Tests of Seiberg-like Duality in Three Dimensions

TL;DR

This work tests Seiberg-like dualities for three-dimensional supersymmetric gauge theories using exact partition-function calculations from localization, focusing on Giveon-Kutasov duality and its relation to level-rank duality. It proves GK duality for N_f=1 and provides substantial numerical evidence for larger N_f, while clarifying the emergence of decoupled free sectors in certain regimes. The analysis also shows ABJ-type dualities for fractional M2-brane theories follow from GK duality, and extends to a broad class of CS-matter theories with product gauge groups. Overall, the paper strengthens the connection between brane constructions, matrix-model localization, and duality webs in 3d supersymmetric field theories.

Abstract

We use localization techniques to study several duality proposals for supersymmetric gauge theories in three dimensions reminiscent of Seiberg duality. We compare the partition functions of dual theories deformed by real mass terms and FI parameters. We find that Seiberg-like duality for N=3 Chern-Simons gauge theories proposed by Giveon and Kutasov holds on the level of partition functions and is closely related to level-rank duality in pure Chern-Simons theory. We also clarify the relationship between the Giveon-Kutasov duality and a duality in theories of fractional M2 branes and propose a generalization of the latter. Our analysis also confirms previously known results concerning decoupled free sectors in N=4 gauge theories realized by monopole operators.

Figures (5)

• Figure 1: Brane manipulations in type IIB string theory which yield a naive dual. Solid vertical lines are NS5 branes. Horizontal lines are coincident D3 branes. Dashed lines are D5 branes. The legend indicates the compactification direction (t or $x_6$) and the directions of possible triplet mass (m) terms (3,4,5), and possible triplet FI (w) terms (7 8 9). Directions (0 1 2) are common to the world volume of all branes and are suppressed. We first move $N_f$ D5 branes through the right NS5 brane, creating $N_f$ D3 branes in the process. We then exchange the two NS5 branes, changing the number of suspended D3 branes in the interval.
• Figure 2: Brane manipulations in type IIB string theory which yield a duality between Chern Simons theories. Panels (b) through (d) relate a pair of theories without CS terms. The deformations of the theory needed to go from (b) to (a) and from (d) to (e) are identified.
• Figure 3: Brane manipulations in type IIB string theory which yield a duality between Chern Simons theories of an elliptical quiver. An NS5 brane moves past a $(1,k)$ brane creating $k$ and destroying $l$ D3 branes in the process. Reproduced from Aharony:2008gk.
• Figure 4: A comparison of the magnitude of the partition functions with FI deformation ($\eta$) for 8 dual pairs and values of $\eta$ from $.1$ to $.9$ and a best fit line, which, to the accuracy of the numerical evaluation, is of slope $1$ and intercept $0$.
• Figure 5: A plot of the phase difference of the partition functions with FI deformation ($\eta$) for 8 dual pairs and values of $\eta$ from $.1$ to $.9$ and a best fit parabola.