2d N=(0,1) gauge theories, Spin(7) orientifolds and triality

I will introduce a new brane engineering for 2d minimally supersymmetric, i.e. N=(0,1), gauge theories. Starting with 2d N=(0,2) gauge theories on D1-branes probing Calabi-Yau 4-folds, a brand new orientifold configuration named ’Spin(7) orientifold’ is constructed and the resultant 2d N=(0,1) theories on D1-branes are derived. Using this method, one can build an infinite family of 2d N=(0,1) gauge theories explicitly. Furthermore, the N=(0,1) triality, proposed by Gukov, Pei and Putrov, enjoys a geometric interpretation as the non-uniqueness of the map between gauge theories and Spin(7) orientifolds. The (0,1) triality can then be regarded as inherited from the N=(0,2) triality of gauge theories associated with Calabi-Yau 4-folds. Furthermore, there are theories with N=(0,1) sector coupled to (0,2) sector, where both sectors respectively enjoy (0,1) and (0,2) trialities.