Nonlocal Field Theories and their Gravity Duals

TL;DR

This work constructs and analyzes the gravity duals of dipole (nonlocal) field theories within the AdS/CFT framework. By realizing dipole theories via twisted Type II backgrounds and performing a four-step supergravity construction, it shows that near the boundary the metric degenerates in a way that encodes nonlocality, and it compares this to the nonlocal structure of NCSYM. A key result is that the boundary nonlocality manifests as a fibered circle whose T-dual description exposes dipole shifts along the boundary, with the fermionic sector requiring a type-0A dual to resolve subtleties in spin and boundary conditions. The paper also computes correlation functions in the large-N limit, finding oscillatory high-momentum behavior tied to the dipole scale $\lambda\tilde{L}$, and discusses the generality of these features for nonlocal gravity duals and the role of instability considerations in twisted backgrounds.

Abstract

The gravity duals of nonlocal field theories in the large N limit exhibit a novel behavior near the boundary. To explore this, we present and study the duals of dipole theories - a particular class of nonlocal theories with fundamental dipole fields. The nonlocal interactions are manifest in the metric of the gravity dual and type-0 string theories make a surprising appearance. We compare the situation to that in noncommutative SYM.

Figures (1)

• Figure 1: An $r$-point amplitude with vertex operators that carry winding numbers. It requires $r$ cuts on the worldsheet.