Excitations of bubbling geometries for line defects

Abstract

The half-Bogomolny-Prasad-Sommerfield (BPS) Wilson line operators in the irreducible representations labeled by the Young diagrams for <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi mathvariant="script">N</a:mi><a:mo>=</a:mo><a:mn>4</a:mn></a:math> <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"><d:mi>U</d:mi><d:mo stretchy="false">(</d:mo><d:mi>N</d:mi><d:mo stretchy="false">)</d:mo></d:math> super Yang-Mills theory have gravity dual descriptions. When the number <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:mi>k</h:mi></h:math> of boxes of the diagram grows as <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"><j:mi>k</j:mi><j:mo>∼</j:mo><j:msup><j:mi>N</j:mi><j:mn>2</j:mn></j:msup></j:math>, the bubbling geometries emerge. We evaluate the spectra of quantum fluctuations on the particular bubbling geometry involving the largest degeneracy from the large <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"><l:mi>N</l:mi></l:math> and large <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"><n:mi>k</n:mi></n:math> limit of the supersymmetric indices decorated by the Wilson lines. The spectra of excitations over multiparticle <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"><p:mrow><p:mn>1</p:mn><p:mo>/</p:mo><p:mn>8</p:mn></p:mrow></p:math>- and <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"><r:mrow><r:mn>1</r:mn><r:mo>/</r:mo><r:mn>2</r:mn></r:mrow></r:math>-BPS states agree with the numbers of conjugacy classes of general linear group over finite fields while degeneracies of single particle BPS states are given by the general necklace polynomial. The bubbling geometry exhibits a new class of asymptotic degeneracy of states. Published by the American Physical Society 2024

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