Duality Orbits Research Articles

The holography of duality in mathcal{N} = 4 Super-Yang-Mills theory

The space of mathcal{N} = 4 supersymmetric Yang-Mills theories exhibits an intricate structure of global one-form symmetries and SL(2, ℤ) duality orbits. In this paper we study this structure from the point of view of the holographic dual Type IIB string theory. Generalizing work by Witten, we map the different theories based on the gauge algebras su(N), so(N), and sp(N) to a choice of boundary conditions on bulk gauge fields. We show how the one-form symmetries and their anomalies, as well as the duality properties of the gauge theories, arise in the holographic picture. Along the way we prove that the number of disjoint SL(2, ℤ) duality orbits for the su(N) theories is given by the number of square divisors of N.

The geometry, branes and applications of exceptional field theory

This is a review of exceptional field theory: a generalisation of Kaluza–Klein theory that unifies the metric and [Formula: see text]-form gauge field degrees of freedom of supergravity into a generalised or extended geometry, whose additional coordinates may be viewed as conjugate to brane winding modes. This unifies the maximal supergravities, treating their previously hidden exceptional Lie symmetries as a fundamental geometric symmetry. Duality orbits of solutions simplify into single objects, that in many cases have simple geometric interpretations, for instance as wave or monopole-type solutions. It also provides a route to explore exotic or nongeometric aspects of M-theory, such as exotic branes, [Formula: see text]-folds, and more novel sorts of non-Riemannian spaces.

Electromagnetic dual Einstein-Maxwell-scalar models

Electromagnetic duality is discussed in the context of Einstein-Maxwell-scalar (EMS) models including axionic-type couplings. This family of models introduces two non-minimal coupling functions f(ϕ) and g(ϕ), depending on a real scalar field ϕ. Interpreting the scalar field as a medium, one naturally defines constitutive relations as in relativistic non-linear electrodynamics. Requiring these constitutive relations to be invariant under the SO(2) electromagnetic duality rotations of Maxwell’s theory, defines 1-parameter, closed duality orbits in the space of EMS models, connecting different electromagnetic fields in “dual” models with different coupling functions, but leaving both the scalar field and the spacetime geometry invariant. This mapping works as a solution generating technique, extending any given solution of a specific model to a (different) solution for any of the dual models along the whole duality orbit. We illustrate this technique by considering the duality orbits seeded by specific EMS models wherein solitonic and black hole solutions are known. For dilatonic models, specific rotations are equivalent to S-duality.

Orbits in nonsupersymmetric magic theories

We determine and classify the electric-magnetic duality orbits of fluxes supporting asymptotically flat, extremal black branes in [Formula: see text] space–time dimensions in the so-called nonsupersymmetric magic Maxwell–Einstein theories, which are consistent truncations of maximal supergravity and which can be related to Jordan algebras (and related Freudenthal triple systems) over the split complex numbers [Formula: see text] and the split quaternions [Formula: see text]. By studying the stabilizing subalgebras of suitable representatives, realized as bound states of specific weight vectors of the corresponding representation of the electric-magnetic duality symmetry group, we obtain that, as for the case of maximal supergravity, in magic nonsupersymmetric Maxwell–Einstein theories there is no splitting of orbits, namely there is only one orbit for each nonmaximal rank element of the relevant Jordan algebra (in [Formula: see text] and 6) or of the relevant Freudenthal triple system (in [Formula: see text]).

Four-derivative couplings and BPS dyons in heterotic CHL orbifolds

Three-dimensional string models with half-maximal supersymmetry are believed to be invariant under a large U-duality group which unifies the S and T dualities in four dimensions. We propose an exact, U-duality invariant formula for four-derivative scalar couplings of the form F(\Phi) (\nabla\Phi)^4F(Φ)(∇Φ)4 in a class of string vacua known as CHL \IZ_N heterotic orbifolds with NN prime, generalizing our previous work which dealt with the case of heterotic string on T^6T6. We derive the Ward identities that F(\Phi)F(Φ) must satisfy, and check that our formula obeys them. We analyze the weak coupling expansion of F(\Phi)F(Φ), and show that it reproduces the correct tree-level and one-loop contributions, plus an infinite series of non-perturbative contributions. Similarly, the large radius expansion reproduces the exact F^4F4 coupling in four dimensions, including both supersymmetric invariants, plus infinite series of instanton corrections from half-BPS dyons winding around the large circle, and from Taub-NUT instantons. The summation measure for dyonic instantons agrees with the helicity supertrace for half-BPS dyons in 4 dimensions in all charge sectors. In the process we clarify several subtleties about CHL models in D=4D=4 and D=3D=3, in particular we obtain the exact helicity supertraces for 1/2-BPS dyonic states in all duality orbits.

Nonsupersymmetric magic theories and Ehlers truncations

We consider the nonsupersymmetric “magic” theories based on the split quaternion and the split complex division algebras. We show that these theories arise as “Ehlers” [Formula: see text] and [Formula: see text] truncations of the maximal supergravity theory, exploiting techniques related to the very-extended Kac–Moody algebras. We also generalize the procedure to other [Formula: see text] truncations, resulting in additional classes of nonsupersymmetric theories, as well as to truncations of nonmaximal theories. Finally, we discuss duality orbits of extremal black hole solutions in some of these nonsupersymmetric theories.

Electric-magnetic deformations of D = 4 gauged supergravities

We discuss duality orbits and symplectic deformations of D=4 gauged supergravity theories, with focus on N$\ge$2. We provide a general constructive framework for computing symplectic deformations starting from a reference gauging, and apply it to many interesting examples. We prove that no continuous deformations are allowed for Fayet-Iliopoulos gaugings of the N=2 STU model and in particular that any $\omega$ deformation is classically trivial. We further show that although in the N=6 truncation of SO(8) maximal supergravity the $\omega$ parameter can be dualized away, in the 'twin' N=2 truncation $\omega$ is preserved and a second, new deformation appears. We further provide a full classification and appropriate duality orbits of certain N=4 gauged supergravities, including all inequivalent SO(4)$^2$ gaugings and several non-compact forms.

Real weights, bound states and duality orbits

We show that the duality orbits of extremal black holes in supergravity theories with symmetric scalar manifolds can be derived by studying the stabilizing subalgebras of suitable representatives, realized as bound states of specific weight vectors of the corresponding representation of the duality symmetry group. The weight vectors always correspond to weights that are real, where the reality properties are derived from the Tits–Satake diagram that identifies the real form of the Lie algebra of the duality symmetry group. Both [Formula: see text] magic Maxwell–Einstein supergravities and the semisimple infinite sequences of [Formula: see text] and [Formula: see text] theories in [Formula: see text] and [Formula: see text] are considered, and various results, obtained over the years in the literature using different methods, are retrieved. In particular, we show that the stratification of the orbits of these theories occurs because of very specific properties of the representations: in the case of the theory based on the real numbers, whose symmetry group is maximally noncompact and therefore all the weights are real, the stratification is due to the presence of weights of different lengths, while in the other cases it is due to the presence of complex weights.

All gaugings and stable de Sitter in D = 7 half-maximal supergravity

We study the general formulation of gauged supergravity in seven dimensions with sixteen supercharges keeping duality covariance by means of the embedding tensor formalism. We first classify all inequivalent duality orbits of consistent deformations. Secondly, we analyse the complete set of critical points in a systematic way. Interestingly, we find the first examples of stable de Sitter solutions within a theory with such a large amount of supersymmetry.

On extremal limits and duality orbits of stationary black holes

With reference to the effective three-dimensional description of stationary, single center solutions to (ungauged) symmetric supergravities, we complete a previous analysis on the definition of a general geometrical mechanism for connecting global symmetry orbits (duality orbits) of non-extremal solutions to those of extremal black holes. We focus our attention on a generic representative of these orbits, providing its explicit description in terms of D=4 fields. As a byproduct, using a new characterization of the angular momentum in terms of quantities intrinsic to the geometry of the D=3 effective model, we are able to prove on general grounds its invariance, as a function of the boundary data, under the D=4 global symmetry. In the extremal under-rotating limit it becomes moduli-independent. We also discuss the issue of the fifth parameter characterizing the four-dimensional seed solution, showing that it can be generated by a transformation in the global symmetry group which is manifest in the D=3 effective description.

Exploring double field theory

We consider a flux formulation of Double Field Theory in which fluxes are dynamical and field-dependent. Gauge consistency imposes a set of quadratic constraints on the dynamical fluxes, which can be solved by truly double configurations. The constraints are related to generalized Bianchi Identities for (non-)geometric fluxes in the double space, sourced by (exotic) branes. Following previous constructions, we then obtain generalized connections, torsion and curvatures compatible with the consistency conditions. The strong constraint-violating terms needed to make contact with gauged supergravities containing duality orbits of non-geometric fluxes, systematically arise in this formulation.

Evidence for a Family of SO(8) Gauged Supergravity Theories

In this note we discuss the classification of duality orbits of N=8 gauged supergravity models. Using tensor classifiers, we show that there is a one-parameter family of inequivalent SO(8) gauged supergravity theories. We briefly discuss the couplings of such models and show that, although the maximally symmetric vacuum has the same quadratic spectrum, the supersymmetry transformations, the couplings, and the scalar potential are parameter dependent. We also comment on the possible M theory uplift and on the meaning of the parameter for the dual gauge theories.

Duality orbits of non‐geometric fluxes

AbstractCompactifications in duality covariant constructions such as generalised geometry and double field theory have proven to be suitable frameworks to reproduce gauged supergravities containing non‐geometric fluxes. However, it is a priori unclear whether these approaches only provide a reformulation of old results, or also contain new physics. To address this question, we classify the T‐ and U‐duality orbits of gaugings of (half‐)maximal supergravities in dimensions seven and higher. It turns out that all orbits have a geometric supergravity origin in the maximal case, while there are non‐geometric orbits in the half‐maximal case. We show how the latter are obtained from compactifications of double field theory.

Four-Qubit Entanglement Classification from String Theory

We invoke the black-hole-qubit correspondence to derive the classification of four-qubit entanglement. The U-duality orbits resulting from timelike reduction of string theory from D=4 to D=3 yield 31 entanglement families, which reduce to nine up to permutation of the four qubits.