Vanishing Polyakov loop for QCD with twelve massless quarks
We consider continuum-formulation QCD in four dimensions with twelve massless fundamental quark flavors. Splitting the SU(N) gauge field into background and fluctuation parts, we use well-developed techniques to calculate the one-loop effective action for the theory. We find that for constant self-d...
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Elsevier
2025-03-01
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| Series: | Physics Letters B |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S037026932500070X |
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| author | Seth Grable Paul Romatschke |
| author_facet | Seth Grable Paul Romatschke |
| author_sort | Seth Grable |
| collection | DOAJ |
| description | We consider continuum-formulation QCD in four dimensions with twelve massless fundamental quark flavors. Splitting the SU(N) gauge field into background and fluctuation parts, we use well-developed techniques to calculate the one-loop effective action for the theory. We find that for constant self-dual background field-strength tensor the notorious infrared divergences of the effective action cancel between gauge and matter sectors if the number of massless quark flavors is exactly Nf=4N. The ultraviolet divergencies of the effective action are non-perturbatively renormalized with a β-function that matches the known perturbative result in the high energy limit. The resulting UV- and IR-finite effective action possesses a non-trivial saddle which has lower free energy than the perturbative vacuum, and for which the expectation value of the Polyakov loop vanishes. Inclusion of finite temperature effects points to the presence of a first-order phase transition to the perturbative vacuum with a calculable critical temperature. |
| format | Article |
| id | doaj-art-d952e2a9c8fe4dbfa560cfac1cb25db2 |
| institution | DOAJ |
| issn | 0370-2693 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Physics Letters B |
| spelling | doaj-art-d952e2a9c8fe4dbfa560cfac1cb25db22025-08-20T02:59:53ZengElsevierPhysics Letters B0370-26932025-03-0186213931010.1016/j.physletb.2025.139310Vanishing Polyakov loop for QCD with twelve massless quarksSeth Grable0Paul Romatschke1Department of Physics, University of Colorado, Boulder, CO 80309, USADepartment of Physics, University of Colorado, Boulder, CO 80309, USA; Center for Theory of Quantum Matter, University of Colorado, Boulder, CO 80309, USAWe consider continuum-formulation QCD in four dimensions with twelve massless fundamental quark flavors. Splitting the SU(N) gauge field into background and fluctuation parts, we use well-developed techniques to calculate the one-loop effective action for the theory. We find that for constant self-dual background field-strength tensor the notorious infrared divergences of the effective action cancel between gauge and matter sectors if the number of massless quark flavors is exactly Nf=4N. The ultraviolet divergencies of the effective action are non-perturbatively renormalized with a β-function that matches the known perturbative result in the high energy limit. The resulting UV- and IR-finite effective action possesses a non-trivial saddle which has lower free energy than the perturbative vacuum, and for which the expectation value of the Polyakov loop vanishes. Inclusion of finite temperature effects points to the presence of a first-order phase transition to the perturbative vacuum with a calculable critical temperature.http://www.sciencedirect.com/science/article/pii/S037026932500070X |
| spellingShingle | Seth Grable Paul Romatschke Vanishing Polyakov loop for QCD with twelve massless quarks Physics Letters B |
| title | Vanishing Polyakov loop for QCD with twelve massless quarks |
| title_full | Vanishing Polyakov loop for QCD with twelve massless quarks |
| title_fullStr | Vanishing Polyakov loop for QCD with twelve massless quarks |
| title_full_unstemmed | Vanishing Polyakov loop for QCD with twelve massless quarks |
| title_short | Vanishing Polyakov loop for QCD with twelve massless quarks |
| title_sort | vanishing polyakov loop for qcd with twelve massless quarks |
| url | http://www.sciencedirect.com/science/article/pii/S037026932500070X |
| work_keys_str_mv | AT sethgrable vanishingpolyakovloopforqcdwithtwelvemasslessquarks AT paulromatschke vanishingpolyakovloopforqcdwithtwelvemasslessquarks |