Nonperturbative phase diagram of two-dimensional N=(2, 2) super-Yang-Mills theory

We consider two-dimensional <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi mathvariant="script">N</a:mi><a:mo>=</a:mo><a:mo stretchy="false">(</a:mo><a:mn>2</a:mn><a:mo>,</a:mo><a:mn>2</a:mn><a:mo stretchy="false">)</a:mo></a:math> Yang-Mills theory with gauge group <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:mrow><f:mi>SU</f:mi><f:mo stretchy="false">(</f:mo><f:mi>N</f:mi><f:mo stretchy="false">)</f:mo></f:mrow></f:math> in Euclidean signature compactified on a torus with thermal fermion boundary conditions imposed on one cycle. We perform nonperturbative lattice analyses of this theory for large <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"><j:mn>12</j:mn><j:mo>≤</j:mo><j:mi>N</j:mi><j:mo>≤</j:mo><j:mn>20</j:mn></j:math>. Although no holographic dual of this theory is yet known, we conduct numerical investigations to check for features similar to the two-dimensional <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"><l:mi mathvariant="script">N</l:mi><l:mo>=</l:mo><l:mo stretchy="false">(</l:mo><l:mn>8</l:mn><l:mo>,</l:mo><l:mn>8</l:mn><l:mo stretchy="false">)</l:mo></l:math> Yang–Mills theory, which has a well-defined gravity dual. We perform lattice field theory calculations to determine the phase diagram, observing a spatial deconfinement transition similar to the maximally supersymmetric case. However, the transition does not continue to low temperature, implying the absence of a topology-changing transition between black hole geometries in any holographic dual for this four-supercharge theory.