Revisiting the tensionless limit of pure-Ramond-Ramond AdS3/CFT2

TL;DR

This work analyzes the tensionless limit of pure-RR AdS3/CFT2 by reexamining the mirror TBA with a revised massless dressing factor, focusing on k=0 and h << 1. The authors show that massive Y_Q modes decouple and that the physically consistent massless sector corresponds to N0=1, yielding a simplified, non-relativistic, interacting spectrum dominated by T^4 excitations. They derive difference-form TBA equations in gamma-rapidity, study their asymptotics, and implement a careful numerical scheme to solve the coupled TBA and Bethe equations, revealing finite-volume wrapping corrections and state-dependent energy shifts. The results differ quantitatively from previous work that used a different dressing factor but remain qualitatively similar, supporting a dual CFT interpretation as interacting torus excitations rather than a symmetric-product orbifold, and paving the way for QSC cross-checks and extensions to mixed-flux backgrounds.

Abstract

We revisit the numerical solution of the mirror TBA equations for pure--Ramond-Ramond strings on $AdS_3\times S^3\times T^4$ in the tensionless limit. Our analysis uses the recently-proposed modification of the dressing factors which account for non-trivial exchange relations of the massless modes. At leading order in the tension, the dynamics is driven by the massless excitations associated to $T^4$ modes and their superpartners, but it is non-relativistic and interacting unlike what happens in the symmetric-product orbifold CFT of $T^4$.

Figures (7)

• Figure 1: Y-functions with divergent asymptotics. A new feature of the revised TBA equations is that, for odd $M$, the Y-functions exhibit the asymptotic behaviour \ref{['eq:divergentY']}. We plot the numerical solution for $Y_0(\gamma)$ and $Y(\gamma)$ for $M=1$. The red crosses indicate the positions of the Bethe roots $\gamma_1$ and $\gamma_2=-\gamma_1$, which are zeros of the auxiliary Y-function $Y(\gamma)$. The insets provide a zoomed-in view around $\gamma=0$.
• Figure 2: Energies of two-particle states. We consider two particle states ($M=1$) with $\nu_1=-\nu_2$ and plot their energy as function of the mode numbers $\nu_1$ for various values of the volume $L$. The dashed line is the result obtained by discarding the finite-volume effects, cf. \ref{['eq:free']}. Note that the energy for $\nu_1=\nu_2=0$ is protected in accordance with Baggio:2017kza.
• Figure 3: Finite-size corrections as $L$ varies. We plot the deviation of the energy of two-particle states ($M=1$) from the free approximation.
• Figure 4: Energies of four-particle states. We plot some energies of four-particle states ($M=2$) with $\nu_1=-\nu_2$ and $\nu_3=-\nu_4$; each trajectory has fixed $\nu_1$.
• Figure 5: Comparison with the previous results. We compare with the results of Brollo:2023pklBrollo:2023rgp, which used a different dressing factor. In the top two plots we compare the energies, while in the bottom two we compare their deviation from the free result \ref{['eq:free']}. We indicate the results of Brollo:2023pklBrollo:2023rgp with $\mathcal{E}$ (blue crosses) and the current ones with $E$ (red dots).