11D Supergravity Research Articles

UV Shadows in EFTs: Accidental Symmetries, Robustness and No‐Scale Supergravity

AbstractWe argue that accidental approximate scaling symmetries are robust predictions of weakly coupled string vacua, and show that their interplay with supersymmetry and other (generalised) internal symmetries underlies the ubiquitous appearance of no‐scale supergravities in low‐energy 4D EFTs. We identify 4 nested types of no‐scale supergravities, and show how leading quantum corrections can break scale invariance while preserving some no‐scale properties (including non‐supersymmetric flat directions). We use these ideas to classify corrections to the low‐energy 4D supergravity action in perturbative 10D string vacua, including both bulk and brane contributions. Our prediction for the Kähler potential at any fixed order in and string loops agrees with all extant calculations. p‐form fields play two important roles: they spawn many (generalised) shift symmetries; and space‐filling 4‐forms teach 4D physics about higher‐dimensional phenomena like flux quantisation. We argue that these robust symmetry arguments suffice to understand obstructions to finding classical de Sitter vacua, and suggest how to get around them in UV complete models.

Current algebra formulation of quantum gravity and its application to cosmology

Abstract Gravity theory based on current algebra is formulated. The gauge principle rather than general covariance combined with the equivalence principle plays a pivotal role in the formalism, and the latter principles are derived as a consequence of the theory. In this approach, it turns out that gauging the Poincaré algebra is not appropriate but gauging the $SO(N,M)$ algebra gives a consistent theory. This makes it possible to have anti-de Sitter and de Sitter space-time by adopting a relation between the spin connection and the tetrad field. The Einstein equation is part of our basic equation for gravity, which is written in terms of the spin connection. When this formalism is applied to the $E(11)$ algebra in which the three-form antisymmetric tensor is part of a gravity multiplet, we have a current algebra gravity theory based on M-theory in the sense that the internal group or the connection space representations of our model are those appearing in 11D supergravity. Moreover, when our formalism in its classical limit is applied to cosmology, by introducing conformal-like modes that connect the tetrad field/current and the spin connection field/current, we can obtain an accelerating universe in the manner of the “inflating” universe at its early stage.

4D mathcal{N} = 1 Kaluza-Klein superspace

Motivated by recent efforts to encode 11D supergravity in 4D mathcal{N} = 1 superfields, we introduce a general covariant framework relevant for describing any higher dimensional supergravity theory in external 4D mathcal{N} = 1 superspace with n additional internal coordinates. The superspace geometry admits both external and internal diffeomorphisms and provides the superfields necessary to encode the components of the higher dimensional vielbein, except for the purely internal sector, in a universal way that depends only on the internal dimension n. In contrast, the mathcal{N} = 1 superfield content of the internal sector of the metric is expected to be highly case dependent and involve covariant matter superfields, with additional hidden higher dimensional Lorentz and supersymmetry transformations realized in a non-linear manner.

On the consistency of a class of R-symmetry gauged 6D = (1,0) supergravities.

R-symmetry gauged 6D (1, 0) supergravities free from all local anomalies, with gauge groups G × G R where G R is the R-symmetry group and G is semisimple with rank greater than one, and which have no hypermultiplet singlets, are extremely rare. There are three such models known in which the gauge symmetry group is G 1 × G 2 × U(1) R , where the first two factors are , G 2 × E 7 and F 4 × Sp(9). These are models with single tensor multiplet, and hyperfermions in the (1, 912), (14, 56) and (52, 18) dimensional representations of G 1 × G 2, respectively. So far, it is not known if these models follow from string theory. We highlight key properties of these theories, and examine constraints which arise from the consistency of the quantization of anomaly coefficients formulated in their strongest form by Monnier and Moore. Assuming that the gauged models accommodate dyonic string excitations, we find that these constraints are satisfied only by the model with the F 4 × Sp(9) × U(1) R symmetry. We also discuss aspects of dyonic strings and potential caveats they may pose in applying the stated consistency conditions to the R-symmetry gauged models.

Swampland constraints on 5d mathcal{N} = 1 supergravity

We propose Swampland constraints on consistent 5-dimensional mathcal{N} = 1 supergravity theories. We focus on a special class of BPS magnetic monopole strings which arise in gravitational theories. The central charges and the levels of current algebras of 2d CFTs on these strings can be calculated by anomaly inflow mechanism and used to provide constraints on the low-energy particle spectrum and the effective action of the 5d supergravity based on unitarity of the worldsheet CFT. In M-theory, where these theories are realized by compactification on Calabi-Yau 3-folds, the special monopole strings arise from wrapped M5-branes on special (“semi-ample”) 4-cycles in the threefold. We identify various necessary geometric conditions for such cycles to lead to requisite BPS strings and translate these into constraints on the low-energy theories of gravity. These and other geometric conditions, some of which can be related to unitarity constraints on the monopole worldsheet, are additional candidates for Swampland constraints on 5-dimensional mathcal{N} = 1 supergravity theories.

Generic Construction of the Standard Model Gauge Group and Matter Representations in F‐theory

AbstractWe describe general classes of 6D and 4D F‐theory models with gauge group . We prove that this set of constructions gives all possible consistent 6D supergravity theories with no tensor multiplets having this gauge group and the corresponding generic matter representations, which include those of the MSSM. We expect, though do not prove, that these models are similarly generic for 6D theories with tensor multiplets and for 4D supergravity theories. The largest class of these constructions come from deforming an underlying geometry with gauge symmetry .

General F-theory models with tuned (SU(3) \xd7 SU(2) \xd7 U(1))/\u21246 symmetry

We construct a general form for an F-theory Weierstrass model over a general base giving a 6D or 4D supergravity theory with gauge group (SU(3) × SU(2) × U(1))/ℤ6 and generic associated matter, which includes the matter content of the standard model. The Weierstrass model is identified by unHiggsing a model with U(1) gauge symmetry and charges q ≤ 4 previously found by the first author. This model includes two distinct branches that were identified in earlier work, and includes as a special case the class of models recently studied by Cvetič, Halverson, Lin, Liu, and Tian, for which we demonstrate explicitly the possibility of unification through an SU(5) unHiggsing. We develop a systematic methodology for checking that a parameterized class of F-theory Weierstrass models with a given gauge group G and fixed matter content is generic (contains all allowed moduli) and confirm that this holds for the models constructed here.

Super-exceptional geometry: origin of heterotic M-theory and super-exceptional embedding construction of M5

In the quest for the mathematical formulation of M-theory, we consider three major open problems: a first-principles construction of the single (abelian) M5-brane Lagrangian density, the origin of the gauge field in heterotic M-theory, and the supersymmetric enhancement of exceptional M-geometry. By combining techniques from homotopy theory and from supergeometry to what we call super-exceptional geometry within super-homotopy theory, we present an elegant joint solution to all three problems. This leads to a unified description of the Nambu-Goto, Perry-Schwarz, and topological Yang-Mills Lagrangians in the topologically nontrivial setting. After explaining how charge quantization of the C-field in Cohomotopy reveals D’Auria-Fré’s “hidden supergroup” of 11d supergravity as the super-exceptional target space, in the sense of Bandos, for M5-brane sigma-models, we prove, in exceptional generalization of the doubly-supersymmetric super-embedding formalism, that a Perry-Schwarz-type Lagrangian for single (abelian) mathcal{N} = (1, 0) M5-branes emerges as the super-exceptional trivialization of the M5-brane cocycle along the super-exceptional embedding of the “half ” M5-brane locus, super-exceptionally compactified on the Hořava-Witten circle fiber. From inspection of the resulting 5d super Yang-Mills Lagrangian we find that the extra fermion field appearing in super-exceptional M-geometry, whose physical interpretation had remained open, is the M-theoretic avatar of the gaugino field.

Spinor Moving Frame, Polarized Scattering Equation for 11D Supergravity, and Ambitwistor Superstring

We reveal and discuss the spinor moving frame origin of the formalism of the 11D polarized scattering equation by Geyer and Mason [21]. In particular, we use the spinor moving frame formulation of the 11D ambitwistor superstring [35] considered as a dynamical system in the 11D superspace enlarged by tensorial central charge coordinates to rigorously obtain the expression for the spinor function on a Riemann sphere and the polarized scattering equation which that obeys.

Supersymmetric Liouville theory in AdS2 and AdS/CFT

In a series of recent papers, a special kind of AdS2/CFT1 duality was observed: the boundary correlators of elementary fields that appear in the Lagrangian of a 2d conformal theory in rigid AdS2 background are the same as the correlators of the corresponding primary operators in the chiral half of that 2d CFT in flat space restricted to the real line. The examples considered were: (i) the Liouville theory where the operator dual to the Liouville scalar in AdS2 is the stress tensor; (ii) the abelian Toda theory where the operators dual to the Toda scalars are the mathcal{W} -algebra generators; (iii) the non-abelian Toda theory where the Liouville field is dual to the stress tensor while the extra gauged WZW theory scalars are dual to non-abelian parafermionic operators. By direct Witten diagram com- putations in AdS2 one can check that the structure of the boundary correlators is indeed consistent with the Virasoro (or higher) symmetry. Here we consider a supersymmetric generalization: the mathcal{N} = 1 superconformal Liouville theory in AdS2. We start with the super Liouville theory coupled to 2d supergravity and show that a consistent restriction to rigid AdS2 background requires a non-zero value of the supergravity auxiliary field and thus a modification of the Liouville potential from its familiar flat-space form. We show that the Liouville scalar and its fermionic partner are dual to the chiral half of the stress tensor and the supercurrent of the super Liouville theory on the plane. We perform tests supporting the duality by explicitly computing AdS2 Witten diagrams with bosonic and fermionic loops.

Carroll membranes

We explore Carroll limit corresponding to M2 as well as M3 branes propagating over 11D supergravity backgrounds in M theory. In the first part of the analysis, we introduce the membrane Carroll limit associated to M2 branes propagating over M theory supergravity backgrounds. Considering two specific M2 brane embeddings, we further outline the solutions corresponding to the Hamilton’s dynamical equations in the Carroll limit. We further consider the so called stringy Carroll limit associated to M2 branes and outline the corresponding solutions to the underlying Hamilton’s equations of motion by considering specific M2 brane embeddings over 11D target space geometry. As a further illustration of our analysis, considering the Nambu-Goto action, we show the equivalence between different world-volume descriptions in the Carroll limit of M2 branes. Finally, considering the stringy Carroll limit, we explore the constraint structure as well as the Hamiltonian dynamics associated to unstable M3 branes in 11D supergravity and obtain the corresponding effective world-volume description around their respective tachyon vacua.

F‐theory and Dark Energy

AbstractMotivated by its potential use as a starting point for solving various cosmological constant problems, we study F‐theory compactified on the warped product where Y8 is a manifold, and the S3 factor is the target space of an Wess–Zumino–Witten (WZW) model at level N. Reduction to M‐theory exploits the abelian duality of this WZW model to an orbifold. In the large N limit, the untwisted sector is captured by 11D supergravity. The local dynamics of intersecting 7‐branes in the geometry is controlled by a Donaldson–Witten twisted gauge theory coupled to defects. At late times, the system is governed by a 1D quantum mechanics system with a ground state annihilated by two real supercharges, which in four dimensions would appear as “ supersymmetry” on a curved background. This leads to a cancellation of zero point energies in the 4D field theory but a split mass spectrum for superpartners of order specified by the IR and UV cutoffs of the model. This is suggestively close to the TeV scale in some scenarios. The classical 4D geometry has an intrinsic instability which can produce either a collapsing or expanding Universe, the latter providing a promising starting point for a number of cosmological scenarios. The resulting 1D quantum mechanics in the time direction also provides an appealing starting point for a more detailed study of quantum cosmology.

Understanding KKLT from a 10d perspective

Some of the most well-celebrated constructions of metastable de Sitter vacua from string theory, such as the KKLT proposal, involve the interplay of gaugino condensation on a D7-brane stack and an uplift by a positive tension object. These constructions have recently been challenged using arguments that rely on the trace-reversed and integrated 10d Einstein equation. We give a critical assessment of such concerns. We first relate an integrated 10d Einstein equation to the extremization condition for a 10d-derived 4d effective potential. Then we argue how to obtain the latter from a 10d action which incorporates gaugino condensation in a (recently proposed) manifestly finite, perfect-square form. This effective potential is consistent with 4d supergravity and does not present obstacles for an uplifted minimum. Moreover, within standard approximations, we understand the uplift explicitly in one of the popular versions of the integrated 10d equation. Our conclusion is that de Sitter constructions of the KKLT type cannot be dismissed simply based on the integrated 10d equations considered so far.

Higher Forms and Membranes in 4D Supergravities

AbstractWe review the dynamical generation of coupling constants in 4D supergravity by means of gauge three‐form fields. The latter are introduced as components of particular chiral supermultiplets and can be coupled to membranes preserving local supersymmetry. Such a set‐up naturally arises from type‐II string compactifications on Calabi–Yau manifolds with fluxes. We present generic 4D supergravity models with three‐form multiplets and study domain wall solutions supported by membranes, which interpolate between vacua with different values of the cosmological constant.

A Modern Point of View on Anomalies

AbstractWe review the concept of anomaly field theory, namely the fact that the anomalies of a d‐dimensional field theory can be encoded in a ‐dimensional field theory functor. We give numerous examples of anomaly field theories, explain how classical facts about anomalies are recovered from the anomaly field theory, and review recent work on global anomaly cancellation in 6d supergravity where this concept was instrumental. We also sketch the status of global anomaly cancellation checks in string theory. This paper is based on a talk given at the Durham Symposium ‘Higher Structures in M‐theory’ in August 2018.

Generic matter representations in 6D supergravity theories

In six-dimensional supergravity, there is a natural sense in which matter lying in certain representations of the gauge group is “generic,” in that other “exotic” matter representations require more fine tuning. From considerations of the dimensionality of the moduli space and anomaly cancellation conditions, we find that the generic sets of matter representations are well-defined for 6D supergravity theories with gauge groups containing arbitrary numbers of nonabelian factors and U(1) factors. These generic matter representations also match with those that arise in the most generic F-theory constructions, both in 6D and in 4D, with non-generic matter representations requiring more exotic singularity types. The analysis of generic versus exotic matter illuminates long-standing puzzles regarding F-theory models with multiple U(1) factors and provides a useful framework for analyzing the 6D “swampland” of apparently consistent low-energy theories that cannot be realized through known string constructions. We note also that the matter content of the standard model is generic by the criteria used here only if the global structure is SU(3)c × SU(2)L × U(1)Y/ℤ6.

All Tree Amplitudes of 6D (2,0) Supergravity: Interacting Tensor Multiplets and the K3 Moduli Space.

We present a twistorlike formula for the complete tree-level S matrix of six-dimensional (6D) (2,0) supergravity coupled to 21 Abelian tensor multiplets. This is the low-energy effective theory that corresponds to type IIB superstring theory compactified on a K3 surface. The formula is expressed as an integral over the moduli space of certain rational maps of the punctured Riemann sphere. By studying soft limits of the formula, we are able to explore the local moduli space of this theory, {[SO(5,21)]/[SO(5)×SO(21)]}. Finally, by dimensional reduction, we also obtain a new formula for the tree-level S matrix of 4D N=4 Einstein-Maxwell theory.

Remarks on the Green–Schwarz Terms of Six-Dimensional Supergravity Theories

We construct the Green-Schwarz terms of six-dimensional supergravity theories on spacetimes with non-trivial topology and gauge bundle. We prove the cancellation of all global gauge and gravitational anomalies for theories with gauge groups given by products of $U(n)$, $SU(n)$ and $Sp(n)$ factors, as well as for $E_8$. For other gauge groups, anomaly cancellation is equivalent to the triviality of a certain 7-dimensional spin topological field theory. We show in the case of a finite Abelian gauge group that there are residual global anomalies imposing constraints on the 6d supergravity. These constraints are compatible with the known F-theory models. Interestingly, our construction requires that the gravitational anomaly coefficient of the 6d supergravity theory is a characteristic element of the lattice of string charges, a fact true in six-dimensional F-theory compactifications but that until now was lacking a low-energy explanation. We also discover a new anomaly coefficient associated with a torsion characteristic class in theories with a disconnected gauge group.

A Geometric Construction of Solutions to 11D Supergravity

Necessary and sufficient conditions are provided for a class of warped product manifolds with non-vanishing flux to be supersymmetric solutions of 11D supergravity. Many noncompact, but complete solutions can be obtained in this manner, including the multi-membrane solution initially found by Duff and Stelle. In a different direction, an explicit 5-parameter moduli space of solutions to 11D supergravity is also constructed which can be viewed as nonsupersymmetric deformations of the Duff-Stelle solution.

The Tension between 10D Supergravity and dS Uplifts

AbstractWe elaborate on the recent work of Moritz et al. where it is argued that anti‐brane uplifting in KKLT models never leads to dS vacua. This is due to flattening effects in the effective potential found when treating the gaugino condensate energy momentum in ten‐dimensional supergravity. We point out that the Silverstein‐Saltman uplift, which effectively dissolves the anti‐brane in 3‐form fluxes, is a conceptually simpler setting in which flattening effects can be present, without requiring assumptions about UV/IR mixings. Along the way we revise and improve on the arguments of Moritz et al. and discuss various subleties when studying gaugino condensates from a ten‐dimensional point‐of‐view. In particular, the “no dS” argument is slightly weaker and we emphasize a technical loophole that might allow dS vacua. Finally we suggest that AdS vacua which are parametrically controlled from these flattening effects belong to the Swampland. We comment on the relation with the recent refined dS Swampland inequalities.