arXiv subjects

Bernard de Wit

Publications and source records attributed to Bernard de Wit.

At least 19 recordsLinked to original sources

arXiv2020

Supersymmetric traversable wormholes

We study traversable wormhole solutions in pure gauged $N\!=\!2$ supergravity with and without electromagnetic fields, which are locally isometric under $\mathrm{SO}(2,1)\!\times\!\mathrm{SO}(1,1)$. The model allows for 1/2-BPS wormhole solutions whose corresponding globally defined Killing spinors are presented. A non-contractible cycle can be obtained by compactifying one of the coordinates which leaves the residual supersymmetry unaffected, the isometry group is now globally $\mathrm{SO}(2,1)\!\times\!\mathrm{SO}(2)$. The wormholes connect two asymptotic, locally $\mathrm{AdS}_4$ regions and depend on certain electric and magnetic charge parameters and, implicitly, on the range of the compact coordinate around the throat. We provide an analysis of the boundary of the spacetime and show that it can be either disconnected or not, depending on the values of the parameters in the metric. Finally, we show how that these space-times avoid a topological censorship theorem.

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arXiv2018

BRST quantization and equivariant cohomology: localization with asymptotic boundaries

We develop BRST quantization of gauge theories with a soft gauge algebra on spaces with asymptotic boundaries. The asymptotic boundary conditions are imposed on background fields, while quantum fluctuations about these fields are described in terms of quantum fields that vanish at the boundary. This leads us to construct a suitable background field formalism that is generally applicable to soft gauge algebras, and therefore to supergravity. We define a nilpotent BRST charge that acts on both the background and the quantum fields, as well as on the background and quantum ghosts. When the background is restricted to be invariant under a residual isometry group, the background ghosts must be restricted accordingly and play the role of the parameters of the background isometries. Requiring in addition that the background ghosts will be BRST invariant as well then converts the BRST algebra into an equivariant one. The background fields and ghosts are then invariant under the equivariant transformations while the quantum fields and ghosts transform under both the equivariant and the background transformations. We demonstrate how this formalism is suitable for carrying out localization calculations in a large class of theories, including supergravity defined on asymptotic backgrounds that admit supersymmetry.

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arXiv2017

Construction of all N=4 conformal supergravities

All N=4 conformal supergravities in four space-time dimensions are constructed. These are the only N=4 supergravity theories whose actions are invariant under off-shell supersymmetry. They are encoded in terms of a holomorphic function that is homogeneous of zeroth degree in scalar fields that parametrize an SU(1,1)/U(1) coset space. When this function equals a constant the Lagrangian is invariant under continuous SU(1,1) transformations. The construction of these higher-derivative invariants also opens the door to various applications for non-conformal theories.

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arXiv2017

Euclidean Supergravity

Supergravity with eight supercharges in a four-dimensional Euclidean space is constructed at the full non-linear level by performing an off-shell time-like reduction of five-dimensional supergravity. The resulting four-dimensional theory is realized off-shell with the Weyl, vector and tensor supermultiplets and a corresponding multiplet calculus. Hypermultiplets are included as well, but they are themselves only realized with on-shell supersymmetry. The off-shell reduction leads to a full understanding of the Euclidean theory. A complete multiplet calculus is presented along the lines of the Minkowskian theory. Unlike in Minkowski space, chiral and anti-chiral multiplets are real and supersymmetric actions are generally unbounded from below. Precisely as in the Minkowski case, where one has different formulations of Poincaré supergravity by introducing different compensating supermultiplets, one can also obtain different versions of Euclidean supergravity.

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arXiv2016

The off-shell c-map

The off-shell version of the c-map is presented, based on a systematic off-shell reduction from four to three space-time dimensions for supergravity theories with eight supercharges. In the reduction, the R-symmetry group is enhanced to local [SU(2) x SU(2)]/Z2 =SO(4) and the c-map is effected by a parity transformation in the internal space that interchanges the two SU(2) factors. Vector and tensor supermultiplets are each others conjugate under the c-map and both can be dualized in three dimensions to (on-shell) hypermultiplets. As shown in this paper the off-shell formulation indeed leads to a clarification of many of the intricate issues that play a role in the c-map. The results for off-shell Lagrangians quadratic in space-time derivatives are analyzed in detail and compared to the literature. The underlying reasons are identified why not all of the four-dimensional tensor multiplet Lagrangians can be in the image of the c-map. The advantage of the off-shell approach is, that it also enables a systematic analysis of theories with higher-derivative couplings. This is demonstrated for a particular subclass of such theories, which, under certain conditions, are consistent under the c-map. In principle, explicit results for realistic four-dimensional type-II string compactifications can be explored in this way.

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arXiv2015

IIB Supergravity and the E6(6) covariant vector-tensor hierarchy

IIB supergravity is reformulated with a manifest local USp(8) invariance that makes the embedding of five-dimensional maximal supergravities transparent. In this formulation the ten-dimensional theory exhibits all the 27 one-form fields and 22 of the 27 two-form fields that are required by the vector-tensor hierarchy of the five-dimensional theory. The missing 5 two-form fields must transform in the same representation as a descendant of the ten-dimensional `dual graviton'. The invariant E6(6) symmetric tensor that appears in the vector-tensor hierarchy is reproduced. Generalized vielbeine are derived from the supersymmetry transformations of the vector fields, as well as consistent expressions for the USp(8) covariant fermion fields. Implications are discussed for the consistency of the truncation of IIB supergravity compactified on the five-sphere to maximal gauged supergravity in five space-time dimensions with an SO(6) gauge group.

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arXiv2014

Non-renormalization theorems and N=2 supersymmetric backgrounds

The conditions for fully supersymmetric backgrounds of general N=2 locally supersymmetric theories are derived based on the off-shell superconformal multiplet calculus. This enables the derivation of a non-renormalization theorem for a large class of supersymmetric invariants with higher-derivative couplings. The theorem implies that the invariant and its first order variation must vanish in a fully supersymmetric background. The conjectured relation of one particular higher-derivative invariant with a specific five-dimensional invariant containing the mixed gauge-gravitational Chern-Simons term is confirmed.

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arXiv2013

New higher-derivative invariants in N=2 supergravity and the Gauss-Bonnet term

A new class of N=2 locally supersymmetric higher-derivative invariants is constructed based on logarithms of conformal primary chiral superfields. They characteristically involve a coupling to R_{μν}^2 - 1/3*R^2, which equals the non-conformal part of the Gauss-Bonnet term. Upon combining one such invariant with the known supersymmetric version of the square of the Weyl tensor, one obtains the supersymmetric extension of the Gauss-Bonnet term. The construction is carried out in the context of both conformal superspace and the superconformal multiplet calculus. The new class of supersymmetric invariants resolves two open questions. The first concerns the proper identification of the 4D supersymmetric invariants that arise from dimensional reduction of the 5D mixed gauge-gravitational Chern-Simons term. The second is why the pure Gauss-Bonnet term without supersymmetric completion has reproduced the correct result in calculations of the BPS black hole entropy in certain models.

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arXiv2013

Deformations of gauged SO(8) supergravity and supergravity in eleven dimensions

Motivated by the fact that there exists a continuous one-parameter family of gauged SO(8) supergravities, possible eleven-dimensional origins of this phenomenon are explored. Taking the original proof of the consistency of the truncation of 11D supergravity to SO(8) gauged supergravity as a starting point, a number of critical issues is discussed, such as the preferred electric-magnetic duality frame in four dimensions and the existence of dual magnetic gauge fields and related quantities in eleven dimensions. Some of those issues are resolved but others seem to point to obstructions in embedding the continuous degeneracy in 11D supergravity. While the final outcome of these efforts remains as yet inconclusive, several new results are obtained. Among those is the full non-linear ansatz for the seven-dimensional flux expressed in terms of the scalars and pseudoscalars of 4D supergravity, valid for both the S^7 and the T^7 truncations without resorting to tensor-scalar duality.

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arXiv2012

Non-holomorphic deformations of special geometry and their applications

The aim of these lecture notes is to give a pedagogical introduction to the subject of non-holomorphic deformations of special geometry. This subject was first introduced in the context of N=2 BPS black holes, but has a wider range of applicability. A theorem is presented according to which an arbitrary point-particle Lagrangian can be formulated in terms of a complex function F, whose features are analogous to those of the holomorphic function of special geometry. A crucial role is played by a symplectic vector that represents a complexification of the canonical variables, i.e. the coordinates and canonical momenta. We illustrate the characteristic features of the theorem in the context of field theory models with duality invariances. The function F may depend on a number of external parameters that are not subject to duality transformations. We introduce duality covariant complex variables whose transformation rules under duality are independent of these parameters. We express the real Hesse potential of N=2 supergravity in terms of the new variables and expand it in powers of the external parameters. Then we relate this expansion to the one encountered in topological string theory. These lecture notes include exercises which are meant as a guidance to the reader.

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arXiv2012

The off-shell 4D/5D connection

A systematic off-shell reduction scheme from five to four space-time dimensions is presented for supergravity theories with eight supercharges. It is applicable to theories with higher-derivative couplings and it is used to address a number of open questions regarding BPS black holes in five dimensions. Under this reduction the 5D Weyl multiplet becomes reducible and decomposes into the 4D Weyl multiplet and an extra Kaluza-Klein vector multiplet. The emergence of the pseudoscalar field of the latter multiplet and the emergence of the 4D R-symmetry group are subtle features of the reduction. The reduction scheme enables to determine how a 5D supersymmetric Lagrangian with higher-derivative couplings decomposes upon dimensional reduction into a variety of independent 4D supersymmetric invariants, without the need for imposing field equations. In this way we establish, for example, the existence of a new N=2 supersymmetric invariant that involves the square of the Ricci tensor. Finally we resolve the questions associated with the 5D Chern-Simons terms for spinning BPS black holes and their relation to the corresponding 4D black holes.

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arXiv2011

Electric and magnetic charges in N=2 conformal supergravity theories

General Lagrangians are constructed for N=2 conformal supergravity theories in four space-time dimensions involving gauge groups with abelian and/or non-abelian electric and magnetic charges. The charges are encoded in the gauge group embedding tensor. The scalar potential induced by the gauge interactions is quadratic in this tensor, and, when the embedding tensor is treated as a spurionic quantity, it is formally covariant with respect to electric/magnetic duality. This work establishes a general framework for studying any deformation induced by gauge interactions of matter-coupled N=2 supergravity theories. As an application, full and residual supersymmetry realizations in maximally symmetric space-times are reviewed. Furthermore, a general classification is presented of supersymmetric solutions in $\mathrm{AdS}_2\times S^2$ space-times. As it turns out, these solutions allow either eight or four supersymmetries. With four supersymmetries, the spinorial parameters are Killing spinors of $\mathrm{AdS}_2$ that are constant on $S^2$, so that they carry no spin, while the bosonic background is rotationally invariant.

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arXiv2011

New supersymmetric higher-derivative couplings: Full N=2 superspace does not count!

An extended class of N=2 locally supersymmetric invariants with higher-derivative couplings based on full superspace integrals, is constructed. These invariants may depend on unrestricted chiral supermultiplets, on vector supermultiplets and on the Weyl supermultiplet. Supersymmetry is realized off-shell. A non-renormalization theorem is proven according to which none of these invariants can contribute to the entropy and electric charges of BPS black holes. Some of these invariants may be relevant for topological string deformations.

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arXiv2010

Near-horizon analysis of D=5 BPS black holes and rings

A comprehensive analysis is presented based exclusively on near-horizon data to determine the attractor equations and the entropy of BPS black holes and rings in five space-time dimensions, for a Lagrangian invariant under eight supersymmetries with higher-derivative couplings. For spinning black holes the results only partially agree with the results of previous work, where often additional input was used beyond the near-horizon behaviour. A number of discrepancies remains, for example, pertaining to small black holes and to large spinning black holes, which are related to the presence of the higher-derivative couplings. Arguments are presented to explain some of them. For the black rings, the analysis is intricate due to the presence of Chern-Simons terms and due to the fact that the gauge fields are not globally defined. The contributions from the higher-derivative couplings take a systematic form in line with expectations based on a variety of arguments.

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arXiv2009

Supergravity and M-Theory

Supergravity provides the effective field theories for string compactifications. The deformation of the maximal supergravities by non-abelian gauge interactions is only possible for a restricted class of charges. Generically these `gaugings' involve a hierarchy of p-form fields which belong to specific representations of the duality group. The group-theoretical structure of this p-form hierarchy exhibits many interesting features. In the case of maximal supergravity the class of allowed deformations has intriguing connections with M/string theory.

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arXiv2009

The end of the p-form hierarchy

The introduction of a non-abelian gauge group embedded into the rigid symmetry group G of a field theory with abelian vector fields and no corresponding charges, requires in general the presence of a hierarchy of p-form gauge fields. The full gauge algebra of this hierarchy can be defined independently of a specific theory and is encoded in the embedding tensor that determines the gauge group. When applied to specific Lagrangians, the algebra is deformed in an intricate way and in general will only close up to equations of motion. The group-theoretical structure of the hierarchy exhibits many interesting features, which have been studied starting from the low-p forms. Here the question is addressed what happens generically for high values of p. In addition a number of other features is discussed concerning the role that the p-forms play in various deformations of the theory.

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arXiv2008

Gauged Supergravities, Tensor Hierarchies, and M-Theory

Deformations of maximal supergravity theories induced by gauging non-abelian subgroups of the duality group reveal the presence of charged M-theory degrees of freedom that are not necessarily contained in supergravity. The relation with M-theory degrees of freedom is confirmed by the representation assignments under the duality group of the gauge charges and the ensuing vector and tensor gauge fields. The underlying hierarchy of these gauge fields is required for consistency of general gaugings. As an example gauged maximal supergravity in three space-time dimensions is presented in a version where all possible tensor fields appear.

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arXiv2007

Lagrangians with electric and magnetic charges of N=2 supersymmetric gauge theories

General Lagrangians are constructed for N=2 supersymmetric gauge theories in four space-time dimensions involving gauge groups with (non-abelian) electric and magnetic charges. The charges induce a scalar potential, which, when the charges are regarded as spurionic quantities, is invariant under electric/magnetic duality. The resulting theories are especially relevant for supergravity, but details of the extension to local supersymmetry will be discussed elsewhere. The results include the coupling to hypermultiplets. Without the latter, it is demonstrated how an off-shell representation can be constructed based on vector and tensor supermultiplets.

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