# On N-spike strings in conformal gauge with NS-NS fluxes

## TL;DR

This paper investigates the spectrum of twist operators in the integrable $AdS_3\times S^3$ string theory with mixed NS-NS and R-R fluxes, deriving exact dispersion relations for semiclassical strings and exploring flux-dependent effects.

## Contribution

It provides the first detailed semiclassical analysis of multi-cusp strings in $AdS_3$ with mixed fluxes, revealing flux-dependent modifications to the dispersion relations of dual operators.

## Key findings

- Derived exact dispersion relations for long strings with mixed fluxes.
- Found that NS-NS flux scales the coupling in the dispersion relation.
- Simplified dispersion relation in the pure NS flux case.

## Abstract

The $AdS_3\times S^3$ string sigma model supported both by NS-NS and R-R fluxes has become a well known integrable model, however a putative dual field theory description remains incomplete. We study the anomalous dimensions of twist operators in this theory via semiclassical string methods. We describe the construction of a multi-cusp closed string in conformal gauge moving in $AdS_3$ with fluxes, which supposedly is dual to a general higher twist operator. After analyzing the string profiles and conserved charges for the string, we find the exact dispersion relation between the charges in the `long' string limit. This dispersion relation in leading order turns out to be similar to the case of pure RR flux, with the coupling being scaled by a factor that depends on the amount of NS-NS flux turned on. We also analyse the case of pure NS flux, where the dispersion relation simplifies considerably. Furthermore, we discuss the implications of these results at length.