AdS Witten diagrams to Carrollian correlators

Abstract

Carrollian Conformal Field Theories (CFTs) have been proposed as co-dimension one holographic duals to asymptotically flat spacetimes as opposed to Celestial CFTs which are co-dimension two. In this paper, drawing inspiration from Celestial holography, we show by a suitable generalisation of the flat space limit of AdS that keeps track of the previously disregarded null direction, one can reproduce Carrollian CFT correlation functions from AdS Witten diagrams. In particular, considering Witten diagrams in AdS4, we reproduce two and three-point correlation functions for three dimensional Carrollian CFTs in the so-called delta-function branch. Along the way, we construct non-trivial Carrollian three-point functions in the delta-branch by considering a collinear limit. We also obtain a generalised anti-podal matching condition that now depends on the retarded time direction.

Carroll black holes

“…As the subleading terms in the X -expansion do not play a role in the following and both sides are invariant under Carroll boosts this is just a convenient definition. The first goal is to rewrite all quantities in the relativistic action (35) in terms of the variables on the left-hand side of (40). The relativistic Levi-Civitá connection is thereby organized in a specific way, (LC)…”

“…Additionally, Carroll symmetries may be relevant for cosmology [19], black hole microstates [20], CFT deformations [21][22][23][24], and govern Bjorken flow [25]. Finally, the conformal Carroll algebra is isomorphic to BMS in one higher dimension [4], which led to numerous developments in flat space holography, especially in 2+1 bulk dimensions [26][27][28][29][30][31][32][33][34][35][36] and in 3+1 bulk dimensions [37][38][39][40].…”

BMS modular covariance and structure constants

“…Carrollian holography, on the other hand, seems to be more natural from the point of view of the original ideas of holography and proposes a co-dimension one holographic dual where one not only uses the Lorentz sub-group of the Poincare group but fits translations naturally into the formulation [18]. Recent successes include [19][20][21][22][23][24]. The initial success of the formulation was in lower dimensions, specifically in understanding 3d asymptotically flat spacetime, which we describe below.…”

Entanglement of edge modes in (very) strongly correlated topological insulators

“…If one neglects the hopping terms at very large coupling, the theory becomes ultra-local. Ultra-local models like these are called Carrollian field theories, which have recently gained interest in condensed matter [60,61], fluid dynamics [62][63][64][65], high energy [66][67][68] and gravitational physics [69,70] for diverse inquiries. In particular, fermionic models with these symmetries have been dealt with in detail in [71][72][73].…”