Letter from S. H. Estes to T. B. Larimore

Letter from S. H. Estes to T. B. Larimore. The four-page handwritten letter is dated 16 November 1912. There is a transcript of the correspondence in the item PDF

G3-homogeneous gravitational instantons

We provide an exhaustive classification of self-dual four-dimensional gravitational instantons foliated with three-dimensional homogeneous spaces, i.e. homogeneous self-dual metrics on four-dimensional Euclidean spaces admitting a Bianchi simply transitive isometry group. The classification pattern is based on the algebra homomorphisms relating the Bianchi group and the duality group SO(3). New and general solutions are found for Bianchi III.Comment: 24 pages, few correction

Paraphrases and summaries: A means of clarification or a vehicle for articulating a preferred version of student accounts?

The use of group discussions as a means to facilitate learning from experiences is well documented in adventure education literature. Priest and Naismith (1993) assert that the use of the circular discussion method, where the leader poses questions to the participants, is the most common form of facilitation in adventure education. This paper draws on transcripts of facilitation sessions to argue that the widely advocated practice of leader summaries or paraphrases of student responses in these sessions functions as a potential mechanism to control and sponsor particular knowledge(s). Using transcripts from recorded facilitation sessions the analysis focuses on how the leader paraphrases the students’ responses and how these paraphrases or ‘formulations’ function to modify or exclude particular aspects of the students’ responses. I assert that paraphrasing is not simply a neutral activity that merely functions to clarify a student response, it is a subtle means by which the leader of the session can, often inadvertently or unknowingly, alter the student’s reply with the consequence of favouring particular knowledge(s). Revealing the subtle work that leader paraphrases perform is of importance for educators who claim to provide genuine opportunities for students to learn from their experience

Exact Half-BPS Flux Solutions in M-theory III: Existence and rigidity of global solutions asymptotic to AdS4 x S7

The BPS equations in M-theory for solutions with 16 residual supersymmetries, $SO(2,2)\times SO(4)\times SO(4)$ symmetry, and $AdS_4 \times S^7$ asymptotics, were reduced in [arXiv:0806.0605] to a linear first order partial differential equation on a Riemann surface with boundary, subject to a non-trivial quadratic constraint. In the present paper, suitable regularity and boundary conditions are imposed for the existence of global solutions. We seek regular solutions with multiple distinct asymptotic $AdS_4 \times S^7$ regions, but find that, remarkably, such solutions invariably reduce to multiple covers of the M-Janus solution found by the authors in [arXiv:0904.3313], suggesting rigidity of the half-BPS M-Janus solution. In particular, we prove analytically that no other smooth deformations away from the M-Janus solution exist, as such deformations invariably violate the quadratic constraint. These rigidity results are contrasted to the existence of half-BPS solutions with non-trivial 4-form fluxes and charges asymptotic to $AdS_7 \times S^4$. The results are related to the possibility of M2-branes to end on M5-branes, but the impossibility of M5-branes to end on M2-branes, and to the non-existence of half-BPS solutions with simultaneous $AdS_4 \times S^7$ and $AdS_7 \times S^4$ asymptotic regions.Comment: 52 pages, 2 figures, pdf-latex. Minor change

Exact half-BPS Type IIB interface solutions I: Local solution and supersymmetric Janus

The complete Type IIB supergravity solutions with 16 supersymmetries are obtained on the manifold $AdS_4 \times S^2 \times S^2 \times \Sigma$ with $SO(2,3) \times SO(3) \times SO(3)$ symmetry in terms of two holomorphic functions on a Riemann surface $\Sigma$, which generally has a boundary. This is achieved by reducing the BPS equations using the above symmetry requirements, proving that all solutions of the BPS equations solve the full Type IIB supergravity field equations, mapping the BPS equations onto a new integrable system akin to the Liouville and Sine-Gordon theories, and mapping this integrable system to a linear equation which can be solved exactly. Amongst the infinite class of solutions, a non-singular Janus solution is identified which provides the AdS/CFT dual of the maximally supersymmetric Yang-Mills interface theory discovered recently. The construction of general classes of globally non-singular solutions, including fully back-reacted $AdS_5 \times S^5$ and supersymmetric Janus doped with D5 and/or NS5 branes, is deferred to a companion paper.Comment: LaTeX, 69 pages, 3 figures, v2: references adde

Entanglement entropy of Wilson surfaces from bubbling geometries in M-theory

We consider solutions of eleven-dimensional supergravity constructed in [1,2] that are half-BPS, locally asymptotic to $AdS_7\times S^4$ and are the holographic dual of heavy Wilson surfaces in the six-dimensional $(2,0)$ theory. Using these bubbling solutions we calculate the holographic entanglement entropy for a spherical entangling surface in the presence of a planar Wilson surface. In addition, we calculate the holographic stress tensor and, by evaluating the on-shell supergravity action, the expectation value of the Wilson surface operator.Comment: 42 pages, 4 figures, v2: minor modification

Massless D-strings and moduli stabilization in type I cosmology

We consider the cosmological evolution induced by the free energy F of a gas of maximally supersymmetric heterotic strings at finite temperature and weak coupling in dimension D>=4. We show that F, which plays the role of an effective potential, has minima associated to enhanced gauge symmetries, where all internal moduli can be attracted and dynamically stabilized. Using the fact that the heterotic/type I S-duality remains valid at finite temperature and can be applied at each instant of a quasi-static evolution, we find in the dual type I cosmology that all internal NS-NS and RR moduli in the closed string sector and the Wilson lines in the open string sector can be stabilized. For the special case of D=6, the internal volume modulus remains a flat direction, while the dilaton is stabilized. An essential role is played by light D-string modes wrapping the internal manifold and whose contribution to the free energy cannot be omitted, even when the type I string is at weak coupling. As a result, the order of magnitude of the internal radii expectation values on the type I side is (lambda_I alpha')^{1/2}, where lambda_I is the ten-dimensional string coupling. The non-perturbative corrections to the type I free energy can alternatively be described as effects of "thermal E1-instantons", whose worldsheets wrap the compact Euclidean time cycle.Comment: 39 pages, 1 figur