TY - JOUR

T1 - N = 1 supersymmetric indices and the four-dimensional A-model

AU - Closset, Cyril

AU - Kim, Heeyeon

AU - Willett, Brian

N1 - Funding Information:
We would like to thank Ofer Aharony, Benjamin Assel, Lorenzo di Pietro, Zohar Komargod-ski, Victor Mikhaylov, Greg Moore, Shlomo Razamat, Nathan Seiberg, Edgar Shaghoulian, Itamar Yaakov and Piljin Yi for interesting discussions and comments. This research was supported in part by Perimeter Institute for Theoretical Physics. Research at Perimeter Institute is supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Economic Development & Innovation. The work of HK was made possible through the support of a grant from the John Templeton Foundation. The opinions expressed in this publication are those of the author and do not necessarily reflect the views of the John Templeton Foundation. BW was supported in part by the National Science Foundation under Grant No. NSF PHY11-25915.
Publisher Copyright:
© 2017, The Author(s).

PY - 2017/8/1

Y1 - 2017/8/1

N2 - We compute the supersymmetric partition function of N = 1 supersymmetric gauge theories with an R-symmetry on ℳ 4≅ ℳ g , p× S1, a principal elliptic fiber bundle of degree p over a genus-g Riemann surface, Σg. Equivalently, we compute the generalized supersymmetric index Iℳg,p, with the supersymmetric three-manifold ℳ g , p as the spatial slice. The ordinary N = 1 supersymmetric index on the round three-sphere is recovered as a special case. We approach this computation from the point of view of a topological A-model for the abelianized gauge fields on the base Σg. This A-model — or A-twisted two-dimensional N = (2, 2) gauge theory — encodes all the information about the generalized indices, which are viewed as expectations values of some canonically-defined surface defects wrapped on T2 inside Σg × T2. Being defined by compactification on the torus, the A-model also enjoys natural modular properties, governed by the four-dimensional ’t Hooft anomalies. As an application of our results, we provide new tests of Seiberg duality. We also present a new evaluation formula for the three-sphere index as a sum over two-dimensional vacua.

AB - We compute the supersymmetric partition function of N = 1 supersymmetric gauge theories with an R-symmetry on ℳ 4≅ ℳ g , p× S1, a principal elliptic fiber bundle of degree p over a genus-g Riemann surface, Σg. Equivalently, we compute the generalized supersymmetric index Iℳg,p, with the supersymmetric three-manifold ℳ g , p as the spatial slice. The ordinary N = 1 supersymmetric index on the round three-sphere is recovered as a special case. We approach this computation from the point of view of a topological A-model for the abelianized gauge fields on the base Σg. This A-model — or A-twisted two-dimensional N = (2, 2) gauge theory — encodes all the information about the generalized indices, which are viewed as expectations values of some canonically-defined surface defects wrapped on T2 inside Σg × T2. Being defined by compactification on the torus, the A-model also enjoys natural modular properties, governed by the four-dimensional ’t Hooft anomalies. As an application of our results, we provide new tests of Seiberg duality. We also present a new evaluation formula for the three-sphere index as a sum over two-dimensional vacua.

KW - Anomalies in Field and String Theories

KW - Duality in Gauge Field Theories

KW - Supersymmetric Gauge Theory

KW - Supersymmetry and Duality

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U2 - 10.1007/JHEP08(2017)090

DO - 10.1007/JHEP08(2017)090

M3 - Article

AN - SCOPUS:85028332875

VL - 2017

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 8

M1 - 90

ER -