Abstract
Starting with some known localization (matrix model) representations for correlators involving 1/2 BPS circular Wilson loop mathcal{W} in mathcal{N} = 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}}^2sim lambda /N and string tension Tsim sqrt{lambda } . Keeping only the leading in 1/T term at each order in gs we observe that while the expansion of leftlangle mathcal{W}rightrangle is a series in {g}_{mathrm{s}}^2/T , the correlator of the Wilson loop with chiral primary operators {mathcal{O}}_J has expansion in powers of {g}_{mathrm{s}}^2/{T}^2 . Like in the case of leftlangle mathcal{W}rightrangle where these leading terms are known to resum into an exponential of a “one-handle” contribution sim {g}_{mathrm{s}}^2/T , the leading strong coupling terms in leftlangle {mathcal{WO}}_Jrightrangle sum up to a simple square root function of {g}_{mathrm{s}}^2/{T}^2 . Analogous expansions in powers of {g}_{mathrm{s}}^2/T 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.
Highlights
Introduction and summaryAn important direction is to extend checks of AdS/CFT correspondence to subleading orders in 1/N expansion on the gauge theory side or higher genus corrections on the dual string theory side
Keeping only the leading in 1/T term at each order in gs we observe that while the expansion of W is a series in gs2/T, the correlator of the Wilson loop with chiral primary operators OJ has expansion in powers of gs2/T 2
We find similar expansions for correlators of coincident 1/2 BPS Wilson loops in the ABJM theory
Summary
An important direction is to extend checks of AdS/CFT correspondence to subleading orders in 1/N expansion on the gauge theory side or higher genus corrections on the dual string theory side. Our aim below will be to extract similar predictions about the structure of small gs, large T string theory corrections and their possible resummation for other closely related observables for which the exact gauge theory results can be found from matrix model representations following from localization (in some cases generalizing partial results in the literature). The reason why the large T expansion (1.8) has a different structure than (1.3) and why the resummed expressions in (1.5) and in (1.10) are not directly related by (1.11) is that subleading in 1/T terms at each order in gs in W in (1.3) contribute to log W and, as a result, reorganize its large T expansion (see (2.45)– (2.46) for details). Where b(ij) are polynomials in J1, J2 (see (3.16), (3.22), (3.23))
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