Exactly solvable model of superstring in Ramond-Ramond plane wave background

We describe in detail the solution of type IIB superstring theory in the maximally supersymmetric plane-wave background with constant null Ramond-Ramond 5-form field strength. The corresponding light-cone Green-Schwarz action found in hep-th/0112044 is quadratic in both bosonic and fermionic coordinates. We find the spectrum of the light-cone Hamiltonian and the string representation of the supersymmetry algebra. The superstring Hamiltonian has a ``harmonic-oscillator'' form in both the string-oscillator and the zero-mode parts and thus has discrete spectrum in all 8 transverse directions. We analyze the structure of the zero-mode sector of the theory, establishing the precise correspondence between the lowest-lying ``massless'' string states and the type IIB supergravity fluctuation modes in the plane-wave background. The zero-mode spectrum has certain similarity to the supergravity spectrum in AdS_5 x S^5 of which the plane-wave background is a special limit. We also compare the plane-wave string spectrum with expected form of the light-cone gauge spectrum of superstring in AdS_5 x S^5.Comment: 33 pages, latex. v4: minor sign corrections in (1.5) and (3.62), to appear in PR

Gauge invariant formulation of massive totally symmetric fermionic fields in (A)dS space

Massive arbitrary spin totally symmetric free fermionic fields propagating in d-dimensional (Anti)-de Sitter space-time are investigated. Gauge invariant action and the corresponding gauge transformations for such fields are proposed. The results are formulated in terms of various mass parameters used in the literature as well as the lowest eigenvalues of the energy operator. We apply our results to a study of partial masslessness of fermionic fields in (A)dS(d), and in the case of d=4 confirm the conjecture made in the earlier literature.Comment: 14 pages, LaTeX -2e. v3: misprint in equation (2.24) corrected, footnotes 1,2,8,10 and references added, notation for the cosmological constant and operator of gauge transformation change

Superparticle and superstring in AdS_3 x S^3 Ramond-Ramond background in light-cone gauge

We discuss superparticle and superstring dynamics in AdS_3 x S^3 supported by R-R 3-form background using light-cone gauge approach. Starting with the superalgebra psu(1,1|2) + psu(1,1|2) representing the basic symmetry of this background we find the light-cone superparticle Hamiltonian. We determine the harmonic decomposition of light-cone superfield describing fluctuations of type IIB supergravity fields expanded near AdS_3 x S^3 background and compute the corresponding Kaluza-Klein spectrum. We fix the fermionic and bosonic light-cone gauges in the covariant Green-Schwarz AdS_3 x S^3 superstring action and find the light-cone string Hamiltonian. We also obtain a realization of the generators of psu(1,1|2) + psu(1,1|2) in terms of the superstring 2-d fields in the light-cone gauge.Comment: 32 pages, late

CFT adapted gauge invariant formulation of massive arbitrary spin fields in AdS

Using Poincare parametrization of AdS space, we study massive totally symmetric arbitrary spin fields in AdS space of dimension greater than or equal to four. CFT adapted gauge invariant formulation for such fields is developed. Gauge symmetries are realized by using Stueckelberg formulation of massive fields. We demonstrate that the mass parameter, curvature and radial coordinate contributions to the gauge transformation and Lagrangian of the AdS massive fields can be expressed in terms of ladder operators. Three representations for the Lagrangian are discussed. Realization of the global AdS symmetries in the conformal algebra basis is obtained. Modified de Donder gauge leading to simple gauge fixed Lagrangian is found. The modified de Donder gauge leads to decoupled equations of motion which can easily be solved in terms of the Bessel function. New simple representation for gauge invariant Lagrangian of massive (A)dS field in arbitrary coordinates is obtained. Light-cone gauge Lagrangian of massive AdS field is also presented.Comment: 14 pages, LaTeX-2e. v3: Typo corrected in 2nd line below Eq.(4.34

Cubic interaction vertices for massive and massless higher spin fields

Using the light-cone formulation of relativistic dynamics, we develop various methods for constructing cubic interaction vertices and apply these methods to the study of higher spin fields propagating in flat space of dimension greater than or equal to four. Generating functions of parity invariant cubic interaction vertices for massive and massless higher spin fields of arbitrary symmetry are obtained. We derive restrictions on the allowed values of spins and the number of derivatives, which provide a classification of cubic interaction vertices for totally symmetric fields. As an example of application of the light-cone formalism, we obtain simple expressions for the minimal Yang-Mills and gravitational interactions of massive totally symmetric arbitrary spin fields. We give the complete list of parity invariant and parity violating cubic interaction vertices that can be constructed for massless fields in five and six-dimensional spaces.Comment: 55 pages, LaTeX-2e, v3: Equations (3.15),(3.16) added to Section 3. Discussion of vertices for massless fields in d=4 and footnotes 16,17 added to Section 5.1. New vertices added to Table I. Misprints in equations (7.4), (C.5), and (D.58) correcte

Light-cone Superstring in AdS Space-time

We consider fixing the bosonic light-cone gauge for string in AdS in the phase space framework, i.e. by choosing $x^+ = \tau$, and by choosing $\sigma$ so that $P^+$ is distributed uniformly (its density is independent of $\sigma$). We discuss classical bosonic string in AdS space and superstring in AdS_5 x S^5. In the latter case the starting point is the action found in hep-th/0007036 where the kappa-symmetry is fixed by a fermionic light cone gauge. We derive the light cone Hamiltonian in the AdS_5 x S^5 case and in the case of superstring in AdS_3 x S^3. We also obtain a realization of the generators of the basic symmetry superalgebra psu(2,2|4) in terms of the AdS_5 x S^5 superstring coordinate fields.Comment: 34 pages, latex. v3: section 5.4 revised. v4: minor corrections, version to appear in NP

Light-cone form of field dynamics in anti-de Sitter space-time and AdS/CFT correspondence

Light-cone form of field dynamics in anti-de Sitter space-time is developed. Using field theoretic and group theoretic approaches the light-cone representation for generators of anti-de Sitter algebra acting as differential operators on bulk fields is found. We also present light-cone reformulation of the boundary conformal field theory representations. Making use of these explicit representations of AdS algebra as isometry algebra in the bulk and the algebra of conformal transformations at the boundary a precise correspondence between the bulk fields and the boundary operators is established.Comment: 57 pages, LaTeX, typos corrected in Appendice

BRST-BV approach to cubic interaction vertices for massive and massless higher-spin fields

Using BRST-BV formulation of relativistic dynamics, we study arbitrary spin massive and massless fields propagating in flat space. Generating functions of gauge invariant off-shell cubic interaction vertices for mixed-symmetry and totally symmetric fields are obtained. For the case of totally symmetric fields, we derive restrictions on the allowed values of spins and the number of derivatives, which provide a classification of cubic interaction vertices for such fields. As by product, we present simple expressions for the Yang-Mills and gravitational interactions of massive totally symmetric arbitrary spin fields.Comment: 12 pages, LaTeX-2

Supersymmetric D3 brane action in AdS_5 x S^5

We find the space-time supersymmetric and kappa-invariant action for a D3-brane propagating in the AdS_5 x S^5 background. As in the previous construction of the fundamental string action in this maximally supersymmetric string vacuum the starting point is the corresponding superalgebra su(2,2|4). We comment on the super Yang-Mills interpretation of the gauge-fixed form of the action.Comment: 12 pages, latex. v2: misprints corrected, useful representation of the WZ part of the action added in section

Eleven-Dimensional Supergravity in Light-Cone Superspace

We show that Supergravity in eleven dimensions can be described in terms of a constrained superfield on the light-cone, without the use of auxiliary fields. We build its action to first order in the gravitational coupling constant \kappa, by "oxidizing" (N=8,d=4) Supergravity. This is simply achieved, as for N=4 Yang-Mills, by extending the transverse derivatives into superspace. The eleven-dimensional SuperPoincare algebra is constructed and a fourth order interaction is conjectured.Comment: 18 page