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We non-perturbatively study two-dimensional SU($N$) supersymmetricYang--Mills theory with four supercharges and large $12 \leq N \leq 20$.Although this theory has no known holographic dual, we conduct numericalinvestigations to check for features similar to the sixteen-supercharge theory,which has a well-defined gravity dual. We carry out lattice field theorycalculations to determine the phase diagram, observing a spatial deconfinementtransition, similar to the maximally supersymmetric case. However, thetransition does not continue to strong couplings, implying the absence of aholographic interpretation for this four-supercharge theory.

Phase diagram of two-dimensional SU($N$) super-Yang--Mills theory with four supercharges