# $\mathcal{N}=1$ 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.
Document type :
Journal articles

http://hal.in2p3.fr/in2p3-01302362
Contributor : Dominique Girod Connect in order to contact the contributor
Submitted on : Thursday, April 14, 2016 - 10:11:11 AM
Last modification on : Friday, September 10, 2021 - 1:50:15 PM

### Citation

D. Tsimpis, Y. Zhu. $\mathcal{N}=1$ 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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