Strings of Minimal 6d SCFTs

Haghighat, Babak; Klemm, Albrecht; Lockhart, Guglielmo; Vafa, Cumrun

doi:10.1002/prop.201500014

Cited by 107 publications

(268 citation statements)

References 57 publications

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“…The generalization of the construction of the Bridgeland autoequivalence should also be possible in principle. In fact at least in the Calabi-Yau threefold case the results for the all genus amplitudes which can be expressed in terms of Weylinvariant Jacobi-Forms [52,53] indicate that the affine Weyl-group of the singularity will appear as part of the auto-equivalences of the derived category of the A-model. 7 Further details about this highly non-trivial analytic continuation can be found at [48].…”

Section: Jhep01(2018)086mentioning

confidence: 99%

Modular amplitudes and flux-superpotentials on elliptic Calabi-Yau fourfolds

Cota¹,

Klemm

Schimannek³

2018

J. High Energ. Phys.

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We discuss the period geometry and the topological string amplitudes on elliptically fibered Calabi-Yau fourfolds in toric ambient spaces. In particular, we describe a general procedure to fix integral periods. Using some elementary facts from homological mirror symmetry we then obtain Bridgelands involution and its monodromy action on the integral basis for non-singular elliptically fibered fourfolds. The full monodromy group contains a subgroup that acts as PSL(2,Z) on the Kähler modulus of the fiber and we analyze the consequences of this modularity for the genus zero and genus one amplitudes as well as the associated geometric invariants. We find holomorphic anomaly equations for the amplitudes, reflecting precisely the failure of exact PSL(2,Z) invariance that relates them to quasi-modular forms. Finally we use the integral basis of periods to study the horizontal flux superpotential and the leading order Kähler potential for the moduli fields in F-theory compactifications globally on the complex structure moduli space. For a particular example we verify attractor behaviour at the generic conifold given an aligned choice of flux which we expect to be universal. Furthermore we analyze the superpotential at the orbifold points but find no stable vacua.

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Section: Jhep01(2018)086mentioning

confidence: 99%

Modular amplitudes and flux-superpotentials on elliptic Calabi-Yau fourfolds

Cota¹,

Klemm

Schimannek³

2018

J. High Energ. Phys.

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“…For n = 3, the story will be different. One can write down the corresponding N = 2 geometry using mirror symmetry as discussed in section 4 (for this class of models see also [69], in particular, the LG mirror of the O(−3) model presented here was worked out there). The mirror theory has two parts: the T 2 part is described by three C variables x 1 , x 2 , x 3 , and the C 2 part described by two C * variables y 1 , y 2 .…”

Section: Mirror Geometries Of O(−n) Modelsmentioning

confidence: 99%

Geometric engineering, mirror symmetry and 6 d 1 0 → 4 d N = 2 $$ 6{\mathrm{d}}_{\left(1,0\right)}\to 4{\mathrm{d}}_{\left(\mathcal{N}=2\right)} $$

Zotto

Vafa

Xie

2015

J. High Energ. Phys.

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107

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Abstract:We study compactification of 6 dimensional (1,0) theories on T 2 . We use geometric engineering of these theories via F-theory and employ mirror symmetry technology to solve for the effective 4d N = 2 geometry for a large number of the (1, 0) theories including those associated with conformal matter. Using this we show that for a given 6d theory we can obtain many inequivalent 4d N = 2 SCFTs. Some of these respect the global symmetries of the 6d theory while others exhibit SL(2, Z) duality symmetry inherited from global diffeomorphisms of the T 2 . This construction also explains the 6d origin of moduli space of 4d affine ADE quiver theories as flat ADE connections on T 2 . Among the resulting 4d N = 2 CFTs we find theories whose vacuum geometry is captured by an LG theory (as opposed to a curve or a local CY geometry). We obtain arbitrary genus curves of class S with punctures from toroidal compactification of (1, 0) SCFTs where the curve of the class S theory emerges through mirror symmetry. We also show that toroidal compactification of the little string version of these theories can lead to class S theories with no punctures on arbitrary genus Riemann surface.

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“…The six-dimensional parent theory has itself strings and in a compactification to five dimensions they may or may not wrap the circle. In case they do wrap the circle their elliptic genus can be computed through various techniques which have recently been developed [11][12][13][14] and allow to obtain the partition function of the six-dimensional theory on T 2 × R 4 :…”

Section: Jhep01(2016)062mentioning

confidence: 99%

“…These become D4 branes upon compactification to Type IIA and then subsequently D3 branes wrapping P 1 after T-dualizing to Type IIB. As D3 branes wrapping P 1 give rise to strings of minimal 6d SCFTs which have recently been studied in [14], we have managed to map strings in 5d to strings in 6d. To summarize we arrive at the following duality:…”

Section: A 6d/5d Dualitymentioning

confidence: 99%