On Consistent Equations for Massive Spin-2 Field Coupled to Gravity in String Theory

We investigate the problem of derivation of consistent equations of motion for the massive spin 2 field interacting with gravity within both field theory and string theory. In field theory we derive the most general classical action with non-minimal couplings in arbitrary spacetime dimension, find the most general gravitational background on which this action describes a consistent theory and generalize the analysis for the coupling with background scalar dilaton field. We show also that massive spin 2 field allows in principle consistent description in arbitrary background if one builds its action in the form of an infinite series in the inverse mass square. Using sigma-model description of string theory in background fields we obtain in the lowest order in $\alpha'$ the explicit form of effective equations of motion for the massive spin 2 field interacting with gravity from the requirement of quantum Weyl invariance and demonstrate that they coincide with the general form of consistent equations derived in field theory.Comment: 12 pages, Latex file, discussion of coupling with dilaton adde

Cubic vertices for N=1 supersymmetric massless higher spin fields in various dimensions

Using the BRST approach to higher spin field theories we develop a generic technique for constructing the cubic interaction vertices for N =1 supersymmetric massless higher spin fields on four, six and ten dimensional flat backgrounds. Such an approach allows formulation of the equations for cubic vertices including bosonic and fermionic higher spin fields, and the problem of finding the vertices is reduced to finding the consistent solutions to these equations. As a realization of this procedure, we present the particular solutions for the vertices where the fields obey some off-shell constraints. It is shown that the supersymmetry imposes additional constraints on the vertices and singles out a particular subclass of the solutions. As a concrete application of the generic scheme, we consider supersymmetric Yang-Mills-like systems in four, six and ten dimensions where the higher spin fields transform under some internal symmetry group, as well as supergravity-like systems in the same dimensions

Renormalization of the energy-momentum tensor in noncommutative complex scalar field theory

We study the renormalization of dimension four composite operators and the energy-momentum tensor in noncommutative complex scalar field theory. The proper operator basis is defined and it is proved that the bare composite operators are expressed via renormalized ones with the help of an appropriate mixing matrix which is calculated in the one-loop approximation. The number and form of the operators in the basis and the structure of the mixing matrix essentially differ from those in the corresponding commutative theory and in noncommutative real scalar field theory. We show that the energy-momentum tensor in the noncommutative complex scalar field theory is defined up to six arbitrary constants. The canonically defined energy-momentum tensor is not finite and must be replaced by the "improved" one, in order to provide finiteness. Suitable "improving" terms are found. Renormalization of dimension four composite operators at zero momentum transfer is also studied. It is shown that the mixing matrices are different for the cases of arbitrary and zero momentum transfer. The energy-momentum vector, unlike the energy-momentum tensor, is defined unambigously and does not require "improving", in order to be conserved and finite, at least in the one-loop approximation.Comment: 23 pages, pictures using axodraw, references are adde

Gauge invariant Lagrangian construction for massive bosonic mixed symmetry higher spin fields

We develop the BRST approach to gauge invariant Lagrangian construction for the massive mixed symmetry integer higher spin fields described by the rank-two Young tableaux in arbitrary dimensional Minkowski space. The theory is formulated in terms of auxiliary Fock space. No off-shell constraints on the fields and the gauge parameters are imposed. The approach under consideration automatically leads to a gauge invariant Lagrangian for massive theory with all appropriate Stuckelberg fields. It is shown that all the restrictions defining an irreducible representation of the Poincare group arise from Lagrangian formulation as a consequence of the equations of motion and gauge transformations. As an example of the general procedure, we derive the gauge-invariant Lagrangian for massive rank-2 antisymmetric tensor field containing the complete set of auxiliary fields and gauge parameters.Comment: v2: 15 pages, references added, minor changes, version accepted for publication in PL

Renormalization of the energy-momentum tensor in noncommutative scalar field theory

We consider the one-loop renormalization of dimension four composite operators and the energy-momentum tensor in noncommutative \phi^4 scalar field theory. Proper operator bases are constructed and it is proved that the bare composite operators are expressed via renormalized ones, with the help of a mixing matrix, whose explicit form is calculated. The corresponding matrix elements turn out to differ from the commutative theory. The canonically defined energy-momentum tensor is not finite and must be replaced by the "improved" one, in order to provide finiteness. The suitable "improving" terms are found.Comment: 21 pages, pictures using axodra

Quartet unconstrained formulation for massless higher spin fields

We construct simple unconstrained Lagrangian formulations for massless higher spin fields in flat space of arbitrary dimension and on anti de Sitter background. Starting from the triplet equations of Francia and Sagnotti, which describe a chain of spin modes, we introduce an auxiliary field and find appropriate gauge invariant constraints that single out the spin-s mode. The resulting quartet of fields, thus describing an irreducible representation of the Poincare group, is used to construct simple Lagrangian formulations, which are local, free from higher derivative terms and use equal number of auxiliary fields for an unconstrained description of any value of spin. Our method proves to be most efficient for an unconstrained description of massless higher spin fermions in anti de Sitter space. A relation of the minimal models with the universal BRST approach is discussed.Comment: V4: 27 pages; references and acknowledgement adde

Lagrangian formulation of massive fermionic totally antisymmetric tensor field theory in AdS_d space

We apply the BRST approach, developed for higher spin field theories, to Lagrangian construction for totally antisymmetric massive fermionic fields in AdS_d space. As well as generic higher spin massive theories, the obtained Lagrangian theory is a reducible gauge model containing, besides the basic field, a number of auxiliary (Stuckelberg) fields and the order of reducibility grows with the value of the rank of the antisymmetric field. However, unlike the generic higher spin theory, for the special case under consideration we show that one can get rid of all the auxiliary fields and the final Lagrangian for fermionic antisymmetric field is formulated only in terms of basic field.Comment: 22 pages; v2: 1 footnote and 2 references adde

Equations of Motion for Massive Spin 2 Field Coupled to Gravity

We investigate the problems of consistency and causality for the equations of motion describing massive spin two field in external gravitational and massless scalar dilaton fields in arbitrary spacetime dimension. From the field theoretical point of view we consider a general classical action with non-minimal couplings and find gravitational and dilaton background on which this action describes a theory consistent with the flat space limit. In the case of pure gravitational background all field components propagate causally. We show also that the massive spin two field can be consistently described in arbitrary background by means of the lagrangian representing an infinite series in the inverse mass. Within string theory we obtain equations of motion for the massive spin two field coupled to gravity from the requirement of quantum Weyl invariance of the corresponding two dimensional sigma-model. In the lowest order in $\alpha'$ we demonstrate that these effective equations of motion coincide with consistent equations derived in field theory.Comment: 27 pages, LaTeX file, journal versio

Gauge invariant Lagrangian construction for massive bosonic higher spin fields in D dimentions

We develop the BRST approach to Lagrangian formulation for massive higher integer spin fields on a flat space-time of arbitrary dimension. General procedure of gauge invariant Lagrangian construction describing the dynamics of massive bosonic field with any spin is given. No off-shell constraints on the fields (like tracelessness) and the gauge parameters are imposed. The procedure is based on construction of new representation for the closed algebra generated by the constraints defining an irreducible massive bosonic representation of the Poincare group. We also construct Lagrangian describing propagation of all massive bosonic fields simultaneously. As an example of the general procedure, we derive the Lagrangians for spin-1, spin-2 and spin-3 fields containing total set of auxiliary fields and gauge symmetries of free massive bosonic higher spin field theory.Comment: 27 page