Abstract
We conjecture the Quantum Spectral Curve equations for string theory on AdS3× S3× T4 with RR charge and its CFT2 dual. We show that in the large-length regime, under additional mild assumptions, the QSC reproduces the Asymptotic Bethe Ansatz equations for the massive sector of the theory, including the exact dressing phases found in the literature. The structure of the QSC shares many similarities with the previously known AdS5 and AdS4 cases, but contains a critical new feature — the branch cuts are no longer quadratic. Nevertheless, we show that much of the QSC analysis can be suitably generalised producing a self-consistent system of equations. While further tests are necessary, particularly outside the massive sector, the simplicity and self-consistency of our construction suggests the completeness of the QSC.
Highlights
It is believed that AdS3/CFT2 dual pairs with 8+8 supersymmetries are integrable [22,23,24].1 This is the maximal amount of supersymmetry that is allowed for string theory backgrounds of the form AdS3 × M7, with M7 = S3 × T4 or M7 = S3 × S3 × S1
We show that in the large-length regime, under additional mild assumptions, the QSC reproduces the Asymptotic Bethe Ansatz equations for the massive sector of the theory, including the exact dressing phases found in the literature
The exact S matrices can be found by imposing compatibility with the vacuum-preserving symmetry algebras of the two theories [27,28,29,30,31,32], much like what can be done in higherdimensional cases [33]
Summary
The massive Asymptotic Bethe Ansatz (ABA) equations which we will be referring to are those presented in [28]. Where the contours C± denote the upper (resp., lower) half semicircle in the complex w-plane, both running anti-clockwise These expressions are valid in the physical region |x| > 1, |y| > 1. Since we will be merely concerned with the massive modes, it is expected that the Asymptotic Bethe equations which we have written above should be valid exactly in the coupling h but only asymptotically in the length L. In other words, wrapping corrections are expected to be exponentially suppressed [49] This situation would be rather different were we to include massless modes, whose impact on the TBA is not exponentially suppressed — they are expected to be polynomially suppressed in the presence of mixed massive-massless interactions [50], or require exact solutions as in the case of the conformal TBA of [44, 51] (see [52, 53]). Since all interaction between the two psu(1, 1|2) wings go through the branch-cut, the two wings become completely decoupled in the limit of small coupling constant h → 0, except for the level-matching condition
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
