I. L. Buchbinder

Construction of 6D supersymmetric field models in N=(1,0) harmonic superspace

Abstract We consider the six-dimensional hypermultiplet, vector and tensor multiplet models in ( 1 , 0 ) harmonic superspace and discuss the corresponding superfield actions. The actions for free ( 2 , 0 ) tensor multiplet and for interacting vector/tensor multiplet system are constructed. Using the superfield formulation of the hypermultiplet coupled to the vector/tensor system we develop an approach to calculation of the one-loop superfield effective action and find its divergent structure.

The higher derivative regularization and quantum corrections in N=2 supersymmetric theories

We construct a new version of the higher covariant derivative regularization for a general N = 2 supersymmetric gauge theory formulated in terms of N = 1 superfields. This regularization preserves both supersymmetries of the classical action, namely, the invariance under the manifest N = 1 supersymmetry and under the second hidden on-shell supersymmetry. The regularizing N = 2 supersymmetric higher derivative term is found in the explicit form in terms of N = 1 superfields. Thus, N = 2 supersymmetry is broken only by the gauge fixing procedure. Then we analyze the exact NSVZ β-function and prove that in the considered model its higher loop structure is determined by the anomalous dimension of the chiral superfield Φ in the adjoint representation which is the N = 2 superpartner of the gauge superfield V . Using the background field method we find that this anomalous dimension is related with the anomalous dimension of the hypermultiplet and vanishes if the effective action is invariant under N = 2 background supersymmetry. As a consequence, in this case the higher loop contributions to β-function also vanish. The one-loop renormalization structure in the considered regularization is also studied by the explicit calculations of the one-loop renormalization constants.

Manifestly N=2 supersymmetric regularization for N=2 supersymmetric field theories

We formulate the higher covariant derivative regularization for N = 2 supersymmetric gauge theories in N = 2 harmonic superspace. This regularization is constructed by adding the N = 2 supersymmetric higher derivative term to the classical action and inserting the N = 2 supersymmetric Pauli–Villars determinants into the generating functional for removing one-loop divergencies. Unlike all other regularization schemes in N = 2 supersymmetric quantum field theory, this regularization preserves by construction the manifest N = 2 supersymmetry at all steps of calculating loop corrections to the effective action. Together with N = 2 supersymmetric background field method this regularization allows to calculate quantum corrections without breaking the manifest gauge symmetry and N = 2 supersymmetry. Thus, we justify the assumption about existence of a regularization preserving N = 2 supersymmetry, which is a key element of the N = 2 non-renormalization theorem. As a result, we give the prove of the N = 2 non-renormalization theorem which does not require any additional assumptions.

Lagrangian formulation of the massive higher spin supermultiplets in three dimensional space-time

A bstractWe give explicit construction for massive higher spin supermultiplets for the case of minimal supersymmetry in d = 3 and find the corresponding Lagrangian formulations. We show that all such massive supermultiplets can be straightforwardly constructed out of the appropriately chosen set of massless ones exactly in the same way as the gauge invariant description for the massive bosonic (fermionic) field with spin s can be obtained using a set of massless fields with spins s, s − 1, . . . , 0(1/2). Moreover, such construction for the massive supermultiplets turns out to be perfectly consistent with our previous results on the gauge invariant Lagrangian formulation for massive higher spin bosons and fermions in d = 3.

Leading low-energy effective action in the 6D hypermultiplet theory on a vector/tensor background

Abstract We consider a six-dimensional ( 1 , 0 ) hypermultiplet model coupled to an external field of vector/tensor system and study the structure of the low-energy effective action of this model. Manifestly a ( 1 , 0 ) supersymmetric procedure of computing the effective action is developed in the framework of the superfield proper-time technique. The leading low-energy contribution to the effective action is calculated.

Frame-like gauge invariant Lagrangian formulation of massive fermionic higher spin fields in AdS3 space

Abstract We construct the frame-like gauge-invariant Lagrangian formulation for massive fermionic arbitrary spin fields in three-dimensional AdS space. The Lagrangian and complete set of gauge transformations are obtained. We also develop the formalism of gauge-invariant curvatures for the massive theory under consideration and show how the Lagrangian is formulated in their terms. The massive spin-5/2 field is discussed as an example.

BRST analysis of the supersymmetric higher spin field models

A bstractWe develop the BRST approach for all massless integer and half-integer higher spins in 4D Minkowski space, using the two component spinor notation and develop the Lagrangian formulation for supersymmetric higher spin models. It is shown that the problem of second class constraints disappears and the BRST procedure becomes much more simple than in tensorial notation. Furthermore, we demonstrate that the BRST procedure automatically provides extra auxiliary components that belong in the set of supersymmetry auxiliary components. Finally, we demonstrate how supersymmetry transformations transformations are realized in such an approach. As a result, we conclude that the BRST approach to higher spin supersymmetric theories allows to derive both the Lagrangian and the supersymmetry transformations. Although most part of the work is devoted to massless component supersymmetric models, we also discuss generalization for massive component supersymmetric models and for superfield models.

One-loop divergences in the 6D, N=(1,0) abelian gauge theory

Abstract We consider, in the harmonic superspace approach, the six-dimensional N = ( 1 , 0 ) supersymmetric model of abelian gauge multiplet coupled to a hypermultiplet. The superficial degree of divergence is evaluated and the structure of possible one-loop divergences is analyzed. Using the superfield proper-time and background-field technique, we compute the divergent part of the one-loop effective action depending on both the gauge multiplet and the hypermultiplet. The corresponding counterterms contain the purely gauge multiplet contribution together with the mixed contributions of the gauge multiplet and hypermultiplet. We show that the theory is on-shell one-loop finite in the gauge multiplet sector in agreement with the results of [1] . The divergences in the mixed sector cannot be eliminated by any field redefinition, implying the theory to be UV divergent at one loop.

Supergraph analysis of the one-loop divergences in 6D, N=(1,0) and N=(1,1) gauge theories

We study the one-loop effective action for 6D, N = (1, 0) supersymmetric Yang–Mills (SYM) theory with hypermultiplets and 6D, N = (1, 1) SYM theory as a subclass of the former, using the off-shell formulation of these theories in 6D, N = (1, 0) harmonic superspace. We develop the corresponding supergraph technique and apply it to compute the one-loop divergences in the background field method ensuring the manifest gauge invariance. We calculate the two-point Green functions of the gauge superfield and the hypermultiplet, as well as the three-point gauge-hypermultipet Green function. Using these Green functions and exploiting gauge invariance of the theory, we find the full set of the off-shell one-loop divergent contributions, including the logarithmic and power ones. Our results precisely match with those obtained earlier in [1, 2] within the proper time superfield method.

Lagrangian formulation of massive fermionic higher spin fields on a constant electromagnetic background

Abstract We consider massive half-integer higher spin fields coupled to an external constant electromagnetic field in flat space of an arbitrary dimension and construct a gauge invariant Lagrangian in the linear approximation in the external field. A procedure for finding the gauge-invariant Lagrangians is based on the BRST construction where no off-shell constraints on the fields and on the gauge parameters are imposed from the very beginning. As an example of the general procedure, we derive a gauge invariant Lagrangian for a massive fermionic field with spin 3/2 which contains a set of auxiliary fields and gauge symmetries.