$N$-spike string in $AdS_3 \times S^1$ with mixed flux

TL;DR

This paper investigates classical N-spike string solutions in AdS3 x S1 with mixed flux, revealing how angular momentum and flux influence spike shape and deriving related energy-spin relations.

Contribution

It introduces new classical string solutions with mixed flux in AdS3 x S1, analyzing the effects of angular momentum and flux on spike configurations.

Findings

Spikes become rounded with added angular momentum or winding.

Flux does not alter the spike rounding behavior.

Derived energy-spin dispersion relations for large N limit.

Abstract

Sigma model in $AdS_3\times S^3$ background supported by both NS-NS and R-R fluxes is one of the most distinguished integrable models. We study a class of classical string solutions for $N$-spike strings moving in $AdS_3 \times S^1$ with angular momentum $J$ in $S^1 \subset S^5$ in the presence of mixed flux. We observe that the addition of angular momentum $J$ or winding number $m$ results in the spikes getting rounded off and not end in cusp. The presence of flux shows no alteration to the rounding-off nature of the spikes. We also consider the large $N$-limit of $N$-spike string in $AdS_3 \times S^1$ in the presence of flux and show that the so-called Energy-Spin dispersion relation is analogous to the solution we get for the periodic-spike in $AdS_3-pp-$wave $\times S^1$ background with flux.