Leading low-energy effective action in 6D, $$ \mathcal{N}=\left(1,1\right) $$ SYM theory

Abstract

We elaborate on the low-energy effective action of 6D, N = (1, 1) supersymmetric Yang-Mills (SYM) theory in the N = (1, 0) harmonic superspace formulation. The theory is described in terms of analytic N = (1, 0) gauge superfield V ++ and analytic ω-hypermultiplet, both in the adjoint representation of gauge group. The effective action is defined in the framework of the background superfield method ensuring the manifest gauge invariance along with manifest N = (1, 0) supersymmetry. We calculate leading contribution to the one-loop effective action using the on-shell background superfields corresponding to the option when gauge group SU(N) is broken to SU(N −1)×Υ(1) ⊂ SU(N). In the bosonic sector the effective action involves the structure ∼ F 4 X 2 , where F 4 is a monomial of the fourth degree in an abelian field strength F M N and X stands for the scalar fields from the ω-hypermultiplet. It is manifestly demonstrated that the expectation values of the hypermultiplet scalar fields play the role of a natural infrared cutoff.

Supergraph calculation of one-loop divergences in higher-derivative 6D SYM theory

“…The main advantage of such a formulation is the possibility to keep manifest N = (1, 0) supersymmetry at all steps of quantum calculations. In our recent papers [44][45][46][47][48][49][50] we developed the harmonic superfield approach for calculating the lowest off-shell quantum corrections in various 6D, N = (1, 0) and N = (1, 1) supersymmetric theories. In the present paper we apply this superfield technique for studying the one-loop effective action in 6D, N = (1, 0) higher-derivative gauge theory of ref.…”

Dual conformal symmetry and iterative integrals in six dimensions

“…In addition we want to point out similarities between integrals with 1/p 2 and 1/p 4 propagators we have considered here and the integrals one can encounter in so called fishnet models [45,46]. For example in the d = 6 fishnet model with deformation parameter chosen accordingly the single trace 8-point correlation function is exactly given by the (23) integral. Such relations do not end here and we are going to investigate them in a separate publication.…”

“…It is worth mentioning that d = 6 gauge theories, among (2, 0) SYM one, where extensively studied in recent years for different reasons and from different perspectives. In this regard we want to mention [10][11][12][13][14] and [15][16][17] and also [18][19][20][21][22][23][24][25][26].…”

Dual Conformal Symmetry and Iterative Integrals in Six Dimensions

“…It is worth mentioning that d = 6 gauge theories, among (2, 0) SYM one, where extensively studied in recent years for different reasons and from different perspectives. In this regard we want to mention [10][11][12][13][14] and [15][16][17] and also [18][19][20][21][22][23][24][25][26].…”