Nonholomorphic N=2 terms in N=4 SYM: 1-Loop Calculation in N=2 superspace (original) (raw)
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Journal of High Energy Physics, 2001
We write an action, in four dimensional N=1 curved superspace, which contains a pure R^4 term with a coupling constant. Starting from the off-shell solution of the Bianchi identities, we compute the on-shell torsions and curvatures with this term. We show that their complete solution includes, for some of them, an infinite series in the R^4 coupling constant, which can only be computed iteratively. We explicitly compute the superspace torsions and curvatures up to second order in this coupling constant. Finally, we comment on the lifting of this result to higher dimensions.
arXiv: High Energy Physics - Theory, 2017
We study the low-energy effective action of general six-dimensional calN=(1,0){\cal N}=(1,0)calN=(1,0) gauge theory coupled to hypermultiplets in the calN=(1,0){\cal N}=(1,0)calN=(1,0) harmonic superspace formulation and consider the case of gauge group SU(N)SU(N)SU(N) broken to SU(N−1)timesU(1)SU(N-1)\times U(1)SU(N−1)timesU(1). We use the background superfield method ensuring manifest gauge invariance and calN=(1,0){\cal N}=(1,0)calN=(1,0) supersymmetry. The leading non-anomalous contribution to the one-loop effective action depending on both calN=(1,0){\cal N}=(1,0)calN=(1,0) vector multiplet and a hypermultiplet is calculated for the on-shell background superfields. The bosonic part of the effective action in the mixed sector is found to have the structure simfracF4(tildefifi)\sim\frac{F^4}{(\tilde{f}^{i}f_{i})}simfracF4(tildefifi), where F4F^4F4 is a 4th-degree monomial in the U(1)U(1)U(1) gauge field strength FMNF_{MN}FMN and fif_{i}fi are scalar components of the hypermultiplet. This implies that the expectation values of the hypermultiplet scalar fields may play the role of a natural infrared cutoff in the theory under consideration.
Effective action of �-deformed N = 4 SYM theory: Farewell to two-loop BPS diagrams
Nucl Phys B, 2007
Within the background field approach, all two-loop sunset vacuum diagrams, which occur in the Coulomb branch of N = 2 superconformal theories(including N = 4 SYM), obey the BPS condition m_3 = m_1 + m_2, where the masses are generated by the scalars belonging to a background N = 2 vector multiplet. These diagrams can be evaluated exactly, and prove to be homogeneous quadratic functions of the one-loop tadpoles J(m_1^2), J(m_2^2) and J(m_3^2), with the coefficients being rational functions of the squared masses. We demonstrate that, if one switches on the beta-deformation of the N = 4 SYM theory, the BPS condition no longer holds, and then generic two-loop sunset vacuum diagrams with three non-vanishing masses prove to be characterized by the following property: 2(m_1^2 m_2^2 +m_1^2 m_3^2 +m_2^2 m_3^2) > m_1^4 +m_2^4 +m_3^4. In the literature, there exist several techniques to compute such diagrams. For the beta-deformed N = 4 SYM theory, we carry out explicit two-loop calculations of the Kahler potential and F^4 term. Our considerations are restricted to the case of beta real.
Leading low-energy effective action in 6 D , N = ( 1 , 1 ) SYM theory
2018
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 ωhypermultiplet, 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)×U(1) ⊂ SU(N). In the bosonic sector the effective action involves the structure∼ F 4 X2 , where F 4 is a monomial of the fourth degree in an abelian field strength FMN 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 ...