Semiclassical rigid strings with two spins in AdS_5

TL;DR

This paper analyzes classical semiclassical string solutions with two spins in AdS_5, revealing their large spin behavior and connection to universal scaling functions, with implications for understanding energy-spin relations in AdS/CFT correspondence.

Contribution

It provides explicit solutions for rigid two-spin strings in AdS_5 and links their large spin asymptotics to universal scaling functions, extending previous understanding of string energy growth.

Findings

Large spin solutions develop long arcs towards AdS boundary.

Energy grows logarithmically with total spin S.

Coefficient of log S matches universal cusp anomaly function.

Abstract

Semiclassical spinning string states in AdS_5 are, in general, characterised by the three SO(2,4) conserved charges: the energy E and the two spins S_1 and S_2. We discuss several examples of explicit classical solutions for rigid closed strings of (bended) circular shape with two non-zero spins. In particular, we identify a solution that should represent a state that has minimal energy for large values of the two equal spins. Similarly to the spiky string in AdS_3, in the large spin limit this string develops long "arcs" that stretch towards the boundary of AdS_5. This allows the string to increase the spin while having the energy growing only logarithmically with S=S_1 +S_2. The large spin asymptotics of such solutions is effectively controlled by their near-boundary parts which, as in the spiky string case, happen to be SO(2,4) equivalent to segments of the straight folded spinning string. As a result, the coefficient of the \log S term in the string energy should be given, up to an overall 3/2 coefficient, by the same universal scaling function (cusp anomaly) as in the folded string case, to all orders in the inverse string tension or strong-coupling expansion.