A CFT perspective on gravitational dressing and bulk locality

Abstract

Abstract:We revisit the construction of local bulk operators in AdS/CFT with special focus on gravitational dressing and its consequences for bulk locality. Specializing to 2+1-dimensions, we investigate these issues via the proposed identification between bulk operators and cross-cap boundary states. We obtain explicit expressions for correlation functions of bulk fields with boundary stress tensor insertions, and find that they are free of non-local branch cuts but do have non-local poles. We recover the HKLL recipe for restoring bulk locality for interacting fields as the outcome of a natural CFT crossing condition. We show that, in a suitable gauge, the cross-cap states solve the bulk wave equation for general background geometries, and satisfy a conformal Ward identity analogous to a soft graviton theorem. Virasoro symmetry, the large N conformal bootstrap and the uniformization theorem all play a key role in our derivations.

An exact operator that knows its location

“…Then we show that this simple definition follows from considerations of symmetry. We solve for φ explicitly in various cases, and then show how our definition leads to new recursion relations for 1 We believe the proposal in [27,28] is different from ours. 2 The idea of performing bulk reconstruction using a boundary operator expansion was briefly discussed in [29].…”

“…There is a large literature on bulk reconstruction in AdS/CFT employing a variety of philosophies and methods, for example [1,2,4,[12][13][14][15][17][18][19][20][21][22][23][24][25][26][27][28]. 1 The most common approach expresses bulk fields in terms of local CFT operators integrated against a kernel [1,2,18].…”

On the late-time behavior of Virasoro blocks and a classification of semiclassical saddles

“…We emphasize that this expansion always converges [15] away from OPE limits. In this channel the familiar features of semiclassical quantum gravity, including the physics of BTZ black holes, emerge in the large c limit [1][2][3][4][5][6][7][8][9][10][11][16][17][18][19][20]. In particular, information loss appears [11,13] as the exponential decay of correlators at arbitrarily late times.…”

𝜖-expansion in critical ϕ3-theory on real projective space from conformal field theory

“…In [16] [21], they realize that the symmetry of bulk local fields in the context of AdS/CFT correspondence may be related to the crosscap Ishibashi states in dual conformal field theories. This is certainly the case in the large N limit, and how to introduce the bulk interactions to preserve the locality is under a lot of discussions.…”