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

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

Michele Del Zotto
(
- Harvard U.
)
,
Cumrun Vafa
(
- Harvard U., Phys. Dept.
)
,
Dan Xie
(
- Harvard U., Phys. Dept.
)

Apr 30, 2015

58 pages

Published in:

JHEP 11 (2015) 123

Published: Nov 18, 2015

e-Print:

1504.08348 [hep-th]

DOI:

10.1007/JHEP11(2015)123

View in:

reference search126 citations

Citations per year

Abstract: (Springer)

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

\mathcal{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

\mathcal{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

\mathcal{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

\mathcal{S}

with punctures from toroidal compactification of (1, 0) SCFTs where the curve of the class

\mathcal{S}

theory emerges through mirror symmetry. We also show that toroidal compactification of the little string version of these theories can lead to class

\mathcal{S}

theories with no punctures on arbitrary genus Riemann surface.

Note:

58 pages, 8 figures, v2: references added, typos fixed, table 2 updated

Supersymmetry and Duality
Extended Supersymmetry
Field Theories in Higher Dimensions
symmetry: mirror
compactification: torus
symmetry: duality
symmetry: global
engineering: geometrical
matter: conformal
field theory: conformal

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Figures(6)

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