Causal structures and holography

Abstract

We explore the description of bulk causal structure in a dual field theory. We observe that in the spacetime dual to a spacelike non-commutative field theory, the causal structure in the boundary directions is modified asymptotically. We propose that this modification is described in the dual theory by a modification of the microcausal light cone. Previous studies of this micro-causal light cone for spacelike noncommutativite field theories agree with the expectations from the bulk spacetime. We describe the spacetime dual to field theories with lightlike non-commutativity, and show that they generically have a drastic modification of the light cone in the bulk: the spacetime is non-distinguishing. This means that the spacetime while being devoid of closed timelike or null curves, has causal curves that are "almost closed". We go on to show that the micro-causal light cone in the field theory agrees with this prediction from the bulk.

Lunin-Maldacena backgrounds from the classical Yang-Baxter equation — towards the gravity/CYBE correspondence

“…The conjectured relations are summarized in table 1, though it is still necessary to make efforts to get supporting evidence. A support is that the type IIB supergravity solution constructed with a Jordanian twist [49] may be regarded as a null Melvin twist, basically following the argument in appendix C of [69]. We will report on the details in the near future [70].…”

Yang-Baxter deformations and string dualities

“…Through the coordinate transformations (3.1), the above metric and NS-NS two-form agree with the ones in (2.20) when a 1 = −Im(α) = −α I . The NS-NS sector of the background (3.8) has already been obtained in [61].…”

Hot spacetimes for cold atoms

“…Melvinization has largely been used to construct gravity duals of non-commutatitve and non-local field theories [34,35,36,37,38]; in the case at hand, the Null twisting produces an extremely mild form of non-locality, that of non-relativistic theories with instantaneous interactions.…”

“…Along the way we identify a scaling limit which describes the system at zero temperature but nonzero density. To produce these solutions, we will use a solutiongenerating technique called the Null Melvin Twist [34,35,36,37,38], which we will review in detail below. This Melvinizing procedure is the sought-for analog of the plane wave limit described in the introduction and conclusion of [13].…”