Classical geometry from the tensionless string

Abstract

Tensionless string theory on AdS3 × S3 × $$ \mathcal{M} $$ M is explored in the limit that the strings wind the asymptotic boundary a large number of times. Although the worldsheet is usually thought to be localised to the AdS boundary, we argue that the string can actually probe the bulk geometry in this limit. In particular, we show that correlation functions can be expressed in terms of a minimal-area worldsheet propagating in AdS3. We then relate the classical motion of the string to the twistor-like free field description of the tensionless worldsheet theory. Finally, we consider a particular dimensional reduction of AdS3 to AdS2, and show that the effective action of the worldsheet formally resembles the one-dimensional Schwarzian theory of JT gravity with conical defects.

Symmetries and covering maps for the minimal tension string on AdS3 × S3 × T4

“…It was proposed in [24] that a theory of minimal tension strings on AdS 3 ×S 3 × T 4 is in fact independent of the bulk geometry of the spacetime, up to some equivalence classes for the asymptotics of the geometry. Nevertheless, it is thought that a bulk geometry does emerge in the limit of large spectral flow and this geometry contains a conical deficit [24,38]. This fits nicely with the picture given in figure 8, since the worldsheet is localised near the boundary of the (r, θ, t) sphere at every point except near the infinite past, where a conical deficit appears to emerge.…”

“…The delta-function transforms with the opposite sign 39 giving [αK, δ(S)] = 2αδ(S). 38 We have been able to show that this result generalises to states that have been acted on by the ∂ X j n and Ψ A,j r DDF operators of (3.7), but have not verified the radial symmetry when there are insertions containing ∂X j n . We expect the result to fully generalise and hope to return to this elsewhere.…”

“…where the interaction term between Φ and β has negligible effect. 17 In this picture, the worldsheet can only probe spacetime in the vicinity of the boundary and one concludes that it is only in this region in which physical perturbations occur (although there have been suggestions that in the limit of large spectral flow the interior can be probed [24,38]). The large radius description is the perspective that has been largely adopted; however, there is another possible description of the physics which we describe below.…”

“…It will play the role of a picture number: there is a copy of the full psu(1, 1|2) 1 theory at each eigenvalue of Y 0 . We must take account of this in the construction of physical correlators [7,12,38], identifying two correlators that differ only in their Y 0 charge as physically equivalent. To avoid such complications, we will only consider correlation functions where the overall Y 0 charge vanishes in section 3.3.…”

“…The correlation function of ground states is therefore invariant under global radial translations. 38 It is interesting that we needed exactly n + 2g − 2 of the b(µ I ) insertions for a nonanomalous radial translation. We mentioned in section 3.3 that we should include this number of b(µ I ) insertions to cancel the anomalies of the ghost currents of the hybrid formalism (this is shown in detail in appendix B).…”