Generalized structures of N=1 vacua

By M. Graña, R. Minasian, M. Petrini, A. Tomasiello. 2005

352 citations recorded by the source corpus.

We characterize = 1 vacua of type-II theories in terms of generalized complex structure on the internal manifold M. The structure group of T(M)⊕T*(M) being SU(3) × SU(3) implies the existence of two pure spinors Φ1 and Φ2. The conditions for preserving = 1 supersymmetry turn out to be simple generalizations of equations that have appeared in the context of = 2 and topological strings. They are (d+H∧)Φ1 = 0 and (d+H∧)Φ2 = FRR. The equation for the first pure spinor implies that the internal space is a twisted generalized Calabi-Yau manifold of a hybrid complex-symplectic type, while the RR-fields serve as an integrability defect for the second.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c4e0ff4a01552bb4be634d093abd9d2aa7b9c98b

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Citations in the corpus

Double field theory and $ \mathcal{N} = {4} $ gauged supergravity (2011, background): “uivalent formulation of the theory in term of the generalized metric HMN was presented, clarifying the link between DFT and Generalized Complex Geometry in the context of type II ﬂux compactiﬁcations [7, 8]. In the generalized metric version of the theory the ﬁeld Eij is replaced by a symmetric O(D,”
Flux compactifications in string theory: A Comprehensive review (2005, methodology): “We will skip the details of the derivation done in [59] (see also Refs.”
Double Field Theory and N=4 Gauged Supergravity (2011, background): “In a subsequent paper [6], an equivalent formulation of the theory in term of the generalized metric HMN was presented, clarifying the link between DFT and Generalized Complex Geometry in the context of type II flux compactifications [7, 8].”
T-duality, generalized geometry and non-geometric backgrounds (2008, background): “The supersymmetry equations for N = 1 Minkowski vacua given in terms of the pure spinors were found in [20] and read d(eΦ1) = 0 , (3.”
Electric-Magnetic Duality And The Geometric Langlands Program (2006, methodology): “Gualtieri’s thesis [67], as well as [71,68] for applications to sigma-models and [73-75] for”
From ten to four and back again: how to generalize the geometry (2007, methodology): “In [ 7 ] the supersymmetry conditions obtained from the Killing spinor equations were written in terms of polyforms obtained by the Clifford map from the bi-spinors η (1)”
A scan for new N = 1 vacua on twisted tori (2006, background): “This proof was described in words in [ 20 ]; here we give the details.”
All AdS7 solutions of type II supergravity (2013, methodology): “It can be found by direct computation, or also as a consequence of the system for Mink4×M6 in [7]: one takes M6 = R×M4, with warping A = A4, internal metric ds2M6 = e 2A4((dx4)2+ (dx5)2) + ds2M4 , and, in the language of [15],”
D-branes on general Script N = 1 backgrounds: superpotentials and D-terms (2006, background): “her. In this paper we will consider the most general class of N = 1 backgrounds admitting supersymmetric static D-brane conﬁgurations. These backgrounds constitute a subclass of the vacua analyzed in [5] and we will refer to them as D-calibratedbackgrounds. The name is justiﬁed by the fact that, as ”
M-theory, exceptional generalised geometry and superpotentials (2008, methodology): “20) they are automatically compatible [10].”
Supersymmetric sources, integrability and generalized-structure compactifications (2007, background): “: dH e3A−ΦImΨ 1 = e4A 16 F,˜ (C.3a) dH eA−ΦReΨ 1 = 0, (C.3b) dH e2A−ΦΨ 2 = 0. (C.3c) Finally we have the Bianchi identities for the form-ﬁelds: dHFˆ = −4κ2 10jtotal , (C.4a) dH= 0. (C.4b) As shown in [5], conditions (C.3) guarantee that the supersymmetry variation of the gravitino and dilatino (B.3)”
Hitchin functionals in N = 2 supergravity (2005, background): “[10, 11, 12], there has recently been much interest in a generalized class of backgrounds where the Calabi–Yau manifold is replaced by a manifold Y which is no longer Ricci-flat [13]–[44].”