E.S. Fradkin

Non-linear electrodynamics from quantized strings

We compute the effective action for an abelian vector field coupled to the virtual open Bose string. The problem is exactly solved (in the “tree” and “one-loop” approximation for the string theory) for the case of a constant field strength and the number of space-time dimensions D=26. The resulting tree-level effective lagrangian is shown to coincide with the Born-Infeld lagrangian, [det(δμν + 2Πα′Fμν)]12.

Effective Field Theory from Quantized Strings

Abstract We present a covariant definition of the effective action Γ for fields corresponding to different string excitations (scalar, metric, antisymmetric tensor, …) in terms of a string path integral with “external sources”. The problem of deriving the gravitational part of Γ is reduced to that of establishing the effective action for a generalized σ-model on a curved two-dimensional background and subsequent integration over two-metrics. The low-energy approximation for Γ is computed.

Quantum String Theory Effective Action

Abstract We present a covariant background field method for quantum string dynamics. It is based on the effective action Γ for fields corresponding to different string modes. A formalism is developed for the calculation of Γ in the α ′ → 0 limit. It is shown that in the case of closed Bose strings Γ contains the standard kinetic terms for the scalar, external metric and the antisymmetric tensor. Our approach makes possible a consistent formulation and solution of a ground state problem (including the problem of space-time compactification) in the string theory. We suggest a solution to the old “tachyon problem” based on the generation of non-trivial vacuum values for the scalar field, metric and antisymmetric tensor. It is shown that a preferred compactification in the closed Bose string theory is to three (anti-de Sitter) space-time dimensions.

On the gravitational interaction of massless higher-spin fields

Abstract We show that, despite a widespread belief, the gravitational interaction of massless higher-spin fields (s > 2) does exist at least in the first nontrivial order. The principal novel feature of the gravitational higher-spin interaction is its non-analyticity in the cosmological constant. Our construction is based on an infinite-dimensional higher-spin superalgebra proposed previously that leads to an infinite system of all spins s > 1.

Cubic Interaction in Extended Theories of Massless Higher Spin Fields

Abstract A cubic interaction of all massless higher-spin fields with s ⩾ 1 is constructed, based on the extended higher-spin superalgebras suggested previously by one of us (M.V.). This interaction incorporates gravitational and Yang-Mills interactions of massless higher-spin fields, which turn out to be consistent in the cubic order. An essential novel feature of the gravitational higher-spin interaction is its non-analyticity in the cosmological constant. An explicit form is found for deformed higher-spin gauge transformations leaving the action invariant.

Renormalizable asymptotically free quantum theory of gravity

Abstract We prove that higher derivative quantum gravity is asymptotically free in all essential coupling constants by the calculation of one-loop counterterms (correcting the previous result of Julve and Tonin) and the solution of the corresponding renormalization group (RG) equations. Strong arguments are presented in favour of the possibility that renormalizable asymptotically free gravity establishes asymptotic freedom for the effective mass parameters and non-gauge couplings in grand unified gauge theories. We also analyse the RG equations in the Einstein theory with Λ term and in the higher derivative conformal invariant theories. Among other topics discussed are the algorithm for the divergences of the determinant of the fourth-order differential operator, the consistent renormalization of the boundary terms in the action, the one-loop β-function in the fourth derivative vector gauge theory and the RG equations in the “gφ 4 + ηRφ 2 ” theory.

A Generalized Canonical Formalism and Quantization of Reducible Gauge Theories

Abstract A general solution for the S -matrix of relativistic dynamical systems subject to Bose and Fermi first and second class constraints is obtained by canonical quantization in the case of reducibility, i.e. when the first class constraints are linearly dependent. The null-eigenvectors of the constraints may also be linearly dependent and possess null-eigenvectors of their own, which, in their turn, may be linearly dependent, etc. The solution obtained remains valid in the present case of multistage reducibility of constraints.

Operational quantization of dynamical systems subject to second class constraints

Abstract An operational version is proposed for the generalized canonical quantization method of dynamical systems subject to second class constraints. New generating equations are formulated for the generalized algebra of constraints and for the unitarizing hamiltonian.

Candidate for the role of higher-spin symmetry

Infinite-dimensional non-abelian superalgebras, related to interacting massless higher-spin fields of all spins s ⩾ 3/2, are proposed. Conditions are formulated that provide uniqueness for these higher-spin superalgebras, denoted as shsρ(1) (ρ = 0 or 1). Among these conditions, the major role is played by the requirement that linearized curvatures of shsρ(1) coincide with the linearized higher-spin curvatures obtained previously. Subalgebras and contractions of shsρ(1) are considered. A higher-spin interaction, which is introduced in terms of the shsρ(1) curvatures, is discussed briefly. It is found that a gravitational interaction of massless higher spins requires non-analyticity in the cosmological constant.

Quantum equivalence of dual field theories

Abstract Motivated by the study of ultraviolet properties of different versions of supergravities duality transformations at the quantum level are discussed. Using the background field method it is proven on shell quantum equivalence for several pairs of dual field theories known to be classically equivalent. The examples considered include duality in chiral model, duality of scalars and second rank antisymmetric gauge tensors, vector duality and duality of the Einstein theory with cosmological term and the Eddington-Schrodinger theory.