Abstract
We study string theory on the pp-wave geometry obtained by taking the Penrose limit around a certain null geodesic of the non-supersymmetric Schrödinger background. We solve for the spectrum of bosonic excitations and find compelling agreement with the dispersion relation of the giant magnons in the Schrödinger background obtained previously in [47]. Inspired by the pp-wave spectrum we conjecture an exact in the t’Hooft coupling dispersion relation for the magnons in the original Schrödinger background. We show that the pp-wave background admits exactly 16 Killing spinors. We use the explicit form of the latter in order to derive the supersymmetry algebra of the background which explicitly depends on the deformation parameter. Its bosonic subalgebra is of the Newton-Hooke type.
Highlights
Intense activity took place allowing the determination of its planar spectrum for any value of the ’t Hooft coupling λ
We study string theory on the pp-wave geometry obtained by taking the Penrose limit around a certain null geodesic of the non-supersymmetric Schrodinger background
We will show that two of the eigenfrequencies of the bosonic spectrum derived in the previous section is in complete agreement with the dispersion relation of the giant magnon solution in the original background, that is before taking the pp-wave limit
Summary
We review the Schrodinger solution and take the Penrose limit around the null geodesic of [49], to obtain the pp-wave geometry. Dyi , i=1 i=5 enables to rewrite the pp-wave background in the following form (2.10). The Brinkmann form of the pp-wave metric for the Schrodinger geometry is given by ds2 = 2dudv + Hdu2 + dyi , i=1 where H is the following function of u and the coordinates yi’s (2.17). To eliminate the cross terms dyi du and bring the metric in the Brinkmann form, we have inserted u-dependence in the coefficient of du. To eliminate the cross terms dyi du and bring the metric in the Brinkmann form, we have inserted u-dependence in the coefficient of du2 Such a dependence was observed in other kinds of deformations of the AdS5 × S5 background, as in [53, 54]
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