We compute the S-d partition function of the fixed point of non-abelian gauge theories in continuous d, using the e-expansion around d = 4. We illustrate in detail the technical aspects of the calculation, including all the factors arising from the gauge-fixing procedure, and the method to deal with the zero-modes of the ghosts. We obtain the result up to NLO, i.e. including two-loop vacuum diagrams. Depending on the sign of the one-loop beta function, there is a fixed point with real gauge coupling in d > 4 or d < 4. In the first case we extrapolate to d = 5 to test a recently proposed construction of the UV fixed point of 5d SU(2) Yang-Mills via a susy-breaking deformation of the E-1 SCFT. We find that the F theorem allows the proposed RG flow. In the second case we extrapolate to d = 3 to test whether QCD(3) with gauge group SU(n(c)) and n(f) fundamental matter fields flows to a CFT or to a symmetry-breaking case. We find that within the regime with a real gauge coupling near d = 4 the CFT phase is always favored. For lower values of n(f) we compare the average of F between the two complex fixed points with its value at the symmetry-breaking phase to give an upper bound of the critical value n*(f) below which the symmetry-breaking phase takes over.

Free Energy on the Sphere for Non-Abelian Gauge Theories / De Cesare, Fabiana; Di Pietro, Lorenzo; Serone, Marco. - In: JOURNAL OF HIGH ENERGY PHYSICS. - ISSN 1029-8479. - 2023:4(2023), pp. 1-46. [10.1007/JHEP04(2023)099]

Free Energy on the Sphere for Non-Abelian Gauge Theories

De Cesare, Fabiana
;
Di Pietro, Lorenzo
;
Serone, Marco
2023-01-01

Abstract

We compute the S-d partition function of the fixed point of non-abelian gauge theories in continuous d, using the e-expansion around d = 4. We illustrate in detail the technical aspects of the calculation, including all the factors arising from the gauge-fixing procedure, and the method to deal with the zero-modes of the ghosts. We obtain the result up to NLO, i.e. including two-loop vacuum diagrams. Depending on the sign of the one-loop beta function, there is a fixed point with real gauge coupling in d > 4 or d < 4. In the first case we extrapolate to d = 5 to test a recently proposed construction of the UV fixed point of 5d SU(2) Yang-Mills via a susy-breaking deformation of the E-1 SCFT. We find that the F theorem allows the proposed RG flow. In the second case we extrapolate to d = 3 to test whether QCD(3) with gauge group SU(n(c)) and n(f) fundamental matter fields flows to a CFT or to a symmetry-breaking case. We find that within the regime with a real gauge coupling near d = 4 the CFT phase is always favored. For lower values of n(f) we compare the average of F between the two complex fixed points with its value at the symmetry-breaking phase to give an upper bound of the critical value n*(f) below which the symmetry-breaking phase takes over.
2023
2023
4
1
46
099
https://doi.org/10.1007/JHEP04(2023)099
http://arxiv.org/abs/2212.11848v1
De Cesare, Fabiana; Di Pietro, Lorenzo; Serone, Marco
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/136934
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