Operator traces and holography

Unusual Traces on Operator Ideals

In this note we ans~ycr a question of A. Prmsm by constructing an example of a quasi-normed operator ideal on a HILBEBT space which admits more than one continuous trace. We aiso characterize the cIms of uniquely traceable operators as described below. Let H be a separable =BERT space and let a be an ideal in X[H) (the compact operators on H). Then a trace “21) on B i s 8 linear functional t: J...

Traces on Operator Ideals and Arithmetic Means

This article investigates the codimension of commutator spaces [I, B(H)] of operator ideals on a separable Hilbert space, i.e., “How many traces can an ideal support?” We conjecture that the codimension can be only zero, one, or infinity. Using the arithmetic mean (am) operations on ideals introduced in [13] and the analogous arithmetic mean operations at infinity (am-∞) that we develop extensi...

Intertwining Operator Realization of Non-Relativistic Holography

We give a group-theoretic interpretation of non-relativistic holography as equivalence between representations of the Schrödinger algebra describing bulk fields and boundary fields. Our main result is the explicit construction of the boundary-tobulk operators for which we first construct the two-point Green function in the bulk. Further we show that these operators and the bulk-to-boundary oper...

Holography of Wilson-Loop Expectation Values with Local Operator Insertions

We study the expectation values of Wilson-loop operators with the insertions of local operators Z and Z J for large J from the bulk viewpoint of AdS/CFT correspondence. Classical solutions of strings attached to such deformed Wilson loops at the conformal boundary are constructed and are applied to the computation of Wilson-loop expectation values. We argue that in order to have such solutions ...

Conformal field theories at nonzero temperature: Operator product expansions, Monte Carlo, and holography