A universality test of the quantum string Bethe ansatz

Abstract

We show that the quantum corrected string Bethe ansatz passes an important universality test by demonstrating that it correctly incorporates the non-analytical terms in the string sigma model one-loop correction for rational three-spin strings with two out of the three spins identical. Subsequently, we use the quantum corrected string Bethe ansatz to predict the exact form of the non-analytic terms for the generic rational three-spin string.

Gauge-String Dualities and some Applications

“…The perturbative expansion of the phase starts at the 4-loop order, and at strong coupling coincides with the earlier results from string theory [42,45,[47][48][49]. The important requirement of crossing symmetry [50] is satisfied by this phase, and it also obeys the transcendentality principle of [36].…”

Dressing phases ofAdS3/CFT2

“…The next-to-leading term gives the HL phase. This was first found through a one-loop sigma-model computation [16][17][18] and can also be obtained through a semi-classical quantisation of the finite gap equations [19]. This latter derivation shows explicitly that the HL phase is the same for all states in a given background.…”

“…The leading-order contribution to the dressing phase starts at O(h 6 ) [10], and comes from the r = 2, s = 3 terms in the expansion of χ BES . 17 The AdS 3 dressing phases (3.17) contain extra terms besides the BES phase. The coefficients c r,s andc r,s that come from these extra contributions are all order h 0 (see equation (5.7) and (5.6)).…”

“…At small coupling the dressing phase is trivial at the leading two orders: σ BES = 1 + O(λ 3 ), while for large λ it appears already at the leading order. It is conventional to refer to the first two orders in the strong coupling expansion of a dressing phase as the ArutyunovFrolov-Staudacher (AFS) [15] and Hernández-López (HL) [16,17] orders, which appear at (O(λ 1/2 ) and O(λ 0 )), respectively. Expanding σ BES at strong coupling, one finds the leading AFS phase [15] which is expected to be universal for many integrable string theory backgrounds.…”

Finite-size effects from giant magnons

“…Currently, the first two orders in the expansion have been computed in [28,34,35], building upon observations of [36][37][38]. It was demonstrated in [8] that, up to this order, the dressing factor indeed satisfies the functional equation of [4].…”