We give a brief overview of the string landscape and techniques used to construct string compactifications. We then explain how this motivates the notion of the swampland and review a number of conjectures that attempt to characterize theories in the swampland. We also compare holography in the context of superstrings with the similar, but much simpler case of topological string theory. For topological strings, there is a direct definition of topological gravity based on a sum over a "quantum gravitational foam." In this context, holography is the statement of an identification between a gravity and gauge theory, both of which are defined independently of one another. This points to a missing corner in string dualities which suggests the search for a direct definition of quantum theory of gravity rather than relying on its strongly coupled holographic dual as an adequate substitute (Based on TASI 2017 lectures given by C. Vafa).
We give a brief overview of the string landscape and techniques used to construct string compactifications. We then explain how this motivates the notion of the swampland and review a number of conjectures that attempt to characterize theories in the swampland. We also compare holography in the context of superstrings with the similar, but much simpler case of topological string theory. For topological strings, there is a direct definition of topological gravity based on a sum over a "quantum gravitational foam." In this context, holography is the statement of an identification between a gravity and gauge theory, both of which are defined independently of one another. This points to a missing corner in string dualities which suggests the search for a direct definition of quantum theory of gravity rather than relying on its strongly coupled holographic dual as an adequate substitute (Based on TASI 2017 lectures given by C. Vafa). Theoretical Advanced Study Institute in Elementary PoS(TASI2017)015The String Landscape, the Swampland, and the Missing Corner Cumrun VafaThese lecture notes from TASI 2017 give a brief overview of some of the open problems in string theory. We will be generally motivated by the philosophy that string theory is ultimately supposed to describe the fundamental laws of our universe. String theory is so versatile that it can be used to study a wide array of physical problems such as various topics in condensed matter and quark-gluon plasma or aspects of quantum fields theories in diverse dimensions. Much of the recent work using string theory has been focused on using its properties to solve specific problems rather than developing our understanding of string theory as a fundamental description of our universe. Here we aim to discuss topics which we hope will be useful in bringing string theory closer to observable aspects of fundamental physics.With this philosophy in mind, we will begin these lectures by reviewing some of what we know about string theory and its possible application to the universe by describing some generalities about the space of low energy theories theories coming from string theory compactifications: this is called the "string landscape." Supersymmetry plays a key organizing principle in this context. This will naturally lead us to investigate the question of how we know a priori if a low energy theory is in the landscape or it is not. The set of low energy physics models which look consistent but ultimately are not when coupled to gravity, is called the "swampland." Finding simple criteria to distinguish the swampland from the landscape is of great importance. In particular such criteria can lead to concrete predictions for our universe as we will discuss later. We review a number of conjectures which are aimed at distinguishing the swampland from the landscape.The string landscape and the swampland will be the topic of the first two lectures. In the third lecture, which is on a somewhat disjoint topic, we review critically where we are in our current understanding o...
A shared property of several of the known exact solutions to the equations of forcefree electrodynamics is that their charge-current four-vector is null. We examine the general properties of null-current solutions and then focus on the principal congruences of the Kerr black hole spacetime. We obtain a large class of exact solutions, which are in general time-dependent and non-axisymmetric. These solutions include waves that, surprisingly, propagate without scattering on the curvature of the black hole's background. They may be understood as generalizations to Robinson's solutions to vacuum electrodynamics associated with a shear-free congruence of null geodesics. When stationary and axisymmetric, our solutions reduce to those of Menon and Dermer, the only previously known solutions in Kerr. In Kerr, all of our solutions have null electromagnetic fields ( E · B = 0 and E 2 = B 2 ). However, in Schwarzschild or flat spacetime there is freedom to add a magnetic monopole field, making the solutions magnetically dominated (B 2 > E 2 ). This freedom may be used to reproduce the various flat-spacetime and Schwarzschild-spacetime (split) monopole solutions available in the literature (due to Michel and later authors), and to obtain a large class of timedependent, non-axisymmetric generalizations. These generalizations may be used to model the magnetosphere of a conducting star that rotates with arbitrary prescribed time-dependent rotation axis and speed. We thus significantly enlarge the class of known exact solutions, while organizing and unifying previously discovered solutions in terms of their null structure.
We revisit the localization computation of the expectation values of 't Hooft operators in N = 2 * SU(N) theory on R 3 × S 1. We show that the part of the answer arising from "monopole bubbling" on R 3 can be understood as an equivariant integral over a Kronheimer-Nakajima moduli space of instantons on an orbifold of C 2. It can also be described as a Witten index of a certain supersymmetric quiver quantum mechanics with N = (4, 4) supersymmetry. The map between the defect data and the quiver quantum mechanics is worked out for all values of N. For the SU(2) theory, we compute several examples of these line defect expectation values using the Witten index formula and confirm that the expressions agree with the formula derived by Okuda, Ito and Taki [16]. In addition, we present a Type IIB construction-involving D1-D3-NS5-branes-for monopole bubbling in N = 2 * SU(N) SYM and demonstrate how the quiver quantum mechanics arises in this brane picture.
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