 \times S^6$ from a microscopic counting of supersymmetric ground states in a holographically dual field theory. The counting is performed by evaluating the topologically twisted index of three-dimensional $\mathcal{N}=2$ Chern-Simons-matter gauge theories in the large $N$ limit. The $\mathcal{I}$-extremization principle is shown to match the attractor mechanism for the near-horizon geometries constructed in the four-dimensional dyonic $\mathcal{N}=2$ gauged supergravit…
We study compactifications of type IIA supergravity on cosets exhibiting SU(3) structure. We establish the consistency of the truncation based on left-invariance, providing a justification for the choice of expansion forms which yields gauged N=2 supergravity in 4 dimensions. We explore N=1 solutions of these theories, emphasizing the requirements of flux quantization, as well as their non-supersymmetric companions. In particular, we obtain a no-go result for de Sitter solutions at string tree level, and, exploiting the enhanced leverage of the N=2 setup, provide a preliminary analysis of the …
We develop an exceptional generalised geometry formalism for massive type IIA supergravity. In particular, we construct a deformation of the generalised Lie derivative, which generates the type IIA gauge transformations as modified by the Romans mass. We apply this new framework to consistent Kaluza-Klein reductions preserving maximal supersymmetry. We find a generalised parallelisation of the exceptional tangent bundle on S^6, and from this reproduce the consistent truncation ansatz and embedding tensor leading to dyonically gauged ISO(7) supergravity in four dimensions. We also discuss close…
In this paper we investigate in detail the correspondence between E10 and Romans' massive deformation of type IIA supergravity. We analyse the dynamics of a non-linear sigma model for a spinning particle on the coset space E10/K(E10) and show that it reproduces the dynamics of the bosonic as well as the fermionic sector of the massive IIA theory, within the standard truncation. The mass deformation parameter corresponds to a generator of E10 outside the realm of the generators entering the usual D=11 analysis, and is naturally included without any deformation of the coset model for E10/K(E10).…
With the purpose of holographically describing flows from a large family of four dimensional ${\cal N}=1$ and ${\cal N}=2$ conformal field theories, we discuss truncations of seven dimensional supergravity to five dimensions. We write explicitly the reduced gauged supergravity and find BPS equations for simple configurations. Lifting these flows to eleven dimensions or Massive IIA supergravity, we present string duals to RG flows from strongly coupled conformal theories when deformed by marginal and/or relevant operators. We further discuss observables common to infinite families of ${\cal N}=…
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…
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…
In seven dimensions any spin manifold admits an SU(2) structure and therefore very general M-theory compactifications have the potential to allow for a reduction to N=4 gauged supergravity. We perform this general SU(2) reduction and give the relation of SU(2) torsion classes and fluxes to gaugings in the N=4 theory. We furthermore show explicitly that this reduction is a consistent truncation of the eleven-dimensional theory, in other words classical solutions of the reduced theory also solve the eleven-dimensional equations of motion. This reduction generalizes previous M-theory reductions o…
We present a new BPS flow within minimal $\mathcal{N}=1$ supergravity in seven dimensions describing a warped $\textrm{AdS}_{3}$ background supported by a "dyonic" profile of the three-form. Furthermore, we discuss the holographic interpretation of the above solution in terms of a defect $\textrm{SCFT}_{2}$ inside the 6d $(1,0)$ theory dual to the AdS in the asymptotic region. Finally we provide the brane picture of the aforementioned defect CFT as D2- and wrapped D4-branes ending on a D6 - NS5 - D8 funnel in massive type IIA string theory.
We present a new consistent truncation of $D=11$ supergravity to $D=4$ $\mathcal{N}=2$ minimal gauged supergravity, on the seven-dimensional internal Riemannian space corresponding to the most general class of $D=11$ solutions with an AdS$_{4}$ factor and $\mathcal{N}=2$ supersymmetry. A truncation ansatz is proposed and its consistency checked at the level of the $D=11$ Bianchi identity, bosonic equations of motion, and supersymmetry variations of the gravitino. The general class includes an $\mathcal{N}=2$ AdS$_{4}$ solution dual to the conformal, low-energy physics phase corresponding to a …
We clarify the higher-dimensional origin of a class of dyonic gaugings of $D=4$ ${\cal N}=8$ supergravity recently discovered, when the gauge group is chosen to be ISO(7). This dyonically-gauged maximal supergravity arises from consistent truncation of massive IIA supergravity on $S^6$, and its magnetic coupling constant descends directly from the Romans mass. The critical points of the supergravity uplift to new AdS$_4$ massive type IIA vacua. We identify the corresponding CFT$_3$ duals as super-Chern-Simons-matter theories with simple gauge group SU$(N)$, with level $k$ given by the Romans m…
We construct a consistent truncation of six-dimensional matter coupled $F(4)$ gauged supergravity on a cornucopia of two-dimensional surfaces including a spindle, disc, domain wall and other novel backgrounds to four-dimensional minimal gauged supergravity. Using our consistent truncation we uplift known AdS$_2\times Σ_1$ solutions giving rise to four-dimensional orbifold solutions, AdS$_2\timesΣ_1\ltimesΣ_2$. We further uplift our solutions to massive type IIA supergravity by constructing the full uplift formulae for six-dimensional U$(1)^2$-gauged supergravity including all fields and arbitr…
We show that (massive) D=10 type IIA supergravity possesses a hidden rigid SO(9,9) symmetry and a hidden local SO(9) x SO(9) symmetry upon dimensional reduction to one (time-like) dimension. We explicitly construct the associated locally supersymmetric Lagrangian in one dimension, and show that its bosonic sector, including the mass term, can be equivalently described by a truncation of an E10/K(E10) non-linear sigma-model to the level \ell<=2 sector in a decomposition of E10 under its so(9,9) subalgebra. This decomposition is presented up to level 10, and the even and odd level sectors are id…
We study supersymmetric intersections of NS5-, D6- and D8-branes in type IIA string theory. We focus on the supergravity description of this system and identify a "near horizon" limit in which we recover the recently classified supersymmetric seven-dimensional AdS solutions of massive type IIA supergravity. Using a consistent truncation to seven-dimensional gauged supergravity we construct a universal supersymmetric deformation of these AdS vacua. In the holographic dual six-dimensional (1,0) superconformal field theory this deformation describes a universal RG flow on the tensor branch of the…
Supersymmetric $\,\textrm{AdS}_{4}\,$, $\,\textrm{AdS}_{2} \times Σ_{2}\,$ and asymptotically AdS$_{4}$ black hole solutions are studied in the context of non-minimal $\,\mathcal{N}=2\,$ supergravity models involving three vector multiplets (STU-model) and Abelian gaugings of the universal hypermultiplet moduli space. Such models correspond to consistent subsectors of the $\,\textrm{SO}(p,q)\,$ and $\,\textrm{ISO}(p,q)\,$ gauged maximal supergravities that arise from the reduction of 11D and massive IIA supergravity on $\,\textrm{H}^{(p,q)}\,$ spaces down to four dimensions. A unified descript…
We argue that M-theory/massive IIA backgrounds including KK-monopoles are suitably described in the language of G-structures and their intrinsic torsion. To this end, we study classes of minimal supergravity models that admit an interpretation as twisted reductions in which the twist parameters are not restricted to satisfy the Jacobi constraints $ω\, ω=0$ required by an ordinary Scherk-Schwarz reduction. We first derive the correspondence between four-dimensional data and torsion classes of the internal space and, then, check the one-to-one correspondence between higher-dimensional and four-d…
We construct consistent Kaluza-Klein truncations of type IIA supergravity on (i) $Σ_2\times S^3$ and (ii) $Σ_3\times S^3$, where $Σ_2 = S^2/Γ$, $\mathbb{R}^2/Γ$, or $\mathbb{H}^2/Γ$, and $Σ_3 = S^3/Γ$, $\mathbb{R}^3/Γ$, or $\mathbb{H}^3/Γ$, with $Γ$ a discrete group of symmetries, corresponding to NS5-branes wrapped on $Σ_2$ and $Σ_3$. The resulting theories are a $D=5$, $\mathcal{N}=4$ gauged supergravity coupled to three vector multiplets with scalar manifold $SO(1,1)\times SO(5,3)/(SO(5)\times SO(3))$ and gauge group $SO(2)\times\left(SO(2)\ltimes_{Σ_2}\mathbb{R}^4\right)$ which depends on …
Type-IIB supergravity in ten dimensions admits two consistent $Z_2$ truncations. After the insertion of D9-branes, one of them leads to the low-energy action of type-I string theory, and it can be performed in two different ways, in correspondence with the fact that there are two different consistent ten-dimensional type-I string theories, namely the SO(32) superstring and the $USp(32)$ model, in which supersymmetry is broken on the D9-branes. We derive here the same results for Type-IIA theory compactified on a circle in the presence of D8-branes. We also analyze the $κ$-symmetric action for …
Supergravity brane solutions allow for a generalised type of Kaluza-Klein reduction onto brane worldvolumes. The known replacement of a flat worldvolume metric by a Ricci-flat metric constitutes a consistent Kaluza-Klein truncation of the starting higher-dimensional supergravity theory down to a lower-dimensional pure gravity theory. This paper shows how to extend such a brane-worldvolume pure-gravity consistent truncation to that for a full nonlinear supergravity theory for the Type IIB D3-brane and the M-theory/Type IIA M5-brane. The extension of worldvolume supersymmetry is given by the unb…
We give a large class of supersymmetric domain walls in maximal seven-dimensional gauged supergravity with various types of gauge groups. Gaugings are described by components of the embedding tensor transforming in representations $\mathbf{15}$ and $\overline{\mathbf{40}}$ of the global symmetry $SL(5)$. The embedding tensor in $\mathbf{15}$ representation leads to $CSO(p,q,5-p-q)$ gauge groups while gaugings in $\overline{\mathbf{40}}$ representation describes $CSO(p,q,4-p-q)$ gauge groups. These gaugings admit half-supersymmetric domain walls as vacuum solutions. On the other hand, gaugings …
We study metastable nonsupersymmetric configurations in type IIA string theory, obtained by suspending D4-branes and anti-D4-branes between holomorphically curved NS5's, which are related to those of hep-th/0610249 by T-duality. When the numbers of branes and antibranes are the same, we are able to obtain an exact M theory lift which can be used to reliably describe the vacuum configuration as a curved NS5 with dissolved RR flux for g_s<<1 and as a curved M5 for g_s>>1. When our weakly coupled description is reliable, it is related by T-duality to the deformed IIB geometry with flux of hep-th/…
We classify Minkowski$_4$ solutions in type IIA supergravity, with N=2 supersymmetry and an SU(2) R-symmetry of a certain type. Many subcases can be reduced to relatively simple PDEs, among which we recover various intersecting brane systems, and AdS$_d$ solutions, $d=5,6,7$, and in particular the recently found general massive AdS$_7$ solutions. Imposing compactness of the internal six-manifold we obtain promising solutions with localized D-branes and O-planes.
Motivated by their application to holographic RG flows and hairy black holes in Einstein-scalar systems, we present a collection of superpotentials driving the dynamics of $\mathcal{N}=2$ and $\mathcal{N}=1$ four-dimensional supergravities. These theories arise as consistent truncations of the electric/magnetic families of $\textrm{CSO}(p,q,r)_{c}$ maximal supergravities, with ${p+q+r=8}$, discovered by Dall'Agata et al. The $\mathcal{N}=2$ and $\mathcal{N}=1$ truncations describe $\textrm{SU}(3)$ and $\mathbb{Z}_{2} \times \textrm{SO}(3)$ invariant sectors, respectively, and contain AdS$_4$ s…
We study a truncation of four-dimensional maximal gauged supergravity that provides a realization of the minimal model of a holographic superconductor. We find various flow solutions in this truncation at zero and finite temperature with a non-trivial profile for the charged scalar. Below a critical temperature we find holographic superconductor solutions that represent the thermodynamically preferred phase. Depending on the choice of boundary conditions, the superconducting phase transition is either first or second order. For vanishing temperature we find a flow with a condensing charged sca…
We discuss consistent truncations of eleven-dimensional supergravity on a six-dimensional manifold $M$, preserving minimal $\mathcal{N}=2$ supersymmetry in five dimensions. These are based on $G_S \subseteq USp(6)$ structures for the generalised $E_{6(6)}$ tangent bundle on $M$, such that the intrinsic torsion is a constant $G_S$ singlet. We spell out the algorithm defining the full bosonic truncation ansatz and then apply this formalism to consistent truncations that contain warped AdS$_5 \times_{\rm w}M$ solutions arising from M5-branes wrapped on a Riemann surface. The generalised $U(1)$ st…
The main objective of this work is to construct and classify the most general classical and quantum $\mathcal{N}=1$ $\mathcal{W}_\infty$-algebras generated by the same spins as the singlet algebra of $N$ fermions and $N$ bosons in the vector representation of $O(N)$ in the $N\to\infty$ limit. This type of algebras appears in a recent $\mathcal{N}=1$ version of the minimal model holography. Our analysis strongly suggests that there is a one parameter family $\mathcal{W}_\infty[μ]$ of such algebras at every given central charge. Relying on this assumption, we identify various truncations of $\ma…
We study properties of D = 4, N >1 extended supergravities (and related compactifications of superstring theory) and their consistent truncation to the phenomenologically interesting models of N = 1 supergravity. This involves a detailed classification of the "degenerations" of the duality groups of type E7, when the corresponding quartic invariant polynomial built from the symplectic irreducible representation of G4 "degenerates" into a perfect square. With regard to cosmological applications, we conclude that the consistent truncation to N = 1 from higher-dimensional or higher-N theory gives…
We analyse the vacuum structure of isotropic Z_2 x Z_2 flux compactifications, allowing for a single set of sources. Combining algebraic geometry with supergravity techniques, we are able to classify all vacua for both type IIA and IIB backgrounds with arbitrary gauge and geometric fluxes. Surprisingly, geometric IIA compactifications lead to a unique theory with four different vacua. In this case we also perform the general analysis allowing for sources compatible with minimal supersymmetry. Moreover, some relevant examples of type IIB non-geometric compactifications are studied. The computat…
We consider maximal gauged supergravity in 4D with ISO(7) gauge group, which arises from a consistent truncation of massive IIA supergravity on a six-sphere. Within its G$_2$ invariant sector, the theory is known to possess a supersymmetric AdS extremum as well as two non-supersymmetric ones. In this context we provide a first order formulation of the theory by making use of the Hamilton-Jacobi (HJ) formalism. This allows us to derive a positive energy theorem for both non-supersymmetric extrema. Subsequently, we also find novel non-supersymmetric domain walls (DW) interpolating between the su…
Recently, Gaiotto and Rapcak (GR) proposed a new family of the vertex operator algebra (VOA) as the symmetry appearing at an intersection of five-branes to which they refer as Y algebra. Prochazka and Rapcak, then proposed to interpret Y algebra as a truncation of affine Yangian whose module is directly connected to plane partitions (PP). They also developed GR's idea to generate a new VOA by connecting plane partitions through an infinite leg shared by them and referred it as the web of W-algebra (WoW). In this paper, we demonstrate that double truncation of PP gives the minimal models of suc…
The most general class of warped AdS5 x M6 supersymmetric solutions in D=11 supergravity permit a consistent truncation to D=5 N=2 minimal gauged supergravity. Here we extend this truncation, for a particular subclass of M6 manifolds, to D=5 N=4 gauged supergravity coupled to two vector multiplets. We obtain the reduction ansatz by T-duality of a recently discussed type IIB truncation on a generic Sasaki-Einstein five-fold, which becomes non-trivial in D=11 and displays non-standard features due to the G-structure of the internal M6. Using this truncation, we construct two new classes of warpe…
We compute various correlation functions at the planar level in a simple supersymmetric matrix model, whose scalar potential is in shape of a double-well. The model has infinitely degenerate vacua parametrized by filling fractions ν_\pm representing the numbers of matrix eigenvalues around the two minima of the double-well. The computation is done for general filling fractions corresponding to general two-cut solutions for the eigenvalue distribution. The model is mapped to the O(n) model on a random surface with n=-2, and some sector of the model is described by two-dimensional quantum gravit…
A class of conformally flat and asymptotically anti-de Sitter geometries involving profiles of scalar fields is studied from the point of view of gauged supergravity. The scalars involved in the solutions parameterise the SL(N,R)/SO(N) submanifold of the full scalar coset of the gauged supergravity, and are described by a symmetric potential with a universal form. These geometries descend via consistent truncation from distributions of D3-branes, M2-branes, or M5-branes in ten or eleven dimensions. We exhibit analogous solutions asymptotic to AdS_6 which descend from the D4-D8-brane system. We…
Hamiltonian Truncation (HT) is a numerical approach for calculating observables in a Quantum Field Theory non-perturbatively. This approach can be applied to theories constructed by deforming a conformal field theory with a relevant operator of scaling dimension $Δ$. UV divergences arise when $Δ$ is larger than half of the spacetime dimension $d$. These divergences can be regulated by HT or by using a more conventional local regulator. In this work we show that extra UV divergences appear when using HT rather than a local regulator for $Δ\geq d/2+1/4$, revealing a striking breakdown of localit…
This paper summarizes several developments in string-derived (Minimal Supersymmetric) Standard Models. Part one reviews the first string model containing solely the three generations of the Minimal Supersymmetric Standard Model and a single pair of Higgs as the matter in the observable sector of the low energy effective field theory. This model was constructed by Cleaver, Faraggi, and Nanopoulos in the Z_2 x Z_2 free fermionic formulation of weak coupled heterotic strings. Part two examines a representative collection of string/brane-derived MSSMs that followed. These additional models were ob…
We analyse the constraints from supersymmetry on $ \nabla^4 R^4$ type corrections to the effective action in $\mathcal{N}=2$ supergravity in eight dimensions. We prove that there are two classes of invariants that descend respectively from type IIA and type IIB supergravity. We determine the first class as $d$-closed superforms in superspace in eight dimensions, whereas we obtain the second class by dimensional reduction down to four dimensions, in which there is a single class of invariants transforming in the next to minimal unitary representation of $E_{7(7)}$.
