Poincare Supergravity Research Articles

Relaxed hypermultiplet in four dimensional N=2 conformal supergravity

Superconformal matter multiplets play a crucial role in the construction of Poincare supergravity invariants. Off-shell multiplets allow for construction of general matter couplings in supergravity. In Nucl. Phys. B214 (1983) 519-531, relaxed hypermultiplet was constructed in rigid supersymmetry which on coupling with the real scalar multiplet allowed for an off-shell formulation of the rigid hypermultiplet. In this paper, we extend the relaxed hypermultiplet to conformal supergravity. For consistency with the superconformal algebra, we find that the fields have to be allowed to transform in a non-canonical way under SU(2) symmetry. We find suitable field redefinitions to obtain fields which are irreducible representations of SU(2) R-symmetry and present the full non-linear transformation rule.

Component versus superspace approaches to D = 4, N = 1 conformal supergravity

The superspace formulation of N=1 conformal supergravity in four dimensions is demonstrated to be equivalent to the conventional component field approach based on the superconformal tensor calculus. The detailed correspondence between two approaches is explicitly given for various quantities; superconformal gauge fields, curvatures and curvature constraints, general conformal multiplets and their transformation laws, and so on. In particular, we carefully analyze the curvature constraints leading to the superconformal algebra and also the superconformal gauge fixing leading to Poincare supergravity since they look rather different between two approaches.

Conformal a-anomaly of some non-unitary 6d superconformal theories

We compute the conformal anomaly a-coefficient for some non-unitary (higher derivative or non-gauge-invariant) 6d conformal fields and their supermultiplets. We use the method based on a connection between 6d determinants on S^6 and 7d determinants on AdS_7. We find, in particular, that (1,0) supermultiplet containing 4-derivative gauge-invariant conformal vector has precisely the value of a-anomaly as attributed in arXiv:1506.03807 (on the basis of R-symmetry and gravitational 't Hooft matching) to the standard (1,0) vector multiplet. We also show that higher derivative (2,0) 6d conformal supergravity coupled to exactly 26 (2,0) tensor multiplets has vanishing a-anomaly. This is the 6d counterpart of the known fact of cancellation of the conformal anomaly in the 4d system of N=4 conformal supergravity coupled to 4 vector N=4 multiplets. In the case when 5 of tensor multiplets are chosen to be ghost-like and the conformal symmetry is spontaneously broken by a quadratic scalar constraint the resulting IR theory may be identified with (2,0) Poincare supergravity coupled to 21=26-5 tensor multiplets. The latter theory is known to be special: it is gravitational anomaly free and results upon compactification of 10d type IIB supergravity on K3.

Supersymmetric backgrounds from 5d N $$ \mathcal{N} $$ = 1 supergravity

We construct curved backgrounds with Euclidean signature admitting rigid supersymmetry by using a 5d N=1 off-shell Poincare supergravity. We solve the conditions for the background Weyl multiplet and vector multiplets that preserve at least one supersymmetry parameterized by a symplectic Majorana spinor, and represent the solution in terms of several independent fields. We also show that the partition function does not depends on the local degrees of freedom of the background fields. Namely, as far as we focus on a single coordinate patch, we can freely change the independent fields by combining Q-exact deformations and gauge transformations. We also discuss realization of several known examples of supersymmetric theories in curved backgrounds by using the supergravity.

On the supersymmetrization of inflation in f (R) gravity

An N=1 Poincare supergravity action, suitable for describing the Starobinsky inflation, is proposed. It extends f(R) gravity to supergravity in its old-minimal version. The action is parametrized by a single holomorphic potential and a single non-holomorphic potential, and can be dualized into the standard matter-coupled supergravity action, with the "matter" given by two chiral superfields. The action extends the earlier proposals for embedding the Starobinsky inflation into supergravity, and can be further generalized to include quantum corrections to the inflation. Our approach assumes the gravitational origin of inflaton and quintessence in the context of supergravity, by using a single chiral scalar curvature superfield.

On the U(1) duality anomaly and the S-matrix of $ \mathcal{N} $ = 4 supergravity

N=4 Poincare supergravity has a global SU(1,1) duality symmetry that acts manifestly only on shell as it involves duality rotations of vector fields. A U(1) subgroup of this symmetry is known to be anomalous at the quantum level in the presence of a non-trivial gravitational background. We first derive this anomaly from a novel perspective, by relating it to a similar anomaly in conformal supergravity where SU(1,1) acts off shell, using the fact that N=4 Poincare supergravity has a superconformal formulation. We explicitly construct the corresponding local and nonlocal anomalous terms in the one-loop effective action. We then study how this anomaly is reflected in the supergravity S-matrix. Calculating one-loop N=4 supergravity scattering amplitudes (with and without additional matter multiplets) using color/kinematics duality and the double-copy construction we find that a particular U(1) symmetry which was present in the tree-level amplitudes is broken at the quantum level. This breaking manifests itself in the appearance of new one-loop N=4 supergravity amplitudes that have non-vanishing soft-scalar limits (these amplitudes are absent in N>4 supergravities). We discuss the relation between these symmetry-violating amplitudes and the corresponding U(1) anomalous term in the one-loop supergravity effective action.

Conjecture on hidden superconformal symmetry ofN=4supergravity

We argue that the observed UV finiteness of the 3-loop extended supergravities may be a manifestation of a hidden local superconformal symmetry of supergravity. We focus on the $SU(2,2|4)$ dimensionless superconformal model. In the Poincar\'e gauge where the compensators are fixed to ${\ensuremath{\phi}}^{2}=6{M}_{P}^{2}$ this model becomes a pure classical $N=4$ Einstein supergravity. We argue that in $N=4$ the higher-derivative superconformal invariants like ${\ensuremath{\phi}}^{\ensuremath{-}4}{W}^{2}{\overline{W}}^{2}$ and the consistent local anomaly $\ensuremath{\delta}(\mathrm{ln}\ensuremath{\phi}{W}^{2})$ are not available. This conjecture on hidden local $N=4$ superconformal symmetry of Poincar\'e supergravity may be supported by subsequent loop computations.

$ \mathcal{N} = 2 $ supergravity and supercurrents

We address the problem of classifying all N=2 supercurrent multiplets in four space-time dimensions. For this purpose we consider the minimal formulation of N=2 Poincare supergravity with a tensor compensator, and derive its linearized action in terms of three N=2 off-shell multiplets: an unconstrained scalar superfield, a vector multiplet, and a tensor multiplet. Such an action was ruled out to exist in the past. Using the action constructed, one can derive other models for linearized N=2 supergravity by applying N=2 superfield duality transformations. The action depends parametrically on a constant non-vanishing real isotriplet g^{ij}=g^{ji} which originates as an expectation value of the tensor compensator. Upon reduction to N=1 superfields, we show that the model describes two dually equivalent formulations for the massless multiplet (1,3/2)+(3/2,2) depending on a choice of g^{ij}. In the case g^{11}=g^{22}=0, the action describes (i) new minimal N=1 supergravity; and (ii) the Fradkin-Vasiliev-de Wit-van Holten gravitino multiplet. In the case g^{12}=0, on the other hand, the action describes (i) old minimal N=1 supergravity; and (ii) the Ogievetsky-Sokatchev gravitino multiplet.

Massive three-dimensional supergravity from R + R 2 action in six dimensions

We obtain a three-parameter family of massive N=1 supergravities in three dimensions from the 3-sphere reduction of an off-shell N=(1,0) six-dimensional Poincare supergravity that includes a curvature squared invariant. The three-dimensional theory contains an off-shell supergravity multiplet and an on-shell scalar matter multiplet. We then generalise this in three dimensions to an eight-parameter family of supergravities. We also find a duality relationship between the six-dimensional theory and the N=(1,0) six-dimensional theory obtained through a T^4 reduction of the heterotic string effective action that includes the higher-order terms associated with the supersymmetrisation of the anomaly-cancelling \tr(R\wedge R) term.

Four-dimensional conformal supergravity from AdS space

Exploring the role of conformal theories of gravity in string theory, we show that the minimal (N=2) gauged supergravities in five dimensions induce the multiplets and transformations of N=1 four dimensional conformal supergravity on the spacetime boundary. N=1 Poincare supergravity can be induced by explicitly breaking the conformal invariance via a radial cutoff in the 5d space. The AdS/CFT correspondence relates the maximal gauged supergravity in five dimensions to N=4 super Yang-Mills on the 4d spacetime boundary. In this context we show that the conformal anomaly of the gauge theory induces conformal gravity on the boundary of the space and that this theory, via the renormalization group, encapsulates the gravitational dynamics of the skin of asymptotically AdS spacetimes. Our results have several applications to the AdS/CFT correspondence and the Randall-Sundrum scenario.

Geometry of the scalar couplings in N=2 supergravity models

The author describes the quaternionic geometry of various sigma -model target spaces for the hypermultiplet couplings in four-dimensional N=2 conformal and Poincare supergravity models. The process of eliminating the non-physical superconformal gauge fields of chiral SU(2) and dilations is examined in the context of the quaternionic associated bundle. The sigma -model target space X parametrized by the scalar fields of the hypermultiplets in an N=2 conformal supergravity-matter Lagrangian is shown to be the quaternionic associated bundle of the sigma -model quaternionic Kahler target space M of the corresponding N=2 Poincare supergravity-matter system. The manifold X is special hyperKahler manifold with an isomeric SU(2) action rotating the hyperKahler structure and M can be obtained as a certain SU(2) reduction of X. This suggests possible generalizations of the superconformal tensor calculus and the Lagrangian constructed by de Wit et al (1985). The quaternionic Kahler join and some new matter couplings are also discussed.

A general tensor calculus for old-minimal Poincare supergravity

The necessary formulae for a complete tensor calculus adequate for multiplets with arbitrary external Lorentz indices, in old-minimal supergravity, are provided.

ISO(3,1�N) andOSp(N�4) supergravities

We advance anISO(3,1¦N) extended Poincare supergravity and anOSp(N¦4) de Sitter supergravity by using the supergauge action mechanisms of supergroups on the superspaces and by treating the gravitational parts of these two supergravities as the gauge theories of gravity, give a new matrix representation ofISO(3,1¦N) generators and a new one ofOSp(N¦4) ones, obtain the commutation and anticommutation relations ofiso(3, 1¦N) andosp(N¦4) superalgebras, construct the actions of these Supergravities and discuss some other problems. A particle multiplets method based on the supersymmetry transformation is used and the probable numbers of particles of different helicities in the two supergravities are given.

BRS algebras of Poincar� and conformal supergravity

Starting from the geometric BRS differential algebra in superspace, we elucidate a recently given method [1] for deriving the BRS component field algebras of Poincare supergravity and we extend this formalism to conformai supergravity. For the latter, the general procedure is illustrated in detail by the two-dimensional (1, 0) theory. In conclusion, we explicitly check the consistency of the whole approach and apply it to verify the WZ integrability condition for the (1, 0) superconformai anomaly.

Off-shell six-dimensional supergravity in harmonic superspace

A fully off-shell action for N=2, d=6 Poincare supergravity in harmonic superspace is proposed. It consists of the off-shell actions for a scalar multiplet and for a self-dual tensor multiplet in conformal supergravity background. A new mechanism for describing self-dual tensor fields off shell, in which conformal supergravity plays an active role, is found.

Geometric N=4 supergravity

The SU(4) symmetric version of N=4, d=4 Poincare supergravity is constructed geometrically. The underlying gauge algebra is a synthesis of a modified orthosymplectic algebra and the SU(1, 1)/U(1) sigma -model structure of the scalar fields. The author uses the group manifold approach to gauge this algebra.

N = 2 Supersymmetry and the IrreducibleSU(2) -Extended Superfields

The structure of the irreducible SU(2)-extended superfields in the usual N = 2 superspace is investigated in detail. We derive the irreducible superfield contents of a general N = 2 scalar superfield and give the complete off-shell component description of all the irreducible N = 2 scalar superfields, by considering N = 2 supersymmetry as the SU(2)-invariant combination of two simple N = 1 supersymmetries. We give also the systematic method of explicit construction of any irreducible N = 2 superfield with external SL(2, C) ⊗ SU(2) index on the basis of the solution to all the irreducible scalar N = 2 superfields. To demonstrate the applications of the method, the linearized N = 2 conformal and Poincare supergravities are rederived. We apply N = 2 superapace methods to construct various non-linear sigma models with extended supersymmetry. The latter are proved to be non-renormalizable in the four-dimensional space-time, but finite to all orders in a perturbation theory in two space-time dimensions. The couplings of N = 2 nonlinear sigma models under consideration to N = 2 super-Yang-Mills fields are diacuseed too. In conclusion, an outline of the similar approach to the construction of the irreducible superfields in N = 4 superspace is given. The article can be viewed as the Introduction to N = 2 superspace.

The geometry of N=2 supergravity in harmonic superspace

The authors give a complete description of 'standard' N=2 Poincare supergravity in harmonic superspace. The main constraint they impose is preservation of the analytic subspace by supergravity transformations, so as to allow the coupling of supergravity to analytic matter superfields. Supplemented by 'conventional' and conformal breaking constraints, this requirement is shown to define the whole theory in terms of an unconstrained analytic prepotential.

Covariant formalism of reductions of superconformal gauge theories to Poincar� supergravities

A covariant formalism of reductions from general gauges of extended supergroups to Poincare supergravities off the mass shell is considered. The formalism is based on consideration of a field system containing besides gauge fields Goldstone superfields that parametrize the factor space of broken symmetries and are associated with purely gauge degrees of freedom. By the choice of the gauge supergroup, the stability subgroup, the (super)group of diffeomorphisms of the base, and the structure of the Goldstone superfields, which form compensators of the spontaneously broken symmetries, the supermultiplet of physical and auxiliary fields that must be used for the dynamical description of the system is completely determined.

Structure ofN=1 conformal and Poincaré supergravity in 1+1 and 2+1 dimensions

We discuss a component formalism ofN=1 supergravity theories in 2 and 3 spacetime dimensions. Starting from gauge theories of the superconformal group, we derive the tensor calculus for conformal and Poincare supergravity theories. A supersymmetric extension of the non-trivial analog of Einstein's equation for 2 dimensions is given in terms of the scalar curvature multiplet.