Superficial Saturation

On the Higgsing and UnHiggsing of Fano 3-folds

“…A necessary condition of this is that the toric data of the variety includes the origin. There are various blowup and blowdown relations between the smooth Fano 3-folds [15] via contracting divisors to a line or a point and should be describable in string theory.…”

“…Whereas using the results of [13] we recover a subset of them, we are not able to reproduce the full list, inspite of our efforts to find different phases of the theories constructed in [13], although we believe that these should exist. Further, in several examples, the generators of the toric cones of [15] do not seem to be related by a simple GL(4, Z) transformation with those of [13]. We will proceed keeping these in mind, although to us this indicates a necessity of more detailed study of M2-branes probing cones over Fano 3-folds.…”

“…In three complex dimensions, the situation is far more intricate, and it has been shown that there are eighteen smooth Fano varieties (see eg. [15], [16]). The M2-brane theories constructed in [13] (it was possible to construct fourteen of the possible eighteen) describe complex cones over such varieties, which can consequently be described as CY 4-folds that admit a brane tiling description (for a review, see [14]).…”

“…A word of caution before we proceed. In one of the original classification of Fano 3-folds [15], the series of blow ups and blow down relations that exist between these have been tabulated. Whereas using the results of [13] we recover a subset of them, we are not able to reproduce the full list, inspite of our efforts to find different phases of the theories constructed in [13], although we believe that these should exist.…”

Raman spectroscopy

“…Reviews have been published recounting the work carried out on liquid-solid interfaces (388) and adsorbate characterization (389). The nature of the SERS effect is still being reviewed (390)(391)(392) with particular emphasis on how an understanding of the effect itself can help in the understanding of specific systems, e.g.…”