On a structure of the one-loop divergences in 4D harmonic superspace sigma-model

We study the quantum structure of four-dimensional $${{\mathcal {N}}}=2$$ N = 2 superfield sigma-model formulated in harmonic superspace in terms of the omega-hypermultiplet superfield $$\omega $$ ω . The model is described by harmonic superfield sigma-model metric $$g_{ab}(\omega )$$ g ab ( ω ) and two potential-like superfields $$L^{++}_{a}(\omega )$$ L a + + ( ω ) and $$L^{(+4)}(\omega )$$ L ( + 4 ) ( ω ) . In bosonic component sector this model describes some hyper-Kähler manifold. The manifestly $${{\mathcal {N}}}=2$$ N = 2 supersymmetric covariant background-quantum splitting is constructed and the superfield proper-time technique is developed to calculate the one-loop effective action. The one-loop divergences of the superfield effective action are found for arbitrary $$g_{ab}(\omega ), L^{++}_{a}(\omega ), L^{(+4)}(\omega )$$ g ab ( ω ) , L a + + ( ω ) , L ( + 4 ) ( ω ) , where some specific analogy between the algebra of covariant derivatives in the sigma-model and the corresponding algebra in the $${{\mathcal {N}}}=2$$ N = 2 SYM theory is used. The component structure of divergences in the bosonic sector is discussed.

Unconstrained off-shell superfield formulation of 4D, $$ \mathcal{N} $$ = 2 supersymmetric higher spins

We present, for the first time, the complete off-shell 4D,$$ \mathcal{N} $$ N = 2 superfield actions for any free massless integer spin s ≥ 2 fields, using the $$ \mathcal{N} $$ N = 2 harmonic super-space approach. The relevant gauge supermultiplet is accommodated by two real analytic bosonic superfields $$ {h}_{\alpha \left(s-1\right)\dot{\alpha}\left(s-1\right)}^{++} $$ h α s − 1 α ̇ s − 1 + + , $$ {h}_{\alpha \left(s-2\right)\dot{\alpha}\left(s-2\right)}^{++} $$ h α s − 2 α ̇ s − 2 + + and two conjugated complex analytic spinor superfields $$ {h}_{\alpha \left(s-1\right)\dot{\alpha}\left(s-1\right)}^{+3} $$ h α s − 1 α ̇ s − 1 + 3 , $$ {h}_{\alpha \left(s-2\right)\dot{\alpha}\left(s-1\right)}^{+3} $$ h α s − 2 α ̇ s − 1 + 3 , where α(s) := (α1. . . αs),$$ \dot{\alpha} $$ α ̇ (s) := ($$ \dot{\alpha} $$ α ̇ 1. . .$$ \dot{\alpha} $$ α ̇ s). Like in the harmonic superspace formulations of $$ \mathcal{N} $$ N = 2 Maxwell and supergravity theories, an infinite number of original off-shell degrees of freedom is reduced to the finite set (in WZ-type gauge) due to an infinite number of the component gauge parameters in the analytic superfield parameters. On shell, the standard spin content (s,s−1/2,s−1/2,s−1) is restored. For s = 2 the action describes the linearized version of “minimal” $$ \mathcal{N} $$ N = 2 Einstein supergravity.

Higher-dimensional invariants in 6D super Yang-Mills theory

We exploit the 6D,$$ \mathcal{N} $$ N = (1, 0) and $$ \mathcal{N} $$ N = (1, 1) harmonic superspace approaches to construct the full set of the maximally supersymmetric on-shell invariants of the canonical dimension d = 12 in 6D,$$ \mathcal{N} $$ N = (1, 1) supersymmetric Yang-Mills (SYM) theory. Both single- and double-trace invariants are derived. Only four single-trace and two double-trace invariants prove to be independent. The invariants constructed can provide the possible counterterms of $$ \mathcal{N} $$ N = (1, 1) SYM theory at four-loop order, where the first double-trace divergences are expected to appear. We explicitly exhibit the gauge sector of all invariants in terms of $$ \mathcal{N} $$ N = (1, 0) gauge superfields and find the absence of $$ \mathcal{N} $$ N = (1, 1) supercompletion of the F6 term in the abelian limit.

New bi-harmonic superspace formulation of 4D, $$ \mathcal{N} $$ = 4 SYM theory

We develop a novel bi-harmonic $$ \mathcal{N} $$ N = 4 superspace formulation of the $$ \mathcal{N} $$ N = 4 supersymmetric Yang-Mills theory (SYM) in four dimensions. In this approach, the $$ \mathcal{N} $$ N = 4 SYM superfield constraints are solved in terms of on-shell $$ \mathcal{N} $$ N = 2 harmonic superfields. Such an approach provides a convenient tool of constructing the manifestly $$ \mathcal{N} $$ N = 4 supersymmetric invariants and further rewriting them in $$ \mathcal{N} $$ N = 2 harmonic superspace. In particular, we present $$ \mathcal{N} $$ N = 4 superfield form of the leading term in the $$ \mathcal{N} $$ N = 4 SYM effective action which was known previously in $$ \mathcal{N} $$ N = 2 superspace formulation.

Junctions of mass-deformed nonlinear sigma models on SO(2N)/U(N) and Sp(N)/U(N). Part II

We construct three-pronged junctions of mass-deformed nonlinear sigma models on SO(2N)/U(N) and Sp(N )/U(N ) for generic N. We study the nonlinear sigma models on the Grassmann manifold or on the complex projective space. We discuss the relation between the nonlinear sigma model constructed in the harmonic superspace for- malism and the nonlinear sigma model constructed in the projective superspace formalism by comparing each model with the $$ \mathcal{N} $$ N = 2 nonlinear sigma model constructed in the $$ \mathcal{N} $$ N = 1 superspace formalism.

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

We apply the harmonic superspace approach for calculating the divergent part of the one-loop effective action of renormalizable 6D, $$ \mathcal{N} $$ N = (1, 0) supersymmetric higher-derivative gauge theory with a dimensionless coupling constant. Our consideration uses the background superfield method allowing to carry out the analysis of the effective action in a manifestly gauge covariant and $$ \mathcal{N} $$ N = (1, 0) supersymmetric way. We exploit the regularization by dimensional reduction, in which the divergences are absorbed into a renormalization of the coupling constant. Having the expression for the one-loop divergences, we calculate the relevant β-function. Its sign is specified by the overall sign of the classical action which in higher-derivative theories is not fixed a priori. The result agrees with the earlier calculations in the component approach. The superfield calculation is simpler and provides possibilities for various generalizations.

New deformations of N = 4 and N = 8 supersymmetric mechanics

This is a review of two different types of the deformed N = 4 and N = 8 supersymmetric mechanics. The first type is associated with the worldline realizations of the supergroups SU(2|1) (four supercharges), as well as of SU(2|2) and SU(4|1) (eight supercharges). The second type is the quaternion- Kähler (QK) deformation of the hyper-Kähler (HK) N = 4 mechanics models. The basic distinguishing feature of the QK models is a local N = 4 supersymmetry realized in d = 1 harmonic superspace.