Betti numbers of 3-Sasakian manifolds

Galicki, Krzysztof; Salamon, Simon

doi:10.1007/bf00181185

Cited by 52 publications

(52 citation statements)

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“…Einstein metric that provides a weak G 2 holonomy [13,15] (see also [8,12]). A way to present the squashing procedure is to replace the original tri-Sasakian coset G/H…”

Section: G/h = (Su(2) × Su(2))/su(2)mentioning

confidence: 99%

“…This fact is very useful to systematically construct special holonomy manifolds with conical singularities, because the Einstein homogeneous spaces X m−1 = G/H endowed with these geometrical structures are well understood since the old days of Kaluza-Klein supergravity (SUGRA) [17][18][19][20][21][22][23] (and [24] for a review) as well as from the mathematical literature mentioned above [11][12][13][14][15][16] and [25].…”

Section: Introductionmentioning

confidence: 99%

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Supercoset CFT’s for String Theories on Non-compact Special Holonomy Manifolds

Sugawara

Yamaguchi

2003

Ann. Henri Poincaré

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We study aspects of superstring vacua of non-compact special holonomy manifolds with conical singularities constructed systematically using soluble N = 1 superconformal field theories (SCFT's). It is known that Einstein homogeneous spaces G/H generate Ricci flat manifolds with special holonomies on their cones ≃ R + × G/H, when they are endowed with appropriate geometrical structures, namely, the Sasaki-Einstein, triSasakian, nearly Kähler, and weak G 2 structures for SU(n), Sp(n), G 2 , and Spin (7) holonomies, respectively. Motivated by this fact, we consider the string vacua of the type:where we use the affine Lie algebras of G and H in order to capture the geometry associated to an Einstein homogeneous space G/H. Remarkably, we find the same number of spacetime and worldsheet SUSY's in our "CFT cone" construction as expected from the analysis of geometrical cones over G/H in many examples. We also present an analysis on the possible Liouville potential terms (cosmological constant type operators) which provide the marginal deformations resolving the conical singularities.

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“…Einstein metric that provides a weak G 2 holonomy [13,15] (see also [8,12]). A way to present the squashing procedure is to replace the original tri-Sasakian coset G/H…”

Section: G/h = (Su(2) × Su(2))/su(2)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Supercoset CFT’s for String Theories on Non-compact Special Holonomy Manifolds

Sugawara

Yamaguchi

2003

Ann. Henri Poincaré

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show abstract

“…This follows directly from (12) and (15). Keeping the same notations for the projections on N of projectable tensors (like g 0 or I 0 ) we now prove…”

mentioning

confidence: 71%