Abstract
String theory, specifically type-II superstring theory, can be formulated in any ten-dimensional signature. To facilitate the study of supergravity and superstring theories in this setting, we present a uniform construction of supersymmetry algebras in arbitrary dimension and signature, which generalizes the ideas underlying symplectic Majorana spinors. In our formalism R-symmetry acts on an auxiliary multiplicity space which makes its action manifest. This allows us to provide extensive tables which list the R-symmetry groups of extended supersymmetry algebras for all signatures together with other useful information. Twisted (‘type-*’) supersymmetry algebras in Lorentz signature with non-compact R-symmetry groups are shown to be part of a general pattern resulting from the interplay between complex superbrackets and reality conditions. As an application we show how the relations between type-II string theories in ten and nine dimensions can be extracted from their supersymmetry algebras. We also use our results to determine the special geometry of vector and hypermultiplet scalar manifolds of four-dimensional mathcal{N} = 2 and three-dimensional mathcal{N} = 4 supergravity theories for all signatures.
Highlights
String theory extends our concepts of space-time geometry and symmetry in various directions
To facilitate the study of supergravity and superstring theories in this setting, we present a uniform construction of supersymmetry algebras in arbitrary dimension and signature, which generalizes the ideas underlying symplectic Majorana spinors
In this paper we have provided a construction of extended supersymmetry algebras which works uniformly across dimensions and signatures
Summary
String theory extends our concepts of space-time geometry and symmetry in various directions. Together with standard (i.e. spacelike) T-duality and with S-duality, it creates a web of type-II string theories which covers all possible space-time signatures (t, s), t+s = 10 in ten dimensions [2]. This type-II network is related to three versions of eleven-dimensional M-theory with spacetime signature (1, 10), (2, 9), (5, 6). Our formalism provides a systematic way of identifying reality conditions that define real supersymmetry algebras by selecting real forms of the complex R-symmetry group Such a uniform approach useful if one wants to explore the web of string dualities across dimensions and signatures, as we illustrate using type-II string theories and their compactifications as an example. We present tables where we classify the possible R-symmetry groups appearing in our construction up to dimension 12 for all signatures
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