Boundary correlators in WZW model on AdS2

Abstract

Boundary correlators of elementary fields in some 2d conformal field theories defined on AdS 2 have a particularly simple structure. For example, the correlators of the Liouville scalar happen to be the same as the correlators of the chiral component of the stress tensor on a plane restricted to the real line. Here we show that an analogous relation is true also in the WZW model: boundary correlators of the WZW scalars have the same structure as the correlators of chiral Kac-Moody currents. This is checked at the level of the tree and one-loop Witten diagrams in AdS 2. We also compute some tree-level correlators in a generic σ-model defined on AdS 2 and show that they simplify only in the WZW case where an extra Kac-Moody symmetry appears. In particular, the terms in 4point correlators having logarithmic dependence on 1d cross-ratio cancel only at the WZW point. One motivation behind this work is to learn how to compute AdS 2 loop corrections in 2d models with derivative interactions related to the study of correlators of operators on Wilson loops in string theory in AdS.

Mellin amplitudes for 1d CFT

“…The resulting non-local CFTs have a discrete spectrum, making them more similar, in many ways, to their higher dimensional relatives. These theories have explicit realizations in systems such as conformal line JHEP10(2021)095 defects in higher-dimensional CFTs [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21], lines of fixed points in SYK models [22,23], and in general models defined by the set of boundary correlators of quantum field theories in AdS 2 [24][25][26][27][28][29][30]. These various settings have been recently studied via conformal bootstrap methods, in some cases combined with superspace techniques, or via direct Witten diagrammatics.…”

“…In this context, however, the gauge fixing provides a worldsheet effective field theory in AdS 2 background and it is still an interesting open question how the power of integrability can be exploited in this setting. More generally, the study of integrable field theories in curved backgrounds is an active and largely unexplored research subject, which has recently witnessed some interesting developments [26][27][28][29]. It has been pointed out in many places, see for instance [7,40], that a crucial ingredient for our understanding of integrability in curved space would be the analogue of flat space S-matrix factorization and we believe Mellin space may provide the correct setting to look for such a feature.…”

Analytic bootstrap and Witten diagrams for the ABJM Wilson line as defect CFT1

“…A natural development of this work would be to calculate the four-point functions of the displacement supermultiplet beyond tree-level at strong coupling, using loop corrections to Witten diagrams in AdS 2 . The relevant AdS 2 sigma-model should be UV finite [5], but regularization subtleties are anyway expected in AdS 2 models with derivative interactions (for example, see discussion in [35][36][37][38][39][40]). A parallel attempt would be to compute the anomalous dimensions of exchanged operators beyond the first non-trivial order using the bootstrap approach: the potential mixing problem discussed above is expected to arise at this level, and its resolution would require the analysis of different correlators.…”

Deformed WZW Models and Hodge Theory -- Part I

“…Another interesting avenue is to consider the recent works on D-branes in λ-deformations [59,60], which may give an alternative interpretation of the intricate boundary conditions that arise in the study of asymptotic Hodge theory. Alternatively, by studying the boundary limit of the λdeformed G/G model on an AdS 2 worldsheet, along the lines of [86], one may shed new light on the proposed holographic structure of string moduli spaces [8]. In an upcoming second part of this work we will concern ourselves precisely with these boundary aspects in order to make further contact with asymptotic Hodge theory [74].…”