Gauge theories with 16 supersymmetries on spheres

Abstract

We give a unified approach to localization of maximally symmetric gauge theories on spheres, including S 6 and S 7 . The approach follows Pestun's method of dimensionally reducing from 10 dimensional super Yang-Mills. The resulting theories have a reduced R-symmetry which includes an SU(1, 1) subgroup, except in four dimensions where, because of conformal invariance, the full flat-space R-symmetry is maintained, and in seven dimensions where SU(1, 1) is the flat-space R-symmetry. For the case of S 6 and S 7 we discuss the localization of these theories and also present new results for the corresponding matrix models. The matrix models for S 6 and S 7 are qualitatively similar to the matrix models of a vector multiplet on S 4 and S 5 respectively. We also discuss the contributions of instantons in the six and seven dimensional cases.

Phase transitions in 5D super Yang-Mills theory

“…Note that the negative coupling constant does not spoil the convergence of the matrix integral (2.16). Similar phenomenon happens for 4D [40] and 6D [41] theories. Now we are ready to solve the matrix model with described matter content and coupling renormalization.…”

Factorisation and holomorphic blocks in 4d

“…Results on block factorisation of partition functions have been obtained also for 5d N = 1 theories on S 5 [28,29], S 4 × S 1 [30][31][32], on Y p,q [33,34], general toric SasakiEinstein manifolds [35] and for 6d and 7d theories on S 6 , S 7 [36].…”

“…The first factor can be neglected as it contributes to the vanishing of the total gauge anomaly. The factor e − 2πiZQ rω 1 ω 2 combines with an analogue contribution from the chiral multipltes (B.26) 34) to give a total contribution 36) while the ratio of the G functions in (B.33) yields Open Access. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.…”

One-loop tests of supersymmetric gauge theories on spheres

“…Partition functions for theories on S 3 , S 4 , S 5 , S 6 , S 7 were computed in [4,5,16,17]. Partition functions for S d , can be written as 15) where Z vec 1−loop and Z hyp 1−loop are vector-and hyper-multiplet one-loop determinants.…”

“…However, the standard localization procedure often starts with ten-dimensional super Yang-Mills and dimensionally reduces to super Yang-Mills on lower dimensional spheres [4][5][6][7]. As such, the fields are real.…”