Abstract
In the recent publication [1] the spin vertex was introduced as a new approach for computing three-point functions in $$ \mathcal{N}=4 $$ SYM. In this note we consider the BMN limit of the spin vertex for scalar excitations and show that it reproduces the string vertex in the light-cone string field theory which describes the string interactions in the pp-wave background at the leading order of λ ′ expansion. This is achieved by introducing a polynomial representation for the spin vertex. We derive the Neumann coefficients from the spin vertex at weak coupling and show they match with the Neumann coefficients from the string field theory.
Highlights
From string theory side the BMN limit is obtained by taking the Penrose limit of the AdS5 × S5 string sigma model [6]
While the string vertex is applicable in the BMN limit, the spin vertex works for general spin chain states at leading order
In order to derive string field theory (SFT) from spin vertex, we introduce a polynomial representation for the spin vertex in the compact sector
Summary
We review briefly the light-cone string field theory for strings on the pp-wave background [27,28,29,30,31] and refer the interested readers to [32, 33] and references therein for more detail. The string interactions are described by the matrix elements of the Hamiltonian which has the following expansion in coupling constant gs. We focus on the cubic interactions which are described by the following matrix elements λ123 = 2| 3|H3|1 = 1| 2| 3|H3 ,. The integral can be computed straightforwardly, leading to the following form of the bosonic string vertex. In addition to worldsheet continuity, one needs to require that supersymmetry is respected by the string vertex. This can be achieved by acting a new operator P on the exponential part (2.4). After one fixes the string vertex, the matrix elements of H3 can be computed straightforwardly. At higher loop order, the large μ expansion of the function G(∆1, ∆2, ∆3) give rises to non-perturbative terms such as log μ, the interpretation of which is still unclear
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