On the component structure of one-loop effective actions in $6D$, ${\cal N}=(1,0)$ and ${\cal N}=(1,1)$ supersymmetric gauge theories

Abstract

We study the six-dimensional N = (1, 0) and N = (1, 1) supersymmetric Yang-Mills (SYM) theories in the component formulation. The one-loop divergencies of effective action are calculated. The leading one-loop low-energy contributions to bosonic sector of effective action are found. It is explicitly demonstrated that the contribution to effective potential for the constant background scalar fields are absent in the N = (1, 1) SYM theory.

One-loop divergences in the six-dimensional $\cal{N}=(1,0)$ hypermultiplet self-coupling model

“…The one-loop divergent contribution (40) to the effective action of the theory (9) depends on the external gauge multiplet V ++ and background hypermultiplet Q + . Using the definitions (32) we can rewrite (40) in the form…”

“…The study of the ultraviolet behavior of supersymmetric field theories in six dimensions has received considerable attention in recent years. The analysis of the UV divergences is carried out using both symmetry considerations [24][25][26][27][28] and direct calculations of the effective action [20,21,[29][30][31][32][33] (see also earlier analysis [34][35][36][37]) and scattering amplitudes [38][39][40][41][42]. As an application of the developed technique, we calculate the one-loop divergent contribution to the effective action in the gauge-invariant N = (1, 0) supersymmetric sigma-model in six dimensions [14].…”

The renormalization structure of $6D$, ${\cal N}=(1,0)$ supersymmetric higher-derivative gauge theory

“…The superfield propagators of vector multiplet, hypermultiplet and ghosts contain the Grassmann delta-functions [19]. This allows us to represent any loop supergraph as a single integral over anticommuting variables 6 . Taking into account the locality of divergences, we conclude that each contribution to the effective action can be presented as an integral over d 14 z = d 6 x d 8 θ.…”

“…The ordinary N = (1, 0) supersymmetric Yang-Mills (SYM) theory in 6D has a dimensionful coupling constant and for this reason is non-renormalizable. The UV behavior of such a theory was studied by direct quantum calculations in the component approach [2][3][4][5][6], by using the gauge and supersymmetry methods [7][8][9][10][11], by applying the background field method in superspace [12,13] and, recently, by the modern amplitude techniques (see, e.g., [14] and references therein). In contrast to the gauge theory with the standard kinetic term the higher-derivative model with four space-time derivatives [1] possesses a dimensionless coupling constant.…”

Quantum calculation of the low-energy effective action in 5D, N=2 SYM theory

“…The action (3.10) involves terms which mix the quantum gauge multiplet v ++ and the quantum hypermultiplet q + a . These terms can be eliminated in R ξ gauge (see, e.g., [23] for an example of application of the R ξ gauge in 6D, N = (1, 1) SYM theory). In this case the action for the Faddeev-Popov ghosts would depend on both the background gauge multiplet and hypermultiplet and involve inverse powers of the operator ⌢ ✷ .…”