We propose a description of the gluon scattering amplitudes as the inverse Mellin transforms of the conformal correlators of light operators in two-dimensional Liouville theory tensored with WZW-like chiral currents on the celestial sphere. The dimensions of operators are Mellin dual to gluon light cone energies while their positions are determined by the gluon momentum directions. Tree-level approximation in Yang-Mills theory corresponds to the semiclassical limit of Liouville theory. By comparing subleading corrections, we find , where b is the Liouville coupling constant, is the Yang Mills coupling at the renormalization scale M and is the one-loop coefficient of the Yang-Mills beta function.
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"surname": "Stieberger",
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"value": "Department of Physics, Northeastern University, Boston, USA"
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"surname": "Taylor",
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"value": "We propose a description of the gluon scattering amplitudes as the inverse Mellin transforms of the conformal correlators of light operators in two-dimensional Liouville theory tensored with WZW-like chiral currents on the celestial sphere. The dimensions of operators are Mellin dual to gluon light cone energies while their positions are determined by the gluon momentum directions. Tree-level approximation in Yang-Mills theory corresponds to the semiclassical limit of Liouville theory. By comparing subleading corrections, we find <math><msup><mrow><mi>b</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>=</mo><msup><mrow><mo>(</mo><mn>8</mn><msup><mrow><mi>\u03c0</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow><mrow><mo>\u2212</mo><mn>1</mn></mrow></msup><msub><mrow><mi>\u03b2</mi></mrow><mrow><mn>0</mn></mrow></msub><mspace width=\"0.2em\"></mspace><msup><mrow><mi>g</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>(</mo><mi>M</mi><mo>)</mo></math>, where b is the Liouville coupling constant, <math><mi>g</mi><mo>(</mo><mi>M</mi><mo>)</mo></math> is the Yang Mills coupling at the renormalization scale M and <math><msub><mrow><mi>\u03b2</mi></mrow><mrow><mn>0</mn></mrow></msub></math> is the one-loop coefficient of the Yang-Mills beta function."
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