This series consists of talks in the area of Quantum Fields and Strings.
In frustrated systems, competing interactions lead to complex phase diagrams and sometimes entirely new states of matter. Frustration often arises from the lattice geometry, leaving the system delicately balanced between a variety of possible orders. A number of normally weak effects can lead to a lifting of this degeneracy. For example, I will discuss how quantum fluctuations can stabilize a supersolid phase, where the system is at once both a crystal and a superfluid.
We will discuss the missing pieces in the understanding of the effective field theory description of string creation, the T-dual of the Hanany-Witten effect, both in the open and closed string picture. We explain the origin of the \'bare\' Chern-Simons term, so far added in by hand. There however remain unsettled issues concerning the need to modify the DBI action and the interpretation of this term in M-theory.
I will report on some work in progress with Dan Freed and Greg Moore. In an orientifold background, D-brane charge takes values in a certain twisted version of KR Theory. Moreover, there is a nontrivial background charge (\'tadpole\'). Up \'til now, this background charge has only been calculated rationally -- i.e., ignoring torsion. We derive a formula for it, over the integers. Only after \'inverting 2\', does the charge localize to the fixed point sets of the orientifold action, and we can give a compact formula for it.
We discuss recent developments in the study of black holes and similar compact objects in string theory. The focus is on how these solutions are effected by higher-derivative terms in an effective action. The setting of this investigation is an off-shell formulation of five-dimensional supergravity, including terms of order four-derivatives whose precise form are determined by embedding this theory in M-theory.
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The rich network of string dualities provides powerful constraints in the structure of the theory. The connection of ten-dimensional type II theories to eleven-dimensional supergravity compactified on a circle and on a torus allows one to compute many perturbative high genus terms as well as the complete sum of non-perturbative contributions to a given higher derivative coupling of the string effective action. The same duality connection leads to a series of surprising non-renormalization theorems.
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Geometries produced by brane intersections preserving eight supercharges are constructed. Typical examples of such configurations are given by fundamental strings ending on D branes and by brane webs. Consistency conditions of supergravity are shown to impose certain requirements on the locations of the sources, and these restrictions are found to be in a perfect agreement with results of the probe analysis. This agreement serves as a nontrivial test of the duality between open and closed strings. Some applications to AdS/CFT correspondence are also discussed.
F-theory compactifications on Calabi-Yau fourfolds provide one way to obtain N=1 supersymmetric grand unified models of particle physics from string theory. With this motivation in mind, I will consider F-theory on a particularly simple class of local Calabi-Yau fourfolds, for which a low-energy analysis based upon topological gauge theory is valid. For these models, I will explain how the geometry of the fourfold determines the spectrum of massless charged matter and the effective superpotential in four dimensions.