Letter from Representative Burdick to Mr. H. J. Goddard Regarding Garrison Dam Pool Level, May 9, 1955

This letter, dated May 9, 1955 from United States Representative Usher Burdick to Mr. H. J. Goddard, publisher of the Dickey County Leader, of Ellendale, North Dakota, thanks Goddard for the professional way the Garrison Dam reservoir poll level issue was handled in the May 5 issue of the Leader. See also: Letter from H. J. Goddard to Representative Burdick Regarding Garrison Dam Pool Level, June 9, 1955https://commons.und.edu/burdick-papers/1293/thumbnail.jp

Letter from H. J. Goddard to Representative Burdick Regarding Garrison Dam Pool Level, June 9, 1955

This letter, dated June 9, 1955, from H. J. Goddard, publisher of the Dickey County Leader of Ellendale, North Dakota to United States (US) Representative Usher Burdick thanks Burdick for his recent letter and kind words regarding the Leader\u27s handling of the Garrison Reservoir pool level issue. Goddard notes that credit should go to Goddard\u27s son, Malcolm, a recent journalism graduate from the University of North Dakota. Goddard writes that he believes Burdick is correct about the dam\u27s pool level and adds that he does not approve of asking officials to weigh in on the topic when they do not know enough about it. See also: Letter from Representative Burdick to Mr. H. J. Goddard Regarding Garrison Dam Pool Level, May 9, 1955https://commons.und.edu/burdick-papers/1294/thumbnail.jp

On the coset duals of extended higher spin theories

We study the holographic duality between the M x M matrix extension of Vasiliev higher spin theories on AdS3 and the large N limit of SU(N+M)/SU(N) x U(1) type cosets. We present a simplified proof for the agreement of the spectra and clarify the relation between this duality and the version in which the cosets are replaced by Kazama-Suzuki models of Grassmannian type.Comment: 27 pages, 1 tabl

The Primary Spin-4 Casimir Operators in the Holographic SO(N) Coset Minimal Models

Starting from SO(N) current algebra, we construct two lowest primary higher spin-4 Casimir operators which are quartic in spin-1 fields. For N is odd, one of them corresponds to the current in the WB_{\frac{N-1}{2}} minimal model. For N is even, the other corresponds to the current in the WD_{\frac{N}{2}} minimal model. These primary higher spin currents, the generators of wedge subalgebra, are obtained from the operator product expansion of fermionic (or bosonic) primary spin-N/2 field with itself in each minimal model respectively. We obtain, indirectly, the three-point functions with two real scalars, in the large N 't Hooft limit, for all values of the 't Hooft coupling which should be dual to the three-point functions in the higher spin AdS_3 gravity with matter.Comment: 65 pages; present the main results only and to appear in JHEP where one can see the Appendi

The Coset Spin-4 Casimir Operator and Its Three-Point Functions with Scalars

We find the GKO coset construction of the dimension 4 Casimir operator that contains the quartic WZW currents contracted with completely symmetric SU(N) invariant tensors of ranks 4, 3, and 2. The requirements, that the operator product expansion with the diagonal current is regular and it should be primary under the coset Virasoro generator of dimension 2, fix all the coefficients in spin-4 current, up to two unknown coefficients. The operator product expansion of coset primary spin-3 field with itself fixes them completely. We compute the three-point functions with scalars for all values of the 't Hooft coupling in the large N limit. At fixed 't Hooft coupling, these three-point functions are dual to that found by Chang and Yin recently in the undeformed AdS_3 bulk theory (higher spin gravity with matter).Comment: 65 pages; the ambiguity for the two coefficient functions is clarified and the abstract, the introduction, the subsection 3.4 and the conclusion are improved and to appear in JHE

Supersymmetric holography on AdS3

The proposed duality between Vasiliev's supersymmetric higher spin theory on AdS3 and the 't Hooft limit of the 2d superconformal Kazama-Suzuki models is analysed in detail. In particular, we show that the partition functions of the two theories agree in the large N limit.Comment: 25 pages, 3 figures, improved fig.

Limits of minimal models and continuous orbifolds

The lambda=0 't Hooft limit of the 2d W_N minimal models is shown to be equivalent to the singlet sector of a free boson theory, thus paralleling exactly the structure of the free theory in the Klebanov-Polyakov proposal. In 2d, the singlet sector does not describe a consistent theory by itself since the corresponding partition function is not modular invariant. However, it can be interpreted as the untwisted sector of a continuous orbifold, and this point of view suggests that it can be made consistent by adding in the appropriate twisted sectors. We show that these twisted sectors account for the `light states' that were not included in the original 't Hooft limit. We also show that, for the Virasoro minimal models (N=2), the twisted sector of our orbifold agrees precisely with the limit theory of Runkel & Watts. In particular, this implies that our construction satisfies crossing symmetry.Comment: 33 pages; v2: minor improvements and references added, published versio

Higher spin AdS_3 holography with extended supersymmetry

We propose a holographic duality between a higher spin AdS_3 gravity with so(p) extended supersymmetry and a large N limit of a 2-dimensional Grassmannian-like model with a specific critical level k=N and a non-diagonal modular invariant. As evidence, we show the match of one-loop partition functions. Moreover, we construct symmetry generators of the coset model for low spins which are dual to gauge fields in the supergravity. Further, we discuss a possible relation to superstring theory by noticing an N=3 supersymmetry of critical level model at finite k,N. In particular, we examine BPS states and marginal deformations. Inspired by the supergravity side, we also propose and test another large N CFT dual obtained as a Z_2 automorphism truncation of a similar coset model, but at a non-critical level.Comment: 44 pages, published versio

Large N=4 Holography

The class of 2d minimal model CFTs with higher spin AdS3 duals is extended to theories with large N=4 superconformal symmetry. We construct a higher spin theory based on the global D(2,1|alpha) superalgebra, and propose a large N family of cosets as a dual CFT description. We also indicate how a non-abelian version of this Vasiliev higher spin theory might give an alternative description of IIB string theory on an AdS3 x S3 x S3 x S1 background.Comment: 41 pages, LaTe

Molecular evolution: sex accelerates adaptation

An analysis confirms the long-standing theory that sex increases the rate of adaptive evolution by accelerating the speed at which beneficial mutations sweep through sexual, as opposed to asexual, populations