Free Energy on the Sphere for Non-Abelian Gauge Theories
| Title: | Free Energy on the Sphere for Non-Abelian Gauge Theories |
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| Authors: | De Cesare, Fabiana, Di Pietro, Lorenzo, Serone, Marco |
| Publication Year: | 2022 |
| Collection: | Condensed Matter High Energy Physics - Lattice High Energy Physics - Theory |
| Subject Terms: | High Energy Physics - Theory, Condensed Matter - Strongly Correlated Electrons, High Energy Physics - Lattice |
| More Details: | We compute the $S^d$ partition function of the fixed point of non-abelian gauge theories in continuous $d$, using the $\epsilon$-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 phase. 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. Comment: 50 pages, 4 figures |
| Document Type: | Working Paper |
| DOI: | 10.1007/JHEP04(2023)099 |
| Access URL: | http://arxiv.org/abs/2212.11848 |
| Accession Number: | edsarx.2212.11848 |
| Database: | arXiv |
| DOI: | 10.1007/JHEP04(2023)099 |
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