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• W3136127411 abstract "Abstract We introduce and study a surface defect in four-dimensional gauge theories supporting nested instantons with respect to the parabolic reduction of the gauge group at the defect. This is engineered from a $$mathrm{{D3/D7}}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mi>D</mml:mi> <mml:mn>3</mml:mn> <mml:mo>/</mml:mo> <mml:mi>D</mml:mi> <mml:mn>7</mml:mn> </mml:mrow> </mml:math> -branes system on a non-compact Calabi–Yau threefold X . For $$X=T^2times T^*{{mathcal {C}}}_{g,k}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mi>X</mml:mi> <mml:mo>=</mml:mo> <mml:msup> <mml:mi>T</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>×</mml:mo> <mml:msup> <mml:mi>T</mml:mi> <mml:mo>∗</mml:mo> </mml:msup> <mml:msub> <mml:mi>C</mml:mi> <mml:mrow> <mml:mi>g</mml:mi> <mml:mo>,</mml:mo> <mml:mi>k</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> , the product of a two torus $$T^2$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msup> <mml:mi>T</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:math> times the cotangent bundle over a Riemann surface $${{mathcal {C}}}_{g,k}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msub> <mml:mi>C</mml:mi> <mml:mrow> <mml:mi>g</mml:mi> <mml:mo>,</mml:mo> <mml:mi>k</mml:mi> </mml:mrow> </mml:msub> </mml:math> with marked points, we propose an effective theory in the limit of small volume of $${mathcal C}_{g,k}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msub> <mml:mi>C</mml:mi> <mml:mrow> <mml:mi>g</mml:mi> <mml:mo>,</mml:mo> <mml:mi>k</mml:mi> </mml:mrow> </mml:msub> </mml:math> given as a comet-shaped quiver gauge theory on $$T^2$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msup> <mml:mi>T</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:math> , the tail of the comet being made of a flag quiver for each marked point and the head describing the degrees of freedom due to the genus g . Mathematically, we obtain for a single $$mathrm{{D7}}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mi>D</mml:mi> <mml:mn>7</mml:mn> </mml:mrow> </mml:math> -brane conjectural explicit formulae for the virtual equivariant elliptic genus of a certain bundle over the moduli space of the nested Hilbert scheme of points on the affine plane. A connection with elliptic cohomology of character varieties and an elliptic version of modified Macdonald polynomials naturally arises." @default.
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• W3136127411 date "2021-03-11" @default.
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• W3136127411 title "Defects, nested instantons and comet-shaped quivers" @default.
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