On 1/2-BPS Wilson-'t Hooft loops

TL;DR

This work studies 1/2-BPS Wilson-'t Hooft loops in N=4 SYM by evaluating all-genus contributions through a bulk D3-brane carrying both electric (F1) and magnetic (D1) charges. The circular loop observable is computed as a D3-brane action, yielding <WH> = e^{2N(κ√(1+κ^2) + asinh κ)}, with κ^2 = (n^2 λ)/(4N)^2 + (m^2 tilde{λ})/(4N)^2, and reducing to <WH> ≈ e^{√(n^2 λ + m^2 tilde{λ})} in the large-N limit; the result respects SL(2,Z) duality, extended to nonzero axion C0 where κ^2 = (n+mC0)^2 λ/(4N)^2 + m^2 tilde{λ}/(4N)^2 and is equivalently expressed in terms of τ. Supersymmetry analysis confirms a 1/2-BPS D3-brane configuration with combined electric and magnetic flux, and the discussion of 5-brane pictures suggests consistent dual descriptions for antisymmetric representations. Overall, the bulk D3-brane approach provides a nonperturbative all-genus check of the gauge/string duality for dyonic Wilson-'t Hooft loops and motivates further exploration of more general representations and bubbling geometries.

Abstract

We investigate the 1/2-BPS Wilson-'t Hooft loops in ${\cal N}=4$ Super-Yang-Mills theory. We use the bulk D-brane with both electric and magnetic charges to calculate the all genus contribution of the circular loops. The expectation value of Wilson-'t Hooft loops are in perfect agreement with the result through supersymmetric condition and duality transformation in the gauge theory.