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

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

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

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

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

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

Near-Horizon Supergravity Superspace

We present a construction of the superspace of maximally supersymmetric adS_{p+2} x S^{d-p-2} near-horizon geometry based entirely on the supergravity constraints of which the bosonic space is a solution. Besides the geometric superfields, i.e. the vielbeine and the spinconnection, we also derive the isometries of the superspace together with the compensating tangent space transformations to all orders in anticommuting superspace coordinates.Comment: 6 pages, contribution to the proceedings of the "mid-term TMR meeting on Quantum Aspects Theories, Supersymmetry and Unification", Corfu, September 20-26, 199

BRST approach to Lagrangian formulation for mixed-symmetry fermionic higher-spin fields

We construct a Lagrangian description of irreducible half-integer higher-spin representations of the Poincare group with the corresponding Young tableaux having two rows, on a basis of the BRST approach. Starting with a description of fermionic higher-spin fields in a flat space of any dimension in terms of an auxiliary Fock space, we realize a conversion of the initial operator constraint system (constructed with respect to the relations extracting irreducible Poincare-group representations) into a first-class constraint system. For this purpose, we find auxiliary representations of the constraint subsuperalgebra containing the subsystem of second-class constraints in terms of Verma modules. We propose a universal procedure of constructing gauge-invariant Lagrangians with reducible gauge symmetries describing the dynamics of both massless and massive fermionic fields of any spin. No off-shell constraints for the fields and gauge parameters are used from the very beginning. It is shown that the space of BRST cohomologies with a vanishing ghost number is determined only by the constraints corresponding to an irreducible Poincare-group representation. To illustrate the general construction, we obtain a Lagrangian description of fermionic fields with generalized spin (3/2,1/2) and (3/2,3/2) on a flat background containing the complete set of auxiliary fields and gauge symmetries.Comment: 41 pages, no figures, corrected typos, updated introduction, sections 5, 7.1, 7.2 with examples, conclusion with all basic results unchanged, corrected formulae (3.27), (7.138), (7.140), added dimensional reduction part with formulae (5.34)-(5.48), (7.8)-(7.10), (7.131)-(7.136), (7.143)-(7.164), added Refs. 52, 53, 54, examples for massive fields developed by 2 way

Uniform Light-Cone Gauge for Strings in AdS_5 x S^5: Solving su(1|1) Sector

We introduce a uniform light-cone gauge for strings propagating in AdS space-time. We use the gauge to analyze strings from the su(1|1) sector, and show that the reduced model is described by a quadratic action for two complex fermions. Thus, the uniform light-cone gauge allows us to solve the model exactly. We analyze the near BMN spectrum of states from the su(1|1) sector and show that it correctly reproduces the 1/J corrections. We also compute the spectrum in the strong coupling limit, and derive the famous \lambda^{1/4} asymptotics. We then show that the same string spectrum can be also derived by solving Bethe ansatz type equations, and discuss their relation to the quantum string Bethe ansatz for the su(1|1) sector.Comment: 26 pages, Latex, v2: comparison to the strong coupling expansion of the quantum string Bethe ansatz is added, discussion of the winding sector is extended, references adde