# 3d N=1 Chern–Simons-matter theory and localization

Abstract : We consider the most general, classically-conformal, three-dimensional $\mathcal{N}=1$ Chern-Simons-matter theory with global symmetry $Sp(2)$ and gauge group $U(N)\times U(N)$. We show that the Lagrangian in the on-shell formulation of the theory admits one more free parameter as compared to the theory formulated in off-shell $\mathcal{N}=1$ superspace. The theory on $T^3$ can be formally localized to a matrix model. We carry out the localization procedure for the theory on $T^3$ with periodic boundary conditions. In particular we show that restricting to the saddle points with vanishing gauge connection gives a trivial contribution to the partition function, i.e. the bosonic and fermionic contributions exactly cancel each other.
Type de document :
Article dans une revue
Nuclear Physics B, Elsevier, 2016, 911, pp.355 - 387. 〈10.1016/j.nuclphysb.2016.08.013〉

http://hal.in2p3.fr/in2p3-01302362
Contributeur : Dominique Girod <>
Soumis le : jeudi 14 avril 2016 - 10:11:11
Dernière modification le : jeudi 15 mars 2018 - 11:40:10

### Citation

D. Tsimpis, Y. Zhu. 3d N=1 Chern–Simons-matter theory and localization. Nuclear Physics B, Elsevier, 2016, 911, pp.355 - 387. 〈10.1016/j.nuclphysb.2016.08.013〉. 〈in2p3-01302362〉

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