M-theory realization of a N=1 supersymmetric chiral gauge theory in four dimensions

TL;DR

This paper explores M-theory configurations of chiral gauge theories, connecting brane setups with gauge theory properties, and identifies geometric structures corresponding to different gauge theory branches and phase transitions.

Contribution

It provides a detailed M-theory realization of chiral gauge theories with orientifold planes, including the Higgs and Coulomb branches, and introduces geometric interpretations of phase transitions.

Findings

M-theory curves correspond to Coulomb and Higgs branches.

Rational curves represent NS'5-branes on O6 planes.

Fixed points mediating chiral-non-chiral transitions are identified.

Abstract

We study M5-brane configuration of the chiral gauge theory whose Type IIA brane configuration with orientifold 6-plane(O6) is studied by various authors. Much of the paper is devoted to studying M-theory picture of SO/Sp gauge theory with fundamental flavors realized in Type IIA setup with O6-plane. The Higgs branch of N=2 SO/Sp gauge theory is studied and the curve corresponding to rotated brane configuration is presented. In the chiral gauge theory, the middle NS$^{\prime}$5-brane on top of the O6 plane is realized as a detached rational curve. Depending on a location of the rational curve in $x^7$ direction, the same curve plus the rational curve can be interpreted as describing the Coulomb branch of $SU(2N_c)$ chiral gauge theory, $SO(2N_c)/Sp(N_c)$ gauge theory with $N_f/(N_f+4)$ fundamental hypermultiplets. Various consistency checks for this proposal are made. By introducing two more rational curves corresponding to NS$^{\prime}$5-branes, one can produce a non-trivial fixed point which mediates chiral non-chiral transition.