Ioseph Lvovich Buchbinder

We study the gauge structure of interacting antisymmetric tensor field models obtained by the dimensional reduction on a group manifold. In such models a dimensionful parameter related to the size of the compact manifold plays the role of a coupling constant. We focus on open issues of reducibility of the gauge transformations in these theories and show that stages of reducibility of the interacting models coincide with ones of corresponding free counterparts.

We consider a general reducible gauge theory deformed by mass or/and interaction terms violating gauge invariance. It is shown that in the Abelian case, by using the Stueckelberg-type procedure, this theory with broken gauge symmetry can be converted into exactly gauge-invariant theory which under a suitable choice of gauge conditions can be treated within the formalism of minimal wave operators manageable by the covariant Schwinger-DeWitt technique. We carry out quantization of such a theory in general terms when the initial generators of gauge transformations are of the first and second stages of reducibility and derive its partition function in terms of the functional integral with all corresponding ghost fields. This method is applied to quantization of massive fermionic totally antisymmetric tensor field models in anti--de Sitter space. One-loop quantum effective action for these models is derived in the form of the functional determinants of special Dirac-type differential operators in various dimensions.

A bstract: We employ the harmonic superspace methods to study a six-dimensional 𝒩 = (1 , 0) supersymmetric gauge theory with higher derivatives coupled to a hypermultiplet in the adjoint representation. By introducing a certain non-minimal interaction between the gauge multiplet and the hypermultiplet, we demonstrate that the one-loop divergences in gauge superfield sector, which are present in the conventional formulation, are canceled. The resulting theory is off-shell one-loop finite in this sector, while preserving the gauge invariance and 𝒩 = (1 , 0) supersymmetry. The cancelation mechanism is explicitly verified using both the background field method and the supergraph techniques. Thus, we present an example of the higher-derivative supersymmetric gauge theory in six dimensions which is finite in the vector multiplet sector.

Ten years ago, in a paper [1], a brief historical survey of the research activity in the Sector “Supersymmetry” at the Bogoliubov Laboratory of Theoretical Physics (BLTP) for more than 50 years of its existence has been given. Here, in commemoration of the 70th jubilee of the Joint Institute for Nuclear Research, we review some recent sound advancements in this area. Specifically, we consider the issues of constructing the superfield quantum effective actions in 6D, N = (1, 0) supersymmetry and off-shell unconstrained superfield formulations of N = 2 higher spins. In both cases, the harmonic superspace approach plays the decisive role.

We develop the quantization of a recently proposed model describing a totally antisymmetric rank- p tensor-spinor field (a fermionic p -form theory) in d -dimensional anti–de Sitter (AdS) space. The model provides a new nontrivial example of a reducible gauge theory, in which gauge transformations are linearly dependent and the degree of reducibility increases with p . It is well-known that in such cases the standard Faddeev-Popov-DeWitt prescription for the generating functional is not applicable. We quantize the fermionic p -form theory using the general Batalin-Vilkovisky formalism, employing two distinct gauge fermions associated with gauge-fixing functions of different admissible ranks, confirming the independence from the gauge choice. As a result, we obtain the quantum effective action in terms of a sequence of functional determinants corresponding to specific Dirac-like operators on AdS space.

We develop the method adjusting the Faddeev-Popov factorization procedure for the quantization of generic reducible gauge theories with linearly dependent generators and apply it to the first stage reducible model of second rank antisymmetric fermion in d -dimensional anti–de Sitter (AdS) spacetime. The method consists of nested factorizations of the gauge group volume for the determination of the consistently defined delta function of reduced gauge conditions, group integration measure, and gauge-fixed contribution of ghosts. It is compared to the Batalin-Vilkovisky (BV) formalism of quantizing theories with linearly dependent generators and shown to be equivalent to it for first stage reducible theories. Nevertheless, the method under consideration, unlike the BV formalism, from the very beginning leads to the functional integral with fewer number of ghosts. Using this method, we quantized the variant of fermionic totally antisymmetric tensor-spinor theory in AdS space and derived its effective action in terms of the functional determinants of special Dirac-type operators. Limitations of the method are also discussed along with the prospects of its extension to higher reducibility stages and higher rank models of antisymmetric fermions.