An N=1 3d-3d correspondence

作者：Eckhard Julius^*; Schaefer Nameki Sakura; Wong Jin Mann

来源：The Journal of High Energy Physics, 2018, 2018(7): 052.

DOI：10.1007/JHEP07(2018)052

• Duality in Gauge Field Theories
• Field Theories in Higher Dimensions
• Supersymmetric Gauge Theory
• Topological Field Theories

M5-branes on an associative three-cycle M-3 in a G(2)-holonomy manifold give rise to a 3d N = 1 supersymmetric gauge theory, T-N=1 [M-3]. We propose an N = 1 3d-3d correspondence, based on two observables of these theories: the Witten index and the S-3 -partition function. The Witten index of a 3d N = 1 theory T-N=1 [M-3] is shown to be computed in terms of the partition function of a topological field theory, a super-BFmodel coupled to a spinorial hypermultiplet (BFH), on M-3. The BFH-model localizes on solutions to a generalized set of 3d Seiberg-Witten equations on M3. Evidence to support this correspondence is provided in the abelian case, as well as in terms of a direct derivation of the topological fi eld theory by twisted dimensional reduction of the 6d (2; 0) theory. We also consider a correspondence for the S-3 -partition function of the TN=1 [M-3] theories, by determining the dimensional reduction of the M-5-brane theory on S-3. The resulting topological theory is Chern-Simons-Dirac theory, for a gauge fi eld and a twisted harmonic spinor on M-3, whose equations of motion are the generalized 3d Seiberg-Witten equations. For generic G(2) -manifolds the theory reduces to real Chern-Simons theory, in which case we conjecture that the S-3 -partition function of T-N=1 [M-3] is given by the Witten-ReshetikhinTuraev invariant of M-3.