1/N expansion of circular Wilson loop in $$ \mathcal{N} $$ = 2 superconformal SU(N) × SU(N) quiver
M. Beccaria, A.A. Tseytlin
Abstract
A bstract Localization approach to $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 2 superconformal SU( N ) × SU( N ) quiver theory leads to a non-Gaussian two-matrix model representation for the expectation value of BPS circular SU( N ) Wilson loop $$ \left\langle \mathcal{W}\right\rangle $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mfenced> <mml:mi>W</mml:mi> </mml:mfenced> </mml:math> . We study the subleading 1 /N 2 term in the large N expansion of $$ \left\langle \mathcal{W}\right\rangle $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mfenced> <mml:mi>W</mml:mi> </mml:mfenced> </mml:math> at weak and strong coupling. We concentrate on the case of the symmetric quiver with equal gauge couplings which is equivalent to the ℤ 2 orbifold of the SU(2 N ) $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 4 SYM theory. This orbifold gauge theory should be dual to type IIB superstring in AdS 5 × ( S 5 / ℤ 2 ). We present a string theory argument suggesting that the 1 /N 2 term in $$ \left\langle \mathcal{W}\right\rangle $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mfenced> <mml:mi>W</mml:mi> </mml:mfenced> </mml:math> in the orbifold theory should have the same strong-coupling asymptotics λ 3 / 2 as in the $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 4 SYM case. We support this prediction on the gauge theory side by a numerical study of the localization matrix model. We also find a relation between the 1 /N 2 term in the Wilson loop expectation value and the derivative of the free energy of the orbifold gauge theory on 4-sphere.