\( \mathcal{N}=2 \) dilaton-Weyl multiplets in 5D and Nishino-Rajpoot supergravity off-shell

Received: November Published for SISSA by Springer Open Access 0 1 c The Authors. 0 1 0 Repu blica 220 , Santiago , Chile 1 Departamento de Ciencias F sicas, Universidad Andr es Bello We describe in detail the derivation of a superconformal off-shell formulation of the alternative N = 2, d = 5 ungauged supergravity of Nishino and Rajpoot, coupled to n Abelian vector multiplets, using a general dilaton-Weyl multiplet. We generalize the vector multiplet coupling available in the literature and show under which assumptions that the scalar manifold reduces to the known case of SO(1, 1) SO(1, n)/SO(n). As an application of the formalism we propose generalized vector multiplet coupled higher curvature terms, whose construction we sketch briefly. Supergravity Models; Supersymmetry and Duality - 2 dilaton-Weyl multiplets in 5D Nishino-Rajpoot supergravity off-shell 1 Introduction 2 3 4 Higher derivative densities Ricci squared invariant Weyl squared invariant Pure N-R supergravity from the off-shell superconformal formalism Coupling to Abelian vector multiplets A Generalized dilaton-Weyl superconformal multiplets B Explicit field redefinition Vector multiplet composed of a linear multiplet Introduction given in [1, 2] and the U(1) gauged case was first described in [3]. In [47] on-shell methods were used to treat the case of this supergravity coupled to vector multiplets. Hypermultiplet couplings and gaugings were considered in [810] and tensor multiplet matter in [11, 12] along with gaugings of isometries of a subgroup of the isometry group of the scalar manifold. The theory can also be obtained from compactification of M-theory on a Calabi-Yau threefold CY3 [13, 14]. The resulting Lagrangian depends on topological data of the compactification manifold, namely the Calabi-Yau intersection numbers. explicitly and in order to investigate effective descriptions of string theory it became important to include the dilaton and antisymmetric fields, so off-shell formulations [1520] were explored to facilitate the construction of matter coupled supergravities, although these fields [21]. In [22], Nishino and Rajpoot proposed an alternative on-shell formulation of freedom. Vector and hypermultiplets [23] have been coupled to this supergravity theory, structure is different. In fact, it was shown in [25] that the dilaton-Weyl multiplet can be obtained by coupling the standard multiplet to an improved vector multiplet. a superspace perspective, and further work using the superconformal formulation [25, 27] allowed the construction of superconformal multiplets and their corresponding actions [19, formulation [29]. The resulting theories preserve eight supersymmetries1 [30] and can be studied at depth with the tools of special geometry [3134], the condition for which arises in the off-shell theory as a constraint coming from a scalar Lagrange multiplier auxiliary field of the standard-Weyl multiplet. The advantage of the off-shell formulation is that we may find higher derivative densities, which are important from a string theory perspective, without changing the supersymmetry transformations, and therefore inducing corrections to our original action, an iterative process that may never terminate. The higher derivative densities that are supersymmetric completions of the square of the Ricci scalar and the square of the Weyl tensor have been produced in the background of the standard-Weyl superconformal gravitational multiplet in [35, 36]. In [25] dilaton-Weyl multiplets were introduced including the two form, the dilaton and the dilatino, whilst in [27] dilaton-Weyl multiplets incorporating more than one vector multiplet were introduced. In [3742] an off-shell superspace formulation of the superconformal theory has been developed, which should lead to the most general couplings, and indeed the dilaton-Weyl multiplet was considered in these works. We find it useful to add to the literature an explicit derivation of the N-R supergravity from the off-shell formulation by means of gauge fixing and field redefinitions, complimenting the work done in [27]. We shall discuss in detail the vector multiplet couplings of this theory. We shall also discuss simple generalizations of two of the higher derivative densities [35, 36] found in the literature. This paper is organized as follows. In section 2 we discuss the derivation of the minimal N-R supergravity and in section 3 we couple to Abelian vector multiplets and relegate to appendix B the explicit constant field redefinitions needed to arrive at the conventions of [22, 23]. In section 4 we generalize the known higher derivative densities to the extended dilaton-Weyl multiplets that we describe in appendix A, in which we make use of a composition of a vector multiplet in terms of a linear multiplet [43] that we give in appendix C. We conclude in section 5. Acknowledgments The work of the author is supported by FONDECYT Postdoctorado Project number 3130541. The author would like to thank Linda Uruchurtu, Jorge Bellorn and Hitoshi Nishino for useful correspondence and discussions, and Per Sundell and Rodrigo Olea for presented in terms of Dirac spinors. Of course these two descriptions both have 8 real components of the In this section we give the details of the construction of the N-R supergravity [22, 23] from the off-shell formalism based on the superconformal dilaton-Weyl multiplet described in [43]. We also describe an alternative procedure put forward in [27]. To couple the theory of [43] to vector multiplets one may use the results of [36], however following the procedure of [27] we will be led to introduce a larger generalized dilaton-Weyl multiplet, which includes an arbitrary number of vector multiplets. It is instructive to consider the case of the pure N-R supergravity first, and then the coupling to vector multiplets separately. The pure N-R supergravity can be constructed straightforwardly using exactly the results of [43], whose conventions we will follow, which are described in detail in [25]. However we shall construct it in a slightly different way that was suggested in [27], as we will emphasize below. The two derivative theory is constructed by combining a vector multiplet action and a compensating linear multiplet action, obtained in the background of a Weyl multiplet. We suppress the spinor indices in bilinears using the NW-SE convention and we raise and lower the SU(2) indices using the totally antisymmetric tensor ij where j 12 = 12 = 1, e.g. = i i = i ji. We will frequently use the notation that for two p-forms , , we define = 1 p 1 p , and 2 = . There are two types of Weyl multiplet, the so called standard-Weyl multiplet and the dilaton-Weyl multiplet. The standard-Weyl multiplet consists of the vielbien em, gravitino These transform under supersymmetry with parameter i and special supersymmetry with + i V ijj + imnT mn i i i , Di 64 8 1 T 2i + where the the spin covariant derivative i (...truncated)