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Register a new userNon-geometric fluxes as supergravity backgrounds
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We consider examples of D=4 string theory vacua which, although globally non-geometric, admit a local description in terms of D=10 supergravity backgrounds. We analyze such backgrounds and find that the supersymmetry spinors vary non-trivially along the internal manifold, reproducing the interpolating supergravity solutions found by Frey and Grana. Finally, we propose a simple, local expression for non-geometric fluxes in terms of the internal spinors of the compactification.
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We discuss the relation between generalised fluxes and mixed-symmetry potentials. We first consider the NS fluxes, and point out that the `non-geometric $R$ flux is dual to a mixed-symmetry potential with a set of nine antisymmetric indices. We then consider the T-duality family of fluxes whose prototype is the Scherk-Schwarz reduction of the S-dual of the RR scalar of IIB supergravity. Using the relation with mixed-symmetry potentials, we are able to give a complete classification of these fluxes, including the ones that are non-geometric. The non-geometric fluxes again turn out to be dual to potentials containing nine antisymmetric indices. Our analysis suggests that all these fluxes can be understood in the context of double field theory, although for the non-geometric ones one expects a violation of the strong constraint.
In four spacetime dimensions, all ${cal N} =1$ supergravity-matter systems can be formulated in the so-called $mathsf{U}(1)$ superspace proposed by Howe in 1981. This paper is devoted to the study of those geometric structures which characterise a background $mathsf{U}(1)$ superspace and are important in the context of supersymmetric field theory in curved space. We introduce (conformal) Killing tensor superfields $ell_{(alpha_1 dots alpha_m) ({dot alpha}_1 dots {dot alpha}_n)}$, with $m$ and $n$ non-negative integers, $m+n>0$, and elaborate on their significance in the following cases: (i) $m=n=1$; (ii) $m-1=n=0$; and (iii) $m=n>1$. The (conformal) Killing vector superfields $ell_{alpha dot alpha}$ generate the (conformal) isometries of curved superspace, which are symmetries of every (conformal) supersymmetric field theory. The (conformal) Killing spinor superfields $ell_{alpha }$ generate extended (conformal) supersymmetry transformations. The (conformal) Killing tensor superfields with $m=n>1$ prove to generate all higher symmetries of the (massless) massive Wess-Zumino operator.
We derive the Free Differential Algebra for type IIA supergravity in 10 dimensions in the string frame. We provide all fermionic terms for all curvatures. We derive the Green-Schwarz sigma model for type IIA superstring based on the FDA construction and we check its invariance under kappa-symmetry. Finally, we derive the pure spinor sigma model and we check the BRST invariance. The present derivation has the advantage that the resulting sigma model is constructed in terms of the superfields appearing in the FDA and therefore one can directly relate a supergravity background with the corresponding sigma model. The complete explicit form of the BRST transformations is given and some new pure spinor constraints are obtained. Finally, the explicit form of the action is given.
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Sergei M. Kuzenko
, Ulf Lindstrom
, Emmanouil S. N. Raptakis andn Gabriele Tartaglino-Mazzucchelli
2020
General $mathcal{N}=(1,0)$ supergravity-matter systems in six dimensions may be described using one of the two fully fledged superspace formulations for conformal supergravity: (i) $mathsf{SU}(2)$ superspace; and (ii) conformal superspace. With motivation to develop rigid supersymmetric field theories in curved space, this paper is devoted to the study of the geometric symmetries of supergravity backgrounds. In particular, we introduce the notion of a conformal Killing spinor superfield $epsilon^alpha$, which proves to generate extended superconformal transformations. Among its cousins are the conformal Killing vector $xi^a$ and tensor $zeta^{a(n)}$ superfields. The former parametrise conformal isometries of supergravity backgrounds, which in turn yield symmetries of every superconformal field theory. Meanwhile, the conformal Killing tensors of a given background are associated with higher symmetries of the hypermultiplet. By studying the higher symmetries of a non-conformal vector multiplet we introduce the concept of a Killing tensor superfield. We also analyse the problem of computing higher symmetries for the conformal dAlembertian in curved space and demonstrate that, beyond the first-order case, these operators are defined only on conformally flat backgrounds.
Motivated by possible implications on the problem of moduli stabilization and other phenomenological aspects, we study D-brane instanton effects in flux compactifications. We focus on a local model and compute non-perturbative interactions generated by gauge and stringy instantons in a N = 1 quiver theory with gauge group U(N_0) x U(N_1) and matter in the bifundamentals. This model is engineered with fractional D3-branes at a C^3/(Z_2 x Z_2) singularity, and its non-perturbative sectors are described by introducing fractional D-instantons. We find a rich variety of instanton-generated F- and D-term interactions, ranging from superpotentials and Beasley-Witten like multi-fermion terms to non-supersymmetric flux-induced instanton interactions.
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