Unitary minimal models of Script SScript W(3/2,3/2,2) superconformal algebra and manifolds of<i>G</i><sub>2</sub>holonomy

Noyvert, Boris

doi:10.1088/1126-6708/2002/03/030

Cited by 22 publications

(54 citation statements)

References 32 publications

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“…Mirror symmetry of the flux backgrounds should then induce mirror symmetry of these G 2 manifolds. Finally, it would be interesting to study this mirror symmetry for other G 2 manifolds for which a conformal field theory description is available [13,[22][23][24][25][26][27][28]. It may also be interesting to see whether there is a similar construction for Spin(8) manifolds.…”

Section: Discussionmentioning

confidence: 99%

Generalised discrete torsion and mirror symmetry for G₂manifolds

Gaberdiel

Kaste

2004

J. High Energy Phys.

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A generalisation of discrete torsion is introduced in which different discrete torsion phases are considered for the different fixed points or twist fields of a twisted sector. The constraints that arise from modular invariance are analysed carefully. As an application we show how all the different resolutions of the T 7 /Z 3 2 orbifold of Joyce have an interpretation in terms of such generalised discrete torsion orbifolds. Furthermore, we show that these manifolds are pairwise identified under G 2 mirror symmetry. From a conformal field theory point of view, this mirror symmetry arises from an automorphism of the extended chiral algebra of the G 2 compactification.

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Section: Discussionmentioning

confidence: 99%

Generalised discrete torsion and mirror symmetry for G₂manifolds

Gaberdiel

Kaste

2004

J. High Energy Phys.

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“…There is a c = 21/2 sigma model whose target space is a manifold of G 2 holonomy. The full chiral algebra may be obtained from the so-called SW (3/2, 3/2, 2) algebra, which is generated by the N = 1 super-Virasoro algebra together with two superconformal primaries of s = 3/2, 2, modded out by an extra ideal [59][60][61]. This implies c currents = 9/2.…”

Section: Jhep05(2018)092mentioning

confidence: 99%

Constraints on higher spin CFT2

Afkhami-Jeddi

Colville

Hartman

et al. 2018

J. High Energ. Phys.

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We derive constraints on two-dimensional conformal field theories with higher spin symmetry due to unitarity, modular invariance, and causality. We focus on CFTs with W N symmetry in the "irrational" regime, where c > N − 1 and the theories have an infinite number of higher-spin primaries. The most powerful constraints come from positivity of the Kac matrix, which (unlike the Virasoro case) is non-trivial even when c > N − 1. This places a lower bound on the dimension of any non-vacuum higher-spin primary state, which is linear in the central charge. At large c, this implies that the dual holographic theories of gravity in AdS 3 , if they exist, have no local, perturbative degrees of freedom in the semi-classical limit.

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“…• G 2 -holonomy : For the NS sector, the wanted functions are given as They are consistent with the structures of unitary massive representations given in [50].…”

Section: Discussionmentioning

confidence: 70%

“…A characteristic feature of the G 2 extended algebra is the existence of the tri-critical Ising model ( ∼ = SO(7) 1 /(G 2 ) 1 ), and that for the Spin(7) extended algebra is the Ising model ( ∼ = SO(8) 1 /SO(7) 1 ) as discussed in [47]. The unitary massive representations for these algebras are classified in [49,50]: two continuous series with h ≥ 0 and h ≥ 1/2 exist for the each case. Unfortunately, the character formulas for these representations have not been worked out.…”

Section: Discussionmentioning

confidence: 99%

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Supercoset CFTs for string theories on non-compact special holonomy manifolds

Sugawara

Yamaguchi

2003

Nuclear Physics B

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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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Unitary minimal models of Script SScript W(3/2,3/2,2) superconformal algebra and manifolds ofG₂holonomy

Abstract: The SW(3/2, 3/2, 2) superconformal algebra is a W algebra with two free parameters. It consists of 3 superconformal currents of spins 3/2, 3/2 and 2. The algebra is proved to be the symmetry algebra of the coset su(2)⊕su(2)⊕su (2) su (2)

Cited by 22 publications

References 32 publications

Generalised discrete torsion and mirror symmetry for G₂manifolds

Generalised discrete torsion and mirror symmetry for G₂manifolds

Constraints on higher spin CFT2

Supercoset CFTs for string theories on non-compact special holonomy manifolds

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Unitary minimal models of Script SScript W(3/2,3/2,2) superconformal algebra and manifolds ofG2holonomy

Abstract: The SW(3/2, 3/2, 2) superconformal algebra is a W algebra with two free parameters. It consists of 3 superconformal currents of spins 3/2, 3/2 and 2. The algebra is proved to be the symmetry algebra of the coset su(2)⊕su(2)⊕su (2) su (2)

Cited by 22 publications

References 32 publications

Generalised discrete torsion and mirror symmetry for G2manifolds

Generalised discrete torsion and mirror symmetry for G2manifolds

Constraints on higher spin CFT2

Supercoset CFTs for string theories on non-compact special holonomy manifolds

Contact Info

Product

Resources

About

Unitary minimal models of Script SScript W(3/2,3/2,2) superconformal algebra and manifolds ofG₂holonomy

Generalised discrete torsion and mirror symmetry for G₂manifolds

Generalised discrete torsion and mirror symmetry for G₂manifolds