Large $N$ topologically twisted index: necklace quivers, dualities, and Sasaki-Einstein spaces

Hosseini, Seyed Morteza; Mekareeya, Noppadol

doi:10.1007/JHEP08(2016)089

Large $N$ topologically twisted index: necklace quivers, dualities, and Sasaki-Einstein spaces

Seyed Morteza Hosseini
(
- Milan Bicocca U. and
- INFN, Milan Bicocca
)
,
Noppadol Mekareeya
(
- CERN
)

Apr 12, 2016

35 pages

Published in:

JHEP 08 (2016) 089

Published: Aug 12, 2016

e-Print:

1604.03397 [hep-th]

DOI:

10.1007/JHEP08(2016)089

Report number:

CERN-TH-2016-083

View in:

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Abstract: (Springer)

In this paper, we calculate the topological free energy for a number of

\mathcal{N}

≥ 2 Yang-Mills-Chern-Simons-matter theories at large N and fixed Chern-Simons levels. The topological free energy is defined as the logarithm of the partition function of the theory on S

^{2}

× S

^{1}

with a topological A-twist along S

^{2}

and can be reduced to a matrix integral by exploiting the localization technique. The theories of our interest are dual to a variety of Calabi-Yau four-fold singularities, including a product of two asymptotically locally Euclidean singularities and the cone over various well-known homogeneous Sasaki-Einstein seven-manifolds, N

^{0,1,0}

, V

^{5,2}

, and Q

^{1,1,1}

. We check that the large N topological free energy can be matched for theories which are related by dualities, including mirror symmetry and

\mathrm{S}\mathrm{L}\left(2,\mathbb{Z}\right)

duality.

Note:

34 pages, v2: refs added, improvement of section 5.1, published version; v3: typos removed

Duality in Gauge Field Theories
Matrix Models
Supersymmetric gauge theory
Supersymmetry and Duality
space: Sasaki-Einstein
duality
free energy
partition function
Chern-Simons term
quiver

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