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We review the dynamical generation of coupling constants in 4D supergravity by means of gauge three-form fields. The latter are introduced as components of particular chiral supermultiplets and can be coupled to membranes preserving local supersymmetry. Such a set-up naturally arises from type-II string compactifications on Calabi-Yau manifolds with fluxes. We present generic 4D $\mathcal N=1$ supergravity models with three-form multiplets and study domain wall solutions supported by membranes, which interpolate between vacua with different values of the cosmological constant., Comment: 13 pages, Contribution to Proceedings of LMS/EPSRC Durham Symposium Higher Structures in M-Theory, August 2018

We develop a superfield formulation of gauge and matter field theories on a two-dimensional sphere with rigid N=(2,2) as well as extended supersymmetry. The construction is based on a supercoset SU(2|1)/[U(1) x U(1)] containing $S^2$ as the bosonic subspace. We derive an explicit form of supervielbein and covariant derivatives on this coset, and use them to construct classical superfield actions for gauge and matter supermultiplets in this superbackground. We then apply superfield methods for computing one-loop partition functions of these theories and demonstrate how the localization technique works directly in the superspace., Comment: 1+44 pages

With the motivation to develop superconformal field theory on S^3, we introduce a 2n-extended supersphere S^{3|4n}, with n=1,2,..., as a homogeneous space of the three-dimensional Euclidean superconformal group OSp(2n|2,2) such that its bosonic body is S^3. Supertwistor and bi-supertwistor realizations of S^{3|4n} are derived. We study in detail the n=1 case, which is unique in the sense that the R-symmetry subgroup SO^*(2n) of the superconformal group is compact only for n=1. In particular, we show that the OSp(2|2,2) transformations preserve the chiral subspace of S^{3|4}. Several supercoset realizations of S^{3|4n} are presented. Harmonic/projective extensions of the supersphere by auxiliary bosonic fibre directions are sketched., Comment: 44 pages; V2: references added, typos corrected; V3: comments in Appendix B corrected

We consider the superfield formulation of supersymmetric gauge and matter field theories on a three-dimensional sphere with rigid ${\cal N}=2$ supersymmetry, as well as with ${\cal N}> 2$. The construction is based on a supercoset $SU(2|1)/U(1)$ containing $S^3$ as the bosonic subspace. We derive an explicit form of $SU(2|1)/U(1)$ supervielbein and covariant derivatives, and use them to construct classical superfield actions for gauge and matter supermultiplets in this superbackground. We then apply superfield methods for computing one-loop partition functions of these theories and demonstrate how the localization technique works directly in the superspace., Comment: 1+64 pages; v2: Section 4.2 and a reference are added

We consider the type IIB Green-Schwarz superstring theory on AdS(2)xS(2)xT(6) supported by homogeneous Ramond-Ramond 5-form flux and its type IIA T-duals. One motivation is to understand the solution of this theory based on integrability. This background is a limit of a 1/4 supersymmetric supergravity solution describing four intersecting D3-branes and represents a consistent embedding of AdS(2)xS(2) into critical superstring theory. Its AdS(2)xS(2) part with corresponding fermions can be described by a classically integrable PSU(1,1|2)/SO(1,1)xU(1) supercoset sigma-model. We point out that since the RR 5-form field has non-zero components along the 6-torus directions one cannot, in general, factorize the 10d superstring theory into the supercoset part plus 6 bosons and 6 additional massless fermions. Still, we demonstrate that the full superstring model (i) is classically integrable, at least to quadratic order in fermions, and (ii) admits a consistent classical truncation to the supercoset part. Following the analogy with other integrable backgrounds and starting with the finite-gap equations of the PSU(1,1|2)/SO(1,1)xU(1) supercoset we propose a set of asymptotic Bethe ansatz equations for a subset of the quantum string states., Comment: 49 pages, 1 figure; v2: misprints corrected, references added

We construct the half-supersymmetric instanton solutions that are electric-magnetically dual to the recently discussed half-supersymmetric Q7-branes. We call these instantons `Q-instantons'. Whereas the D-instanton is most conveniently described using the RR axion \chi and the dilaton \phi, the Q-instanton is most conveniently described using a different set of fields \chi' and T, where \chi' is an axionic scalar. The real part of the Q-instanton on-shell action is a function of T and the imaginary part is linear in \chi'. Discrete shifts of the axion \chi' correspond to PSL(2,Z) transformations that are of finite order. These are e.g. pure S-duality transformations relating weak and strongly coupled regimes. We argue that near each orbifold point of the quantum axion-dilaton moduli space PSL(2,Z)\PSL(2,R)/SO(2) the higher order R^4 terms in the string effective action contain contributions from an infinite sum of single multiply-charged instantons with the Q-instantons corresponding to the orbifold points \tau=i,\rho where \tau is the complex axion-dilaton field., Comment: 29 pages, 1 figure

The structure and the dynamics of massless higher spin fields in various dimensions are reviewed with an emphasis on conformally invariant higher spin fields. We show that in D=3,4,6 and 10 dimensional space-time the conformal higher spin fields constitute the quantum spectrum of a twistor-like particle propagating in tensorial spaces of corresponding dimensions. We give a detailed analysis of the field equations of the model and establish their relation with known formulations of free higher spin field theory., Comment: JHEP3 style, 40 pages; v2 typos corrected, comments and references added; v3 published version