Spectrum of open confining strings in the large- N c limit

In this study, we conduct a thorough examination of the spectrum of the open confining string in <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:mn>3</a:mn> <a:mo>+</a:mo> <a:mn>1</a:mn> </a:mrow> </a:math> dimensions, commonly referred to as the open flux tube, across various gauge groups of <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mi>S</c:mi> <c:mi>U</c:mi> <c:mo stretchy="false">(</c:mo> <c:msub> <c:mi>N</c:mi> <c:mi>c</c:mi> </c:msub> <c:mo stretchy="false">)</c:mo> </c:math> . Our primary objective is to explore its behavior as we approach the large- <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:msub> <g:mi>N</g:mi> <g:mi>c</g:mi> </g:msub> </g:math> limit and the identification of possible world-sheet axion states. Specifically, we undertake a detailed analysis of the associated spectrum for <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:msub> <i:mi>N</i:mi> <i:mi>c</i:mi> </i:msub> <i:mo>=</i:mo> <i:mn>3</i:mn> </i:math> , 4, 5, 6. This marks the first systematic investigation of the open flux-tube spectrum within the context of the large- <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:msub> <k:mi>N</k:mi> <k:mi>c</k:mi> </k:msub> </k:math> limit. More specifically, we analyze the spectra of flux tubes that form between a static quark-antiquark pair, considering a significant number of radial excitations and eight irreducible representations characterized by the quantum numbers of angular momentum <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:mi mathvariant="normal">Λ</m:mi> </m:math> , charge conjugation and parity <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"> <p:msub> <p:mi>η</p:mi> <p:mrow> <p:mi>C</p:mi> <p:mi>P</p:mi> </p:mrow> </p:msub> </p:math> , and the reflection symmetry <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"> <r:mi>ε</r:mi> </r:math> for <t:math xmlns:t="http://www.w3.org/1998/Math/MathML" display="inline"> <t:mi mathvariant="normal">Λ</t:mi> <t:mo>=</t:mo> <t:mn>0</t:mn> </t:math> . To this purpose we employ a diverse set of suitable operators, an anisotropic action, and smearing techniques, and solve the generalized eigenvalue problem. We compare our findings with predictions from the Nambu-Goto string model to assess potential tensions indicative of novel phenomena such as the existence of axionlike state along the flux-tube world sheet. Notably, we provide undoubted evidence of the existence of a massive axionlike particle with the same mass as the corresponding axion extracted within the context of closed flux tube. This strengthens the conjecture that the axion is a property of the world sheet of the QCD string.