On finite-size spiky strings in $AdS_3 \times S^3\times T^4$ with mixed fluxes

TL;DR

This paper analyzes finite-size corrections to spiky strings in $AdS_3 imes S^3 imes T^4$ with mixed fluxes, expressing dispersion relations via Lambert W-functions and exploring implications for dual gauge theory operators.

Contribution

It introduces a novel formulation of finite-size dispersion relations for spiky strings using Lambert W-functions in the context of mixed flux backgrounds.

Findings

Finite-size corrections expressed with Lambert W-function.

Finite-size scaling relation between energy and angular momentum established.

Comments on pure NS-NS background solutions included.

Abstract

We discuss finite-size corrections to the spiky strings in $AdS$ space which is dual to the long $\mathcal{N}=4$ SYM operators of the form Tr($\Delta_+ ^{J_1}\phi_1\Delta_+ ^{J_2}\phi_2...\Delta_+ ^{J_n}\phi_n$). We express the finite-size dispersion relation in terms of Lambert $\mathbf{W}$-function. We further establish the finite-size scaling relation between energy and angular momentum of the spiky string in presence of mixed fluxes in terms of $\mathbf{W}$-function. We comment on the solution in pure NS-NS background as well.