Perturbative aspects of deformed Yang-Mills theory

Center-stabilized SU(N) Yang-Mills theories on R3 x S1 are QCD-like theories that can be engineered to remain weakly-coupled at all energy scales by taking the S1 circle length L to be sufficiently small. In this regime, these theories admit effective long-distance descriptions as Abelian U(1)N-1 gauge theories on R3, and semiclassics can be reliably employed to study nonperturbative phenomena such as color confinement and the generation of mass gaps in an analytical setting. At the perturbative tree level, the long-distance effective theory contains (N- 1) free photons with identical gauge couplings g23 equivalent to g2=L. Vacuum-polarization effects, from integrating out heavy charged fields, lift this degeneracy to give bN2c distinct values, g2(2L) less than or similar to g23;lL less than or similar to g2(N2 pi L). In this work, we calculate these corrections to one-loop order in theories where the center-symmetric vacuum is stabilized by 2 <= nf <= 5 massive adjoint Weyl fermions with masses of order m lambda similar to N2 pi L, (also known as deformed Yang-Mills,) and show that our results agree with those found in previous studies in the m lambda -0 limit. Then, we show that our result has an intuitive interpretation as the running of the coupling in a lattice momentum in the context of the nonperturbative emergent latticized fourth dimension in the N -infinity, fixed-NL limit.

Automated summary

In this study, we calculate the corrections to the coupling constant in the long-distance effective theory of center-stabilized SU(N) Yang-Mills theories on R3 x S1, and show that the results align with previous studies. Additionally, our findings provide an intuitive interpretation of the coupling constant running in the context of the nonperturbative emergent latticized fourth dimension.