<p>We use equivariant localization and holography to study four-dimensional <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">N</mi> <mo>=</mo> <mn>1</mn> </math></EquationSource> <EquationSource Format="TEX">\( \mathcal{N}=1 \)</EquationSource> </InlineEquation> superconformal field theories arising from M5-branes wrapped on a punctured Riemann surface. We explain how, given a Riemann surface with marked points, one can glue in a “puncture geometry” locally around each point. Using equivariant localization we show that the central charge consists of a bulk contribution plus localized puncture contributions. We recover and generalize the known results for locally <InlineEquation ID="IEq2"> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">N</mi> <mo>=</mo> <mn>2</mn> </math></EquationSource> <EquationSource Format="TEX">\( \mathcal{N}=2 \)</EquationSource> </InlineEquation> preserving punctures, and derive new results for genuinely locally <InlineEquation ID="IEq3"> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">N</mi> <mo>=</mo> <mn>1</mn> </math></EquationSource> <EquationSource Format="TEX">\( \mathcal{N}=1 \)</EquationSource> </InlineEquation> preserving punctures.</p>