SL(2,R) covariant conditions for N=1 flux vacua

Details SL(2,R) covariant conditions for N=1 flux vacua SL(2,R) covariant conditions for N=1 flux vacua

2011-07-15

arxiv.org/abs/1107.3163v2

JHEP 1110 (2011) 057

Physics

High Energy Physics

High Energy Physics - Theory

32 pages, no figures; v2: references and a minor clarification added

Scientific paper

10.1007/JHEP10(2011)057

Four-dimensional supersymmetric N = 1 vacua of type IIB supergravity are elegantly described by generalized complex geometry. However, this approach typically obscures the SL(2, R) covariance of the underlying theory. We show how to rewrite the pure spinor equations of Grana, Minasian, Petrini and Tomasiello (hep-th/0505212) in a manifestly SL(2,R) covariant fashion. Solutions to these equations fall into two classes: "charged" solutions, such as those containing D5-branes, and "chargeless" solutions, such as F-theory solutions in the Sen limit and AdS4 solutions. We derive covariant supersymmetry conditions for the chargeless case, allowing general SU(3)xSU(3) structure. The formalism presented here greatly simplifies the study of the ten-dimensional geometry of general supersymmetric compactifications of F-theory.

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