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$N^{3/2}$ Scaling from $3d$ $\mathcal{N}=2$ Dualities: an Alternative Approach to Chiral Quivers

Antonio Amariti, Giulia Lanzetti

Abstract

We investigate families of 3d $\mathcal{N}=2$ chiral quiver gauge theories conjectured to be dual to M2-branes probing toric SE$_7$ singularities. Geometrically, these families correspond to toric diagrams without internal points. At the field theory level, the models are constructed via an un-higgsing procedure applied to non-chiral quivers. While the moduli space of these theories was shown to match M-theory expectations, determining the $N^{3/2}$ scaling of the free energy remained an open problem for over a decade, with positive results emerging only very recently. In this work, we address this challenge by reformulating the three-sphere partition function as a hyperbolic hypergeometric integral. Using exact integral identities, we show that the free energy reduces precisely to that of non-chiral quivers with chiral flavors, for which the $N^{3/2}$ scaling is already established. Physically, this mathematical identity corresponds to the equivalence of three-sphere partition functions under a generalization of Giveon-Kutasov duality to chiral quivers. Our results thus provide a large $N$ duality between the chiral quivers and non-chiral quivers with chiral flavors, confirming the $N^{3/2}$ scaling for the chiral quivers under study.

$N^{3/2}$ Scaling from $3d$ $\mathcal{N}=2$ Dualities: an Alternative Approach to Chiral Quivers

Abstract

We investigate families of 3d chiral quiver gauge theories conjectured to be dual to M2-branes probing toric SE singularities. Geometrically, these families correspond to toric diagrams without internal points. At the field theory level, the models are constructed via an un-higgsing procedure applied to non-chiral quivers. While the moduli space of these theories was shown to match M-theory expectations, determining the scaling of the free energy remained an open problem for over a decade, with positive results emerging only very recently. In this work, we address this challenge by reformulating the three-sphere partition function as a hyperbolic hypergeometric integral. Using exact integral identities, we show that the free energy reduces precisely to that of non-chiral quivers with chiral flavors, for which the scaling is already established. Physically, this mathematical identity corresponds to the equivalence of three-sphere partition functions under a generalization of Giveon-Kutasov duality to chiral quivers. Our results thus provide a large duality between the chiral quivers and non-chiral quivers with chiral flavors, confirming the scaling for the chiral quivers under study.
Paper Structure (16 sections, 78 equations, 19 figures)

This paper contains 16 sections, 78 equations, 19 figures.

Table of Contents

  1. Introduction
  2. An infinite family of chiral quivers
  3. 3d theories without a 4d parent
  4. GK duality in a chiral quiver
  5. Examples: toric duals of ABJM with chiral flavor
  6. The free energy of $D_3$ and GK duality
  7. The free energy of $\mathcal{C} \times \mathbb{C}$ and GK duality
  8. The free energy of $Q^{111}$ and GK duality
  9. The free energy of the cubic conifold and GK duality
  10. Generalizations
  11. Flavoring SPP: a chiral model with five gauge nodes
  12. Discussion
  13. $\mathcal{N}=2$ CS toric quivers and the moduli space
  14. Computation of the toric diagram
  15. Example: ABJM
  16. ...and 1 more sections

Figures (19)

  • Figure 1: Quiver and CS levels for the 3d model descending from a 4d consistent grand-parent theory and its un-higgsed version descending from a 4d inconsistent (not a SCFT) parent theory.
  • Figure 2: Three dimensional toric diagram for $Q^{111}$, built here from the superpotential (\ref{['figu']}).
  • Figure 3: ABJM quiver and the un-higgsed quiver corresponding to $Q^{111}$ with the CS levels $k_A =-k_B=-1$ and $k_1=k_2=0$.
  • Figure 4: In this figure we represent three $U(N)$ gauge nodes embedded in a generic chiral quiver. This is the typical situation that we encounter in this paper. Each node has a different CS level, $k_{I-1}$, $k_{I}$ and $k_{I+1}$ in the figure. When $k_I\neq 0$ we can dualize the node at the level of the three sphere partition function using an exact mathematical identity, corresponding to the GK duality for a chiral quiver. In the figure we also assigned to the two bifundamentals connecting the three gauge nodes the relative R-charge. At this level of the discussion we did not specify any possible further constraints between such charges, that depend on the detail of the model under inspection.
  • Figure 5: Chiral quiver description of the $D_3$ model. We did not represent the extra $U(1)_{diag}$ gauging in the picture.
  • ...and 14 more figures