Full Lagrangian and Hamiltonian for quantum strings on AdS(4) x CP3 in a near plane wave limit

TY - JOUR

T1 - Full Lagrangian and Hamiltonian for quantum strings on AdS(4) x CP3 in a near plane wave limit

AU - Astolfi, Davide

AU - Puletti, Valentina G. M.

AU - Harmark, Troels

AU - Orselli, Marta

PY - 2010/4/20

Y1 - 2010/4/20

N2 - We find the full interacting Lagrangian and Hamiltonian for quantum strings in a near plane wave limit of AdS4 × CP3,. The leading curvature corrections give rise to cubic and quartic terms in the Lagrangian and Hamiltonian that we compute in full. The Lagrangian is found as the type IIA Green-Schwarz superstring in the light-cone gauge employing a superspace construction with 32 grassmann-odd coordinates. The light-cone gauge for the fermions is non-trivial since it should commute with the supersymmetry condition. We provide a prescription to properly fix the κ-symmetry gauge condition to make it consistent with light-cone gauge. We use fermionic field redefinitions to find a simpler Lagrangian. To construct the Hamiltonian a Dirac procedure is needed in order to properly keep into account the fermionic second class constraints. We combine the field redefinition with a shift of the fermionic phase space variables that reduces Dirac brackets to Poisson brackets. This results in a completely well-defined and explicit expression for the full interacting Hamiltonian up to and including terms quartic in the number of fields.

AB - We find the full interacting Lagrangian and Hamiltonian for quantum strings in a near plane wave limit of AdS4 × CP3,. The leading curvature corrections give rise to cubic and quartic terms in the Lagrangian and Hamiltonian that we compute in full. The Lagrangian is found as the type IIA Green-Schwarz superstring in the light-cone gauge employing a superspace construction with 32 grassmann-odd coordinates. The light-cone gauge for the fermions is non-trivial since it should commute with the supersymmetry condition. We provide a prescription to properly fix the κ-symmetry gauge condition to make it consistent with light-cone gauge. We use fermionic field redefinitions to find a simpler Lagrangian. To construct the Hamiltonian a Dirac procedure is needed in order to properly keep into account the fermionic second class constraints. We combine the field redefinition with a shift of the fermionic phase space variables that reduces Dirac brackets to Poisson brackets. This results in a completely well-defined and explicit expression for the full interacting Hamiltonian up to and including terms quartic in the number of fields.

U2 - 10.1007/jhep04(2010)079

DO - 10.1007/jhep04(2010)079

M3 - Journal article

SN - 1126-6708

VL - 2010

SP - 079

JO - Journal of High Energy Physics (Online)

JF - Journal of High Energy Physics (Online)

IS - 4

ER -