Ising string beyond the Nambu-Goto action

A major result of the effective string theory (EST) description of confinement is the so-called “low-energy universality”, which states that the first few terms of the large distance expansion of any EST are universal and coincide with those of the Nambu-Goto action. Going beyond this approximation is one of the most interesting open problems in the EST. In the higher-order terms beyond Nambu-Goto several important pieces of physical information are encoded, which could improve our understanding of the physical mechanisms behind confinement and of the physical degrees of freedoms which originate the EST. In this paper we evaluate numerically the first two of these corrections in the case of the three-dimensional gauge Ising model. The first of them turns out to be negative; <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:msub><a:mrow><a:mi>γ</a:mi></a:mrow><a:mrow><a:mn>3</a:mn></a:mrow></a:msub><a:mo>=</a:mo><a:mo>−</a:mo><a:mn>0.00048</a:mn><a:mo stretchy="false">(</a:mo><a:mn>4</a:mn><a:mo stretchy="false">)</a:mo></a:mrow></a:math>, similar (but not equal) to the one recently measured in the <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mrow><e:mi>S</e:mi><e:mi>U</e:mi><e:mo stretchy="false">(</e:mo><e:mn>2</e:mn><e:mo stretchy="false">)</e:mo></e:mrow></e:math> Yang-Mills theory in three dimensions and compatible with the bootstrap bound <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mrow><i:msub><i:mrow><i:mi>γ</i:mi></i:mrow><i:mrow><i:mn>3</i:mn></i:mrow></i:msub><i:mo>≥</i:mo><i:mo>−</i:mo><i:mfrac><i:mrow><i:mn>1</i:mn></i:mrow><i:mrow><i:mn>768</i:mn></i:mrow></i:mfrac></i:mrow></i:math>. Published by the American Physical Society 2024