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N=3 four dimensional field theories

Iñaki García-Etxebarria, Diego Regalado

TL;DR

The paper constructs a novel class of four-dimensional N=3 SCFTs by quotienting N=4 U(N) SYM with combined R-symmetry and duality actions, realized on D3 branes at non-perturbative F-theory singularities. It identifies intrinsic, non-perturbative theories for k=3,4,6 called OF3_k planes, showing they preserve 12 supercharges and lack marginal couplings, while admitting a holographic large-N description via AdS5 × (S5/Zk) with nontrivial SL(2,Z) bundles. Circle reduction connects these 4D theories to well-known ABJM theories, illuminating ABJM-4D correspondences and offering avenues to study their indices and dynamics. The work provides a string-theoretic framework for exotic N=3 theories and outlines multiple directions to deepen purely field-theoretic understanding and extend to other non-perturbative orientifolds.

Abstract

We introduce a class of four dimensional field theories constructed by quotienting ordinary $\mathcal{N}=4$ $U(N)$ SYM by particular combinations of R-symmetry and $SL(2,\mathbb{Z})$ automorphisms. These theories appear naturally on the worldvolume of D3 branes probing terminal singularities in F-theory, where they can be thought of as non-perturbative generalizations of the O3 plane. We focus on cases preserving only 12 supercharges, where the quotient gives rise to theories with coupling fixed at a value of order one. These constructions possess an unconventional large $N$ limit described by a non-trivial F-theory fibration with base $AdS_5\times (S^5/\mathbb{Z}_k)$. Upon reduction on a circle the $\mathcal{N}=3$ theories flow to well-known $\mathcal{N}=6$ ABJM theories.

N=3 four dimensional field theories

TL;DR

The paper constructs a novel class of four-dimensional N=3 SCFTs by quotienting N=4 U(N) SYM with combined R-symmetry and duality actions, realized on D3 branes at non-perturbative F-theory singularities. It identifies intrinsic, non-perturbative theories for k=3,4,6 called OF3_k planes, showing they preserve 12 supercharges and lack marginal couplings, while admitting a holographic large-N description via AdS5 × (S5/Zk) with nontrivial SL(2,Z) bundles. Circle reduction connects these 4D theories to well-known ABJM theories, illuminating ABJM-4D correspondences and offering avenues to study their indices and dynamics. The work provides a string-theoretic framework for exotic N=3 theories and outlines multiple directions to deepen purely field-theoretic understanding and extend to other non-perturbative orientifolds.

Abstract

We introduce a class of four dimensional field theories constructed by quotienting ordinary SYM by particular combinations of R-symmetry and automorphisms. These theories appear naturally on the worldvolume of D3 branes probing terminal singularities in F-theory, where they can be thought of as non-perturbative generalizations of the O3 plane. We focus on cases preserving only 12 supercharges, where the quotient gives rise to theories with coupling fixed at a value of order one. These constructions possess an unconventional large limit described by a non-trivial F-theory fibration with base . Upon reduction on a circle the theories flow to well-known ABJM theories.

Paper Structure

This paper contains 9 sections, 26 equations, 2 figures, 4 tables.

Table of Contents

  1. Introduction
  2. D3 branes on the O3 plane
  3. F-theory at $\mathcal{N}_{4d}=3$ singularities
  4. Orientifold variants
  5. Preserved supercharges
  6. $\mathcal{N}=3$ and CPT invariance
  7. Large $N$ limit
  8. Conclusions
  9. Self-duality of O3$^-$

Figures (2)

  • Figure 1: The four types of O3 planes, classified based on their discrete torsion Witten:1998xy. A positive superscript denotes non-trivial NSNS torsion, while a tilde denotes nontrivial RR torsion.
  • Figure 2: $T^2/\mathbb{Z}_k$ for $a)\,k=2$, $b)\,k=3$, $c)\,k=4$ and $d)\,k=6$. The black, red, blue and green dots represent the $\mathbb{Z}_k$ fixed points for $k=2,3,4$ and $6$ respectively. The grey regions denote the fundamental domains in each case.