N=2 Chern-Simons-Matter Theories Without Vortices
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We study ${\cal N}=2$ Chern-Simons-matter theories with gauge group $U_{k_1}(1)\times U_{k_2}(1)$. We find that, when $k_1+k_2=0$, the partition function computed by localization dramatically simplifies and collapses to a single term. We show that the same condition prevents the theory from having supersymmetric vortex configurations. The theories include mass-deformed ABJM theory with $U(1)_{k}\times U_{-k}(1)$ gauge group as a particular case. Similar features are shared by a class of CS-matter theories with gauge group $U_{k_1}(1)\times \cdots \times U_{k_N}(1)$.
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Cited by 2 Pith papers
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Twisted traces and quantization of moduli stacks of 3d $\mathcal{N}=4$ Chern-Simons-matter theories
Sphere partition functions of 3d N=4 Chern-Simons-matter theories are conjectured to equal sums of twisted traces on Verma modules over quantized moduli stacks of vacua.
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Twisted traces and quantization of moduli stacks of 3d $\mathcal{N}=4$ Chern-Simons-matter theories
The sphere partition function of 3d N=4 Chern-Simons-matter theories is conjectured to equal a sum of twisted traces on Verma modules over the quantization of their moduli spaces of vacua, extending prior work and rev...
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