Ilya Tipunin

Bio: Ilya Tipunin is an academic researcher from Lebedev Physical Institute. The author has contributed to research in topics: BRST quantization & Quantum gauge theory. The author has an hindex of 3, co-authored 3 publications receiving 307 citations.

Parent Field Theory and Unfolding in BRST First-Quantized Terms

Abstract: For free-field theories associated with BRST first-quantized gauge systems, we identify generalized auxiliary fields and pure gauge variables already at the first-quantized level as the fields associated with algebraically contractible pairs for the BRST operator. Locality of the field theory is taken into account by separating the space–time degrees of freedom from the internal ones. A standard extension of the first-quantized system, originally developed to study quantization on curved manifolds, is used here for the construction of a first-order parent field theory that has a remarkable property: by elimination of generalized auxiliary fields, it can be reduced both to the field theory corresponding to the original system and to its unfolded formulation. As an application, we consider the free higher-spin gauge theories of Fronsdal.

Parent field theory and unfolding in BRST first-quantized terms

Abstract: For free-field theories associated with BRST first-quantized gauge systems, we identify generalized auxiliary fields and pure gauge variables already at the first-quantized level as the fields associated with algebraically contractible pairs for the BRST operator. Locality of the field theory is taken into account by separating the space--time degrees of freedom from the internal ones. A standard extension of the first-quantized system, originally developed to study quantization on curved manifolds, is used here for the construction of a first-order parent field theory that has a remarkable property: by elimination of generalized auxiliary fields, it can be reduced both to the field theory corresponding to the original system and to its unfolded formulation. As an application, we consider the free higher-spin gauge theories of Fronsdal.

Nonlinear higher spin theories in various dimensions

Abstract: In this article, an introduction to the nonlinear equations for completely symmetric bosonic higher spin gauge fields in anti de Sitter space of any dimension is provided. To make the presentation self-contained we explain in detail some related issues such as the MacDowell-Mansouri-Stelle-West formulation of gravity, unfolded formulation of dynamical systems in terms of free differential algebras and Young tableaux symmetry properties in terms of Howe dual algebras.

Elements of Vasiliev theory

Abstract: We propose a self-contained description of Vasiliev higher-spin theories with the emphasis on nonlinear equations. The main sections are supplemented with some additional material, including introduction to gravity as a gauge theory; the review of the Fronsdal formulation of free higher-spin fields; Young diagrams and tensors as well as sections with advanced topics. The shortest route to Vasiliev equations covers 40 pages. The general discussion is dimension independent, while the essence of the Vasiliev formulation is discussed on the base of the four-dimensional higher-spin theory. Three-dimensional and d-dimensional higher-spin theories follow the same logic.

An Introduction to free higher-spin fields

Abstract: In this article we begin by reviewing the (Fang-)Fronsdal construction and the non-local geometric equations with unconstrained gauge fields and parameters built by Francia and the senior author from the higher-spin curvatures of de Wit and Freedman. We then turn to the triplet structure of totally symmetric tensors that emerges from free String Field Theory in the $\alpha' \to 0$ limit and to its generalization to (A)dS backgrounds, and conclude with a discussion of a simple local compensator form of the field equations that displays the unconstrained gauge symmetry of the non-local equations. Based on the lectures presented by A. Sagnotti at the First Solvay Workshop on Higher-Spin Gauge Theories held in Brussels on May 12-14, 2004

Unfolding mixed-symmetry fields in AdS and the BMV conjecture: I. General formalism

Abstract: We present some generalities of unfolded on-shell dynamics that are useful in analysing the BMV conjecture for mixed-symmetry fields in constantly curved backgrounds. In particular we classify the Lorentz-covariant Harish-Chandra modules generated from primary Weyl tensors of arbitrary mass and shape, and in backgrounds with general values of the cosmological constant. We also discuss the unfolded notion of local degrees of freedom in theories with and without gravity and with and without massive deformation parameters, using the language of Weyl zero-form modules and their duals.