The Vacua of 5d, N=2 Gauged Yang-Mills/Einstein/Tensor Supergravity: Abelian Case

We give a detailed study of the critical points of the potentials of thesimplest non-trivial N=2 gauged Yang-Mills/Einstein supergravity theories withtensor multiplets. The scalar field target space of these examples isSO(1,1)XSO(2,1)/SO(2). The possible gauge groups are SO(2)XU(1)_R andSO(1,1)XU(1)_R, where U(1)_R is a subgroup of the R-symmetry group SU(2)_R, andSO(2) and SO(1,1) are subgroups of the isometry group of the scalar manifold.The scalar potentials of these theories consist of a contribution from theU(1)_R gauging and a contribution that is due to the presence of the tensorfields. We find that the latter contribution can change the form of thesupersymmetric extrema from maxima to saddle points. In addition, it leads tonovel critical points not present in the corresponding gaugedYang-Mills/Einstein supergravity theories without the tensor multiplets. Forthe SO(2)XU(1)_R gauged theory these novel critical points correspond toanti-de Sitter ground states. For the non-compact SO(1,1)XU(1)_R gauging, thenovel ground states are de Sitter. The analysis of the critical points of thepotential carries over in a straightforward manner to the generic family of N=2gauged Yang-Mills/Einstein supergravity theories coupled to tensor multipletswhose scalar manifolds are of the form SO(1,1)XSO(n-1,1)/SO(n-1).We give a detailed study of the critical points of the potentials of the simplest non-trivial N=2 gauged Yang-Mills/Einstein supergravity theories with tensor multiplets. The scalar field target space of these examples is SO(1,1)XSO(2,1)/SO(2). The possible gauge groups are SO(2)XU(1)_R and SO(1,1)XU(1)_R, where U(1)_R is a subgroup of the R-symmetry group SU(2)_R, and SO(2) and SO(1,1) are subgroups of the isometry group of the scalar manifold. The scalar potentials of these theories consist of a contribution from the U(1)_R gauging and a contribution that is due to the presence of the tensor fields. We find that the latter contribution can change the form of the supersymmetric extrema from maxima to saddle points. In addition, it leads to novel critical points not present in the corresponding gauged Yang-Mills/Einstein supergravity theories without the tensor multiplets. For the SO(2)XU(1)_R gauged theory these novel critical points correspond to anti-de Sitter ground states. For the non-compact SO(1,1)XU(1)_R gauging, the novel ground states are de Sitter. The analysis of the critical points of the potential carries over in a straightforward manner to the generic family of N=2 gauged Yang-Mills/Einstein supergravity theories coupled to tensor multiplets whose scalar manifolds are of the form SO(1,1)XSO(n-1,1)/SO(n-1)

Options for Gauge Groups in Five-Dimensional Supergravity

Motivated by the possibility that physics may be effectively five-dimensional over some range of distance scales, we study the possible gaugings of five-dimensional N=2 supergravity. Using a constructive approach, we derive the conditions that must be satisfied by the scalar fields in the vector, tensor and hypermultiplets if a given global symmetry is to be gaugeable. We classify all those theories that admit the gauging of a compact group that is either Abelian or semi-simple, or a direct product of a semi-simple and an Abelian group. In the absence of tensor multiplets, either the gauge group must be semi-simple or the Abelian part has to be U(1)_R and/or an Abelian isometry of the hyperscalar manifold. On the other hand, in the presence of tensor multiplets the gauge group cannot be semi-simple. As an illustrative exercise, we show how the Standard Model SU(3) X SU(2) X U(1) group may be gauged in five-dimensional N=2 supergravity. We also show how previous special results may be recovered within our general formalism

Non-prescription dispensing of emergency oral contraceptives: Recommendations from the German Federal Chamber of Pharmacists [Bundesapothekerkammer].

BACKGROUND: Emergency hormonal contraceptives (EHC) are contraceptives used to prevent unintended pregnancy following unprotected sexual intercourse (USI) or contraceptive failure. The EHCs available without a prescription include medicines containing levonorgestrel (LNG) in more than 80 countries and, recently, based on an EU-switch ellaOne®, which contains ulipristal acetate (UPA). EHCs work by stopping or delaying ovulation. Those containing LNG can be used up to 72 hours after USI or contraceptive failure, while UPA can be used up to 120 hours. In the context of the UPA implementation process, Germany switched LNG to non-prescription status as well. OBJECTIVES: To develop recommendations, a protocol, and a continuing education program for pharmacists to assure quality when giving advice and dispensing EHCs in community pharmacies without a medical prescription. METHODS: The recommendations were developed by an iterative process of drafting, recognizing, and discussing comments and proposals for amendments as well a seeking agreement with a number of stakeholders such as the Federal Ministry of Health (BMG), Federal Institute for Drugs and Medical Devices (BfArM), Federal Chamber of Physicians (BÄK), Drug Commission of German Physicians (AkdÄ), professional organizations/associations of gynaecologists, pharmaceutical OTC-industry as well as government-controlled, private, and church-based organizations and centres providing advice on sex education and family planning. RESULTS: The recommendations were eventually endorsed by the BMG in consultation with the BfArM. CONCLUSIONS: The recommendations were made public, published in the professional journal and used in an uncounted number of continuing education programs based on the curriculum and provided by the State Chambers of Pharmacists

Electric/magnetic duality for chiral gauge theories with anomaly cancellation

We show that 4D gauge theories with Green-Schwarz anomaly cancellation and possible generalized Chern-Simons terms admit a formulation that is manifestly covariant with respect to electric/magnetic duality transformations. This generalizes previous work on the symplectically covariant formulation of anomaly-free gauge theories as they typically occur in extended supergravity, and now also includes general theories with (pseudo-)anomalous gauge interactions as they may occur in global or local N=1 supersymmetry. This generalization is achieved by relaxing the linear constraint on the embedding tensor so as to allow for a symmetric 3-tensor related to electric and/or magnetic quantum anomalies in these theories. Apart from electric and magnetic gauge fields, the resulting Lagrangians also feature two-form fields and can accommodate various unusual duality frames as they often appear, e.g., in string compactifications with background fluxes.Comment: 37 pages; v2: typos corrected and 1 reference adde

Gauging the Full R-Symmetry Group in Five-dimensional, N=2 Yang-Mills/Einstein/tensor Supergravity

We show that certain five dimensional, N=2 Yang-Mills/Einstein supergravity theories admit the gauging of the full R-symmetry group, SU(2)_R, of the underlying N=2 Poincare superalgebra. This generalizes the previously studied Abelian gaugings of U(1)_R subgroup of SU(2)_R and completes the construction of the most general vector and tensor field coupled five dimensional N=2 supergravity theories with gauge interactions. The gauging of SU(2)_R turns out to be possible only in special cases, and leads to a new type of scalar potential. For a large class of these theories the potential does not have any critical points.Comment: Latex file, 15 pages ; section two is split in two and the discussion of the critical points is moved into the new section. Version to appear in Physical Review

The Gauging of Five-dimensional, N=2 Maxwell-Einstein Supergravity Theories coupled to Tensor Multiplets

We study the general gaugings of N=2 Maxwell-Einstein supergravity theories (MESGT) in five dimensions, extending and generalizing previous work. The global symmetries of these theories are of the form SU(2)_R X G, where SU(2)_R is the R-symmetry group of the N=2 Poincare superalgebra and G is the group of isometries of the scalar manifold that extend to symmetries of the full action. We first gauge a subgroup K of G by turning some of the vector fields into gauge fields of K while dualizing the remaining vector fields into tensor fields transforming in a non-trivial representation of K. Surprisingly, we find that the presence of tensor fields transforming non-trivially under the Yang-Mills gauge group leads to the introduction of a potential which does not admit an AdS ground state. Next we give the simultaneous gauging of the U(1)_R subgroup of SU(2)_R and a subgroup K of G in the presence of K-charged tensor multiplets. The potential introduced by the simultaneous gauging is the sum of the potentials introduced by gauging K and U(1)_R separately. We present a list of possible gauge groups K and the corresponding representations of tensor fields. For the exceptional supergravity we find that one can gauge the SO^*(6) subgroup of the isometry group E_{6(-26)} of the scalar manifold if one dualizes 12 of the vector fields to tensor fields just as in the gauged N=8 supergravity.Comment: Latex file, 23 page

Novel supermultiplets of SU(2,2|4) and the AdS_5/CFT_4 duality

We continue our study of the unitary supermultiplets of the N=8, d=5 anti-de Sitter (AdS_5) superalgebra SU(2,2|4), which is also the N=4 extended conformal superalgebra in d=4. We show explicitly how to go from the compact SU(2)XSU(2)XU(1) basis to the non-compact SL(2,C)XD basis of the positive energy unitary representations of the conformal group SU(2,2) in d=4. The doubleton representations of the AdS_5 group SU(2,2), which do not have a smooth Poincare limit in d=5, are shown to represent fields with vanishing masses in four dimensional Minkowski space. The unique CPT self-conjugate irreducible doubleton supermultiplet of SU(2,2|4)is simply the N=4 Yang-Mills supermultiplet in d=4. We study some novel short non-doubleton supermultiplets of SU(2,2|4) that have spin range 2 and that do not appear in the Kaluza-Klein spectrum of type IIB supergravity or in tensor products of the N=4 Yang-Mills supermultiplet with itself. These novel supermultiplets can be obtained from tensoring chiral doubleton supermultiplets, some of which we expect to be related to the massless limits of 1/4 BPS states. Hence, these novel supermultiplets may be relevant to the solitonic sector of IIB superstring and/or (p,q) superstrings over AdS_5 X S^5.Comment: Minor modifications to clarify the role of central charge and the outer automorphism group U(1)_Y in the representation theory of SU(2,2|4); typos corrected; 28 pages; Late

Unified Maxwell-Einstein and Yang-Mills-Einstein Supergravity Theories in Five Dimensions

Unified N=2 Maxwell-Einstein supergravity theories (MESGTs) are supergravity theories in which all the vector fields, including the graviphoton, transform in an irreducible representation of a simple global symmetry group of the Lagrangian. As was established long time ago, in five dimensions there exist only four unified Maxwell-Einstein supergravity theories whose target manifolds are symmetric spaces. These theories are defined by the four simple Euclidean Jordan algebras of degree three. In this paper, we show that, in addition to these four unified MESGTs with symmetric target spaces, there exist three infinite families of unified MESGTs as well as another exceptional one. These novel unified MESGTs are defined by non-compact (Minkowskian) Jordan algebras, and their target spaces are in general neither symmetric nor homogeneous. The members of one of these three infinite families can be gauged in such a way as to obtain an infinite family of unified N=2 Yang-Mills-Einstein supergravity theories, in which all vector fields transform in the adjoint representation of a simple gauge group of the type SU(N,1). The corresponding gaugings in the other two infinite families lead to Yang-Mills-Einstein supergravity theories coupled to tensor multiplets.Comment: Latex 2e, 28 pages. v2: reference added, footnote 14 enlarge

4D Doubleton Conformal Theories, CPT and IIB String on AdS_5 X S^5

We study the unitary supermultiplets of the N=8, d=5 anti-de Sitter (AdS) superalgebra SU(2,2|4) which is the symmetry algebra of the IIB string theory on AdS_5 X S^5. We give a complete classification of the doubleton supermultiplets of SU(2,2|4) which do not have a Poincare limit and correspond to d=4 conformal field theories (CFT) living on the boundary of AdS_5. The CPT self-conjugate irreducible doubleton supermultiplet corresponds to d=4, N = 4 super Yang-Mills theory. The other irreducible doubleton supermultiplets come in CPT conjugate pairs. The maximum spin range of the general doubleton supermultiplets is 2. In particular, there exists a CPT conjugate pair of doubleton supermultiplets corresponding to the fields of N=4 conformal supergravity in d=4 which can be coupled to N=4 super Yang-Mills theory in d=4. We also study the "massless" supermultiplets of SU(2,2|4) which can be obtained by tensoring two doubleton supermultiplets. The CPT self-conjugate "massless" supermultiplet is the N=8 graviton supermultiplet in AdS_5. The other "massless" supermultiplets generally come in conjugate pairs and can have maximum spin range of 4. We discuss the implications of our results for the conjectured CFT/AdS dualities.Comment: An erratum attached at the end to correct an incorrect statement in section 7; 34 pages, Latex fil