Topological Yang-Mills theories in self-dual and anti-self-dual Landau gauges revisited

Abstract

We reconsider the renormalizability of topological Yang-Mills field theories in (anti-)selfdual Landau gauges. By employing algebraic renormalization techniques we show that there is only one independent renormalization. Moreover, due to the rich set of Ward identities, we are able to obtain some important exact features of the (connected and one-particle irreducible) two-point functions. Specifically, we show that all two-point functions are treelevel exact. * octavio@if.uff.br † aduarte@if.uff.br ‡

More about the renormalization properties of topological Yang-Mills theories

“…This is consistent with the fact that topological gauge theories carry only global physical degrees of freedom. In fact, the unphysical nature of the gauge field as a local object is even more appealing at the (A)SDLG, where α = β = 0 and the gauge propagator (2.8) vanishes [6,8]. This property, being a very peculiar result for this gauge choice, has a strong consequence: all connected n-point Green functions are tree-level exact [9].…”

“…In the case of the (A)SDLG, the action (3.3) reduces to Σ (A)SDLG = Σ(α = β = 0). This is the most symmetric case due to the rich set of Ward identities displayed by this gauge, see [8,9]. In particular, the symmetry (A.11) and the vector supersymmetry [6,8] play a fundamental role.…”

“…To study the renormalizability of the action (2.7), the first step is to introduce some external sources in order to control the non-linear nature of the BRST transformations and other possible non-linear symmetries. The required BRST doublets are [8] sτ a µ = Ω a µ , sΩ a µ = 0 , sE a = L a , sL a = 0 , sΛ a µν = K a µν , sK a µν = 0 ,…”

“…Nevertheless, there are three special cases of (3.3) in which all divergences can be absorbed: the case α = β = 0 which is the (A)SDLG; the case α = 0 and β = 0, called α-gauges and; the case α = 0 and β = 0, called β-gauges. Let us start our discussion with the special case of the (A)SDLG (α = β = 0), whose quantum properties were previously studied in [8,9].…”

“…A particular appealing gauge choice in the BS approach is the (anti-)-self-dual Landau gauge ((A)SDLG), first introduced in [6]. This choice encodes a rich set of Ward identities which allow to prove the renormalizability of the theory to all orders in perturbation theory 1 [6,8]. Moreover, the (A)SDLG has two crucial properties [8,9]: all Green functions are tree-level exact and; the gauge propagator vanishes identically.…”