On finite-size spiky strings in $Ad{S}_3\times S^3\times T^4$ with mixed fluxes

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(${\Delta }_{+}^{J_1}{\varphi }_1{\Delta }_{+}^{J_2}{\varphi }_2...{\Delta }_{+}^{J_n}{\varphi }_n$). 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.

23 pages, Added references. To appear in JHEP

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