Generalizations of the AGT correspondence between 4D supersymmetric gauge theory on with Ω-deformation and 2D Liouville conformal field theory include a correspondence between 4D supersymmetric gauge theories, , on , , with Ω-deformation and 2D conformal field theories with (n-th parafermion ) symmetry and symmetry. In this work, we trivialize the factor with symmetry in the 4D instanton partition functions on (by using specific choices of parameters and imposing specific conditions on the N-tuples of Young diagrams that label the states), and extract the 2D WZW conformal blocks, , .
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"value": "Generalizations of the AGT correspondence between 4D <math><mi>N</mi><mo>=</mo><mn>2</mn></math> <math><mi>S</mi><mi>U</mi><mo>(</mo><mn>2</mn><mo>)</mo></math> supersymmetric gauge theory on <math><msup><mrow><mi>C</mi></mrow><mrow><mn>2</mn></mrow></msup></math> with \u03a9-deformation and 2D Liouville conformal field theory include a correspondence between 4D <math><mi>N</mi><mo>=</mo><mn>2</mn></math> <math><mi>S</mi><mi>U</mi><mo>(</mo><mi>N</mi><mo>)</mo></math> supersymmetric gauge theories, <math><mi>N</mi><mo>=</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mo>\u2026</mo></math>, on <math><msup><mrow><mi>C</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>/</mo><msub><mrow><mi>Z</mi></mrow><mrow><mi>n</mi></mrow></msub></math>, <math><mi>n</mi><mo>=</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mo>\u2026</mo></math>, with \u03a9-deformation and 2D conformal field theories with <math><msubsup><mrow><mi>W</mi></mrow><mrow><mi>N</mi><mo>,</mo><mi>n</mi></mrow><mrow><mspace width=\"0.2em\"></mspace><mi>p</mi><mi>a</mi><mi>r</mi><mi>a</mi></mrow></msubsup></math> (n-th parafermion <math><msub><mrow><mi>W</mi></mrow><mrow><mi>N</mi></mrow></msub></math>) symmetry and <math><mover><mrow><mi>sl</mi></mrow><mrow><mo>\u02c6</mo></mrow></mover><msub><mrow><mo>(</mo><mi>n</mi><mo>)</mo></mrow><mrow><mi>N</mi></mrow></msub></math> symmetry. In this work, we trivialize the factor with <math><msubsup><mrow><mi>W</mi></mrow><mrow><mi>N</mi><mo>,</mo><mi>n</mi></mrow><mrow><mspace width=\"0.2em\"></mspace><mi>p</mi><mi>a</mi><mi>r</mi><mi>a</mi></mrow></msubsup></math> symmetry in the 4D <math><mi>S</mi><mi>U</mi><mo>(</mo><mi>N</mi><mo>)</mo></math> instanton partition functions on <math><msup><mrow><mi>C</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>/</mo><msub><mrow><mi>Z</mi></mrow><mrow><mi>n</mi></mrow></msub></math> (by using specific choices of parameters and imposing specific conditions on the N-tuples of Young diagrams that label the states), and extract the 2D <math><mover><mrow><mi>sl</mi></mrow><mrow><mo>\u02c6</mo></mrow></mover><msub><mrow><mo>(</mo><mi>n</mi><mo>)</mo></mrow><mrow><mi>N</mi></mrow></msub></math> WZW conformal blocks, <math><mi>n</mi><mo>=</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mo>\u2026</mo></math>, <math><mi>N</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mo>\u2026</mo></math>."
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