The N3=3→N3

Pietro Fré

¹

,

Alfredo Giambrone

²

,

Pietro Antonio Grassi

³

et al.

Abstract

Considering matter coupled supersymmetric Chern-Simons theories in three dimensions we extend the Gaiotto-Witten mechanism of supersymmetry enhancement N 3 = 3 → N 3 = 4 from the case where the hypermultiplets span a flat HyperKähler manifold to that where they live on a curved one. We derive the precise conditions of this enhancement in terms of generalized Gaiotto-Witten identities to be satisfied by the tri-holomorphic moment maps. An infinite class of HyperKähler metrics compatible with the enhancement condition is provided by the Calabi metrics on T ⋆ P n . In this list we find, for n = 2 the resolution of the metric cone on N 0,1,0 which is the unique homogeneous Sasaki Einstein 7-manifold leading to an N 4 = 3 compactification of M-theory. This leads to challenging perspectives for the discovery of new relations between the enhancement mechanism in D = 3, the geometry of M2-brane solutions and also for the dual description of super Chern Simons theories on curved HyperKähler manifolds in terms of gauged fixed supergroup Chern Simons theories. The relevant supergroup is in this case SU(3|N) where SU(3) is the flavor group and U(N) is the color group.

Vertex Operator Algebras and Topologically Twisted Chern-Simons-Matter Theories

“…These can be yet further generalized to non-linear hypermultiplet and/or twisted hypermultiplet targets, possibly gauged with N = 4 vector multiplets, so long as the fundamental identity is suitably satisfied. The mechanism that allows for these highly supersymmetric Chern-Simons-matter theories was realized as a consequence of the representation theory of metric Lie algebras in [86] and its Mtheory origin was discussed in [87]. Some particularly noteworthy specimens in this collection of Chern-Simons-matter theories are the theories of Aharony-Bergman-Jaffries-Maldacena (ABJM) [88], Aharony-Bergman-Jaffries (ABJ) [89], and Bagger-Lambert-Gustovsson (BLG) [90][91][92] modeling the low energy dynamics of multiple M2 branes.…”