We study <InlineEquation ID="IEq2"> <EquationSource Format="MATHML"><math display="inline"> <mfrac> <mn>1</mn> <mn>4</mn> </mfrac> </math></EquationSource> <EquationSource Format="TEX">$ \frac{1}{4} $</EquationSource> </InlineEquation>-BPS Wilson loops in four-dimensional SU(N) <InlineEquation ID="IEq3"> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">N</mi> </math></EquationSource> <EquationSource Format="TEX">$ \mathcal{N} $</EquationSource> </InlineEquation> = 2 super-Yang-Mills theories with conformal matter in an arbitrary representation <InlineEquation ID="IEq4"> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">R</mi> </math></EquationSource> <EquationSource Format="TEX">$ \mathcal{R} $</EquationSource> </InlineEquation>. These operators are formed of two meridians on the two-sphere separated by an arbitrary opening angle. We conjecture that these observables are encoded in a modification of Pestun’s matrix model. The matrix representation of these operators resembles that of the <InlineEquation ID="IEq5"> <EquationSource Format="MATHML"><math display="inline"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </math></EquationSource> <EquationSource Format="TEX">$ \frac{1}{2} $</EquationSource> </InlineEquation>-BPS circular Wilson loop, differing only for a rescaling in the exponent. We compare the matrix model predictions with an explicit three-loop calculation in flat space based on standard Feynman-diagram techniques, finding perfect agreement. Finally, exploiting the matrix model representation of these Wilson loops, we study the large-N limit at strong coupling of <InlineEquation ID="IEq6"> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">N</mi> </math></EquationSource> <EquationSource Format="TEX">$ \mathcal{N} $</EquationSource> </InlineEquation> = 2 superconformal QCD, finding a surprising transition in the vacuum expectation value for a critical opening angle.

Into the wedge of $ \mathcal{N} $ = 2 superconformal gauge theories

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2025年7月10日

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L. Griguolo,
L. Guerrini,
A. Testa

摘要

We study $\frac{1}{4}$ $ \frac{1}{4} $ -BPS Wilson loops in four-dimensional SU(N) $N$ $ \mathcal{N} $ = 2 super-Yang-Mills theories with conformal matter in an arbitrary representation $R$ $ \mathcal{R} $ . These operators are formed of two meridians on the two-sphere separated by an arbitrary opening angle. We conjecture that these observables are encoded in a modification of Pestun’s matrix model. The matrix representation of these operators resembles that of the $\frac{1}{2}$ $ \frac{1}{2} $ -BPS circular Wilson loop, differing only for a rescaling in the exponent. We compare the matrix model predictions with an explicit three-loop calculation in flat space based on standard Feynman-diagram techniques, finding perfect agreement. Finally, exploiting the matrix model representation of these Wilson loops, we study the large-N limit at strong coupling of $N$ $ \mathcal{N} $ = 2 superconformal QCD, finding a surprising transition in the vacuum expectation value for a critical opening angle.

Into the wedge of \( \mathcal{N} \) = 2 superconformal gauge theories

摘要