On the structure of non-planar strong coupling corrections to correlators of BPS Wilson loops and chiral primary operators
M. Beccaria, A. A. Tseytlin
Abstract
A bstract Starting with some known localization (matrix model) representations for correlators involving 1/2 BPS circular Wilson loop $$ \mathcal{W} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>W</mml:mi> </mml:math> in $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 4 SYM theory we work out their 1 /N expansions in the limit of large ’t Hooft coupling λ . Motivated by a possibility of eventual matching to higher genus corrections in dual string theory we follow arXiv:2007.08512 and express the result in terms of the string coupling $$ {g}_{\mathrm{s}}\sim {g}_{\mathrm{YM}}^2\sim \lambda /N $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>g</mml:mi> <mml:mi>s</mml:mi> </mml:msub> <mml:mo>∼</mml:mo> <mml:msubsup> <mml:mi>g</mml:mi> <mml:mi>YM</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> <mml:mo>∼</mml:mo> <mml:mi>λ</mml:mi> <mml:mo>/</mml:mo> <mml:mi>N</mml:mi> </mml:math> and string tension $$ T\sim \sqrt{\lambda } $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>T</mml:mi> <mml:mo>∼</mml:mo> <mml:msqrt> <mml:mi>λ</mml:mi> </mml:msqrt> </mml:math> . Keeping only the leading in 1/ T term at each order in g s we observe that while the 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> is a series in $$ {g}_{\mathrm{s}}^2/T $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>g</mml:mi> <mml:mi>s</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> <mml:mo>/</mml:mo> <mml:mi>T</mml:mi> </mml:math> , the correlator of the Wilson loop with chiral primary operators $$ {\mathcal{O}}_J $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>O</mml:mi> <mml:mi>J</mml:mi> </mml:msub> </mml:math> has expansion in powers of $$ {g}_{\mathrm{s}}^2/{T}^2 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>g</mml:mi> <mml:mi>s</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> <mml:mo>/</mml:mo> <mml:msup> <mml:mi>T</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:math> . Like in the case 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> where these leading terms are known to resum into an exponential of a “one-handle” contribution $$ \sim {g}_{\mathrm{s}}^2/T $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mo>∼</mml:mo> <mml:msubsup> <mml:mi>g</mml:mi> <mml:mi>s</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> <mml:mo>/</mml:mo> <mml:mi>T</mml:mi> </mml:math> , the leading strong coupling terms in $$ \left\langle {\mathcal{WO}}_J\right\rangle $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mfenced> <mml:msub> <mml:mi>WO</mml:mi> <mml:mi>J</mml:mi> </mml:msub> </mml:mfenced> </mml:math> sum up to a simple square root function of $$ {g}_{\mathrm{s}}^2/{T}^2 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>g</mml:mi> <mml:mi>s</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> <mml:mo>/</mml:mo> <mml:msup> <mml:mi>T</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:math> . Analogous expansions in powers of $$ {g}_{\mathrm{s}}^2/T $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>g</mml:mi> <mml:mi>s</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> <mml:mo>/</mml:mo> <mml:mi>T</mml:mi> </mml:math> are found for correlators of several coincident Wilson loops and they again have a simple resummed form. We also find similar expansions for correlators of coincident 1/2 BPS Wilson loops in the ABJM theory.