Finite-size corrections for quantum strings on AdS₄ x CP³

TY - JOUR

T1 - Finite-size corrections for quantum strings on AdS4 x CP3

AU - Astolfi, D.

AU - Puletti, V.G.M.

AU - Grignani, G.

AU - Harmark, Troels

AU - Orselli, Marta

PY - 2011/5/1

Y1 - 2011/5/1

N2 - We revisit the calculation of curvature corrections to the pp-wave energy of type IIA string states on AdS4×ℂℙ3 initiated in arXiv:0807.1527. Using the near pp-wave Hamiltonian found in arXiv:0912.2257, we compute the first non-vanishing correction to the energy of a set of bosonic string states at order 1/R2, where R is the curvature radius of the background. The leading curvature corrections give rise to cubic, order 1/R, and quartic, order 1/R2, terms in the Hamiltonian, for which we implement the appropriate normal ordering prescription. Including the contributions from all possible fermionic and bosonic string states, we find that there exist logarithmic divergences in the sums over mode numbers which cancel between the cubic and quartic Hamiltonian. We show that from the form of the cubic Hamiltonian it is natural to require that the cutoff for summing over heavy modes must be twice the one for light modes. With this prescription the strong-weak coupling interpolating function h(λ), entering the magnon dispersion relation, does not receive a one-loop correction, in agreement with the algebraic curve spectrum. However, the single magnon dispersion relation exhibits finite-size exponential corrections.

AB - We revisit the calculation of curvature corrections to the pp-wave energy of type IIA string states on AdS4×ℂℙ3 initiated in arXiv:0807.1527. Using the near pp-wave Hamiltonian found in arXiv:0912.2257, we compute the first non-vanishing correction to the energy of a set of bosonic string states at order 1/R2, where R is the curvature radius of the background. The leading curvature corrections give rise to cubic, order 1/R, and quartic, order 1/R2, terms in the Hamiltonian, for which we implement the appropriate normal ordering prescription. Including the contributions from all possible fermionic and bosonic string states, we find that there exist logarithmic divergences in the sums over mode numbers which cancel between the cubic and quartic Hamiltonian. We show that from the form of the cubic Hamiltonian it is natural to require that the cutoff for summing over heavy modes must be twice the one for light modes. With this prescription the strong-weak coupling interpolating function h(λ), entering the magnon dispersion relation, does not receive a one-loop correction, in agreement with the algebraic curve spectrum. However, the single magnon dispersion relation exhibits finite-size exponential corrections.

U2 - 10.1007/JHEP05(2011)128

DO - 10.1007/JHEP05(2011)128

M3 - Journal article

SN - 1126-6708

VL - 2011

SP - 128

JO - Journal of High Energy Physics (Online)

JF - Journal of High Energy Physics (Online)

IS - 5

ER -