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• W3103449478 abstract "A bstract We analyze the classical and quantum vacua of 2d $$ mathcal{N}=left(8,8right) $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>N</mml:mi> <mml:mo>=</mml:mo> <mml:mfenced> <mml:mn>8</mml:mn> <mml:mn>8</mml:mn> </mml:mfenced> </mml:math> supersymmetric Yang-Mills theory with SU( N ) and U( N ) gauge group, describing the worldvolume interactions of N parallel D1-branes with flat transverse directions $$ {mathrm{mathbb{R}}}^8 $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msup> <mml:mi>ℝ</mml:mi> <mml:mn>8</mml:mn> </mml:msup> </mml:math> . We claim that the IR limit of the SU( N ) theory in the superselection sector labeled M (mod N ) — identified with the internal dynamics of ( M , N )-string bound states of the Type IIB string theory — is described by the symmetric orbifold $$ mathcal{N}=left(8,8right) $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>N</mml:mi> <mml:mo>=</mml:mo> <mml:mfenced> <mml:mn>8</mml:mn> <mml:mn>8</mml:mn> </mml:mfenced> </mml:math> sigma model into $$ {left({mathrm{mathbb{R}}}^8right)}^{D-1}/{mathbb{S}}_D $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msup> <mml:mfenced> <mml:msup> <mml:mi>ℝ</mml:mi> <mml:mn>8</mml:mn> </mml:msup> </mml:mfenced> <mml:mrow> <mml:mi>D</mml:mi> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> <mml:mo>/</mml:mo> <mml:msub> <mml:mi>S</mml:mi> <mml:mi>D</mml:mi> </mml:msub> </mml:math> when D = gcd( M , N ) > 1, and by a single massive vacuum when D = 1, generalizing the conjectures of E. Witten and others. The full worldvolume theory of the D1-branes is the U( N ) theory with an additional U(1) 2-form gauge field B coming from the string theory Kalb-Ramond field. This U( N ) + B theory has generalized field configurations, labeled by the $$ mathrm{mathbb{Z}} $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>ℤ</mml:mi> </mml:math> -valued generalized electric flux and an independent $$ {mathrm{mathbb{Z}}}_N $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msub> <mml:mi>ℤ</mml:mi> <mml:mi>N</mml:mi> </mml:msub> </mml:math> -valued ’t Hooft flux. We argue that in the quantum mechanical theory, the ( M , N )-string sector with M units of electric flux has a $$ {mathrm{mathbb{Z}}}_N $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msub> <mml:mi>ℤ</mml:mi> <mml:mi>N</mml:mi> </mml:msub> </mml:math> -valued discrete θ angle specified by M (mod N ) dual to the ’t Hooft flux. Adding the brane center-of-mass degrees of freedom to the SU( N ) theory, we claim that the IR limit of the U( N ) + B theory in the sector with M bound F-strings is described by the $$ mathcal{N}=left(8,8right) $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>N</mml:mi> <mml:mo>=</mml:mo> <mml:mfenced> <mml:mn>8</mml:mn> <mml:mn>8</mml:mn> </mml:mfenced> </mml:math> sigma model into $$ {mathrm{Sym}}^Dleft({mathrm{mathbb{R}}}^8right) $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msup> <mml:mrow> <mml:mi>S</mml:mi> <mml:mi>y</mml:mi> <mml:mi>m</mml:mi> </mml:mrow> <mml:mi>D</mml:mi> </mml:msup> <mml:mfenced> <mml:msup> <mml:mi>ℝ</mml:mi> <mml:mn>8</mml:mn> </mml:msup> </mml:mfenced> </mml:math> . We provide strong evidence for these claims by computing an $$ mathcal{N}=left(8,8right) $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>N</mml:mi> <mml:mo>=</mml:mo> <mml:mfenced> <mml:mn>8</mml:mn> <mml:mn>8</mml:mn> </mml:mfenced> </mml:math> analog of the elliptic genus of the UV gauge theories and of their conjectured IR limit sigma models, and showing they agree. Agreement is established by noting that the elliptic genera are modular-invariant Abelian (multi-periodic and meromorphic) functions, which turns out to be very restrictive." @default.
• W3103449478 created "2020-11-23" @default.
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• W3103449478 date "2017-11-01" @default.
• W3103449478 modified "2023-10-12" @default.
• W3103449478 title "Quantum vacua of 2d maximally supersymmetric Yang-Mills theory" @default.
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• W3103449478 doi "https://doi.org/10.1007/jhep11(2017)140" @default.
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