# Your search: "author:"Nelson, Brent""

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## Scholarly Works (7 results)

By modifying the tracial techniques of Guionnet and Shlyakhtenko in [GS14] we produce free monotone transport in the context of a finitely generated free Araki-Woods factor, which can be considered a non-tracial analogue of the free group factors. We solve a free analogue of the Monge-Ampère equation to produce a criterion for when an N-tuple of non-commutative random variables generate a free Araki-Woods factor. The criterion, that the joint law satisfies a certain non-commutative differential equation involving a canonical potential, is precisely the tracial criterion established in [GS14] modulo modifications to the differential operators and potential that are completely natural in light of the structure of the free Araki-Woods factor. We provide two applications of this result. The first is that for small |q|, the q-deformed free Araki-Woods algebras are isomorphic to the free Araki-Woods factor with the same number of generators and orthogonal representation of R. This is obtained using similar estimates to some found in [Dab14], which were used to prove the tracial analogue in [GS14] that the q-deformed free group factors are isomorphic to the free group factor for small |q|. The second application is to finite depth subfactor planar algebras, where it is shown that the transport machinery can be expressed diagrammatically via planar tangles. From this one obtains a criterion for when towers of von Neumann algebras are isomorphic.

We examine the phenomenological consequences of quadratically divergent contributions to the scalar potential in supergravity effective Lagrangians. We focus specifically on the effect of these corrections on the vacuum configuration of scalar fields in softly-broken supersymmetric theory is and the role these corrections play in generating non-diagonal soft scalar masses. Both effects can only be properly studied when the divergences are regulated in a manifestly supersymmetric manner -- something which has ths far been neglected in past treatments. We show how a supersymmetric regularization can impact past conclusions about both types of phenomena and discuss what types of high-energy theories are likely to be safe from unwanted flavor-changing neutral current interactions in the context of supergravity theories derived from heterotic string compactifications.

We perform a systematic analysis of soft supersymmetry breaking terms at the one loop level ina large class of string effective field theories. This includes the so-called anomaly mediated contribuions. We illustrate our results for several classes of orbifold models. In particlular, we ciscuss a class of models whee soft supersymmetry breaqking terms are determined by quasi model independent anomaly mediated contributions, with possibly non-vanishing scalar masses at the one loop level. We show that the latter contribution depends on the detailed prescription of the regularization process which is assumed to represent the Planck scale physics of the underlying fundamenta theory. The usual anomaly mediation case with vanishing scalr masses at one loop is not found to be generic. However gaugino masses and A-terms always vanish at tree level if supersymmetry breaking is moduli dominated with the moduli stabilized at self-dual points, whereas the manishing of the B-term depends on the origin of the mu-term in the underlying theory. We also discuss the supersymmetric spectrum of O-I and O-II models, as well as a model of gaugino condensation. For reference, explicit spectra corresponding to a Higgs mass of 114 GeV are given. Finally, we address general strategies for distinguishing among these models.