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3D Seiberg-like Dualities and M2 Branes

Antonio Amariti, Davide Forcella, Luciano Girardello, Alberto Mariotti

TL;DR

This work advances the understanding of toric duality for M2 branes by formulating a Seiberg-like duality for 3D N=2 CS-matter theories and proving it yields toric-equivalent mesonic moduli spaces M4. The authors extend the forward algorithm to compute M4 from field-theory data and verify dual pairs via explicit matrix data, including incidence, perfect matching, and CS-level matrices, across non-chiral examples and several chiral cases. They demonstrate toric duality in multiple tilde L aba families and in theories without 4D parents under carefully chosen CS level constraints, and discuss parity anomaly considerations and fractional branes. The results provide a framework for identifying and verifying dual pairs in the holographic AdS4/CFT3 context and point to future directions in relaxing level constraints and exploring more general dualities and moduli spaces.

Abstract

We investigate features of duality in three dimensional N=2 Chern-Simons matter theories conjectured to describe M2 branes at toric Calabi Yau four-fold singularities. For 3D theories with non-chiral 4D parents we propone a Seiberg-like duality which turns out to be a toric duality. For theories with chiral 4D parents we discuss the conditions under which that Seiberg-like duality leads to toric duality. We comment on such duality in 3D theories without 4D parents.

3D Seiberg-like Dualities and M2 Branes

TL;DR

This work advances the understanding of toric duality for M2 branes by formulating a Seiberg-like duality for 3D N=2 CS-matter theories and proving it yields toric-equivalent mesonic moduli spaces M4. The authors extend the forward algorithm to compute M4 from field-theory data and verify dual pairs via explicit matrix data, including incidence, perfect matching, and CS-level matrices, across non-chiral examples and several chiral cases. They demonstrate toric duality in multiple tilde L aba families and in theories without 4D parents under carefully chosen CS level constraints, and discuss parity anomaly considerations and fractional branes. The results provide a framework for identifying and verifying dual pairs in the holographic AdS4/CFT3 context and point to future directions in relaxing level constraints and exploring more general dualities and moduli spaces.

Abstract

We investigate features of duality in three dimensional N=2 Chern-Simons matter theories conjectured to describe M2 branes at toric Calabi Yau four-fold singularities. For 3D theories with non-chiral 4D parents we propone a Seiberg-like duality which turns out to be a toric duality. For theories with chiral 4D parents we discuss the conditions under which that Seiberg-like duality leads to toric duality. We comment on such duality in 3D theories without 4D parents.

Paper Structure

This paper contains 18 sections, 70 equations, 15 figures, 1 table.

Table of Contents

  1. Introduction
  2. M2 branes and $\mathcal{N}=2$ Chern Simons theories
  3. An Algorithm to compute $\mathcal{M}_4$
  4. Non-Chiral Theories
  5. Seiberg-like duality
  6. $\widetilde{L^{121}}_{\{k_1,k_2,k_3\}}$
  7. $\widetilde{L^{222}}_{\{k_i\}}$
  8. The general $\widetilde{L^{aba}}_{\{k_i\}}$
  9. Chiral theories
  10. $\widetilde{\mathbb{F}_0}_{\{ k_i \}}$
  11. $\widetilde{dP_1}_{\{k_i \}}$
  12. $\widetilde{dP_2}_{\{ k_i \}}$
  13. $\widetilde{dP_3}_{\{ k_i \}}$
  14. $\widetilde{Y^{32}}_{\{ k_i \}}$
  15. Dualities for CS theories without 4d parents
  16. ...and 3 more sections

Figures (15)

  • Figure 1: The quiver for the generic $\widetilde{L^{aba}}_{\{k_i\}}$.
  • Figure 2: Brane construction for $\widetilde{L^{121}}_{\{k_1,k_2,k_3\}}$. The D5 branes fill also the vertical directions of the corresponding NS5.
  • Figure 3: Configuration after exchanging the position of the $(1,p_i)$ and $(1,p_{i+1})$ branes. The movement implies that $|p_{i}-p_{i+1}|$$D3$ are created in the middle interval. The rank of the dualized group is $N+|p_{i}-p_{i+1}|=N+|k_i|$. The CS levels change as $(p_{i-1}-p_i,p_i-p_{i+1},p_{i+1}-p_{i+2}) \to (p_{i-1}-p_{i+1},p_{i+1}-p_{i},p_{i}-p_{i+2}).$
  • Figure 4: Quiver, ranks and CS levels for the $\widetilde{L^{121}}_{\{k_1,k_2,k_3\}}$ in the two phases related by Seiberg like duality on node $2$.
  • Figure 5: The quivers for the two phases of $L^{222}$.
  • ...and 10 more figures