Cutoff AdS3 versus $$ T\overline{T} $$ CFT2 in the large central charge sector: correlators of energy-momentum tensor

In this article we probe the proposed holographic duality between $$ T\overline{T} $$ T T ¯ deformed two dimensional conformal field theory and the gravity theory of AdS3 with a Dirichlet cutoff by computing correlators of energy-momentum tensor. We focus on the large central charge sector of the $$ T\overline{T} $$ T T ¯ CFT in a Euclidean plane and a sphere, and compute the correlators of energy-momentum tensor using an operator identity promoted from the classical trace relation. The result agrees with a computation of classical pure gravity in Euclidean AdS3 with the corresponding cutoff surface, given a holographic dictionary which identifies gravity parameters with $$ T\overline{T} $$ T T ¯ CFT parameters.

A Choice Model of University Endowments Governance

The board of committees governing university endowments often chooses between hiring professionals to run funds and trusting denoting entities with the funds. As usual, sophisticated fund managers can construct a well-diversified investment portfolio; however, their interests may not be aligned with the university. On the other hand, donors have the advantage of assuming full liabilities for losses, but they only have access to risky projects due to their limitations in terms of accessing the available investment universe. This paper develops a theoretical framework in an attempt to explain the distinct endowment management strategy adopted by universities, and particularly their choice of endowment operator identity. Our model can provide supports to the governance activities practiced by university endowments both in developed and developing countries. Furthermore, we show theoretically that current capital control regulations imposed by the developing country's government reduce donations and encourage universities to establish donor-advised endowment funds, in which donors surrender ownership of anything they put in the fund, but retain control over how their money is invested.

On the Operator Identity ∑ AkXBk ≡ 0

Let Aj and Bj (1 ≦ j ≦ m) be bounded operators on a Banach space ᚕ and let Φ be the mapping on , the algebra of bounded operators on ᚕ, defined by(1)We give necessary and sufficient conditions for Φ to be identically zero or to be a compact map or (in the Hilbert space case) for the induced mapping on the Calkin algebra to be identically zero. These results are then used to obtain some results about inner derivations and, more generally, about mappings of the formFor example, it is shown that the commutant of the range of C(S, T) is “small” unless S and T are scalars.