# O(D,D) and Double Field Theory

1. Introduction In continuation of a past entry, this week I was intending to write more about double sigma models. I wanted to offer several further remarks on the intrinsic aspects of the doubled world-sheet formalism, and also give the reader a sense of direction when it comes to interesting questions about the geometry of …

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The case of the duality symmetric string is a curious one (in a recent post we began discussing this string in the context of building toward a study of duality symmetric M-theory). In this essay, which may serve as the first of a few on the topic, I want to offer an introduction to some …

# M-theory, the duality symmetric string, and fundamental mathematical structure

In quantum gravity, there presently exists a tight web of hints as well as numerous plausibility arguments in support of the proposed existence of M-theory; however, a systematic formulation of the non-perturbative theory remains an open problem. Without a fundamental formulation of M-theory, all we have is a hypothetical theory of which splinters of clues …

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# Literature: Duality Symmetric String and the Doubled Formalism

When it comes to a T-duality invariant formulation of string theory, there are two primary actions that are useful to study as a point of entry. The first is Tseytlin's non-covariant action. It is found in his formulation of the duality symmetric string, which presents a stringy extension of the Floreanini-Jackiw Lagrangians for chiral fields. …

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# Double Field Theory: The Courant Bracket

1. Introduction In this post we are going to briefly and somewhat schematically discuss the appearance of the Courant bracket in Double Field Theory (DFT), following [1]. The point here is mainly to set the stage, so we jump straight into motivating the Courant bracket. In the next post, we will then study the B-transformations …

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# Generalised Geometry, Non-commutativity, and Emergence

The project I am working on for my dissertation has to do with the notion of emergent de Sitter space. Of course an ongoing problem in string theory concerns whether asymptotic de Sitter spacetime can exist as a solution, and needless to say this question serves as one motivation for the research. With what appears …

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# Notes on the Swampland (3): Testing the Weak Gravity Conjecture – Gauge Fields, Dp-branes, Type II Strings, and F-Theory-Heterotic Duality

The following collection of notes is based on a series of lectures that I attended by Eran Palti at SiftS 2019 at Universidad Autonoma de Madrid. The theme of the lecture series was ‘String Theory and the Swampland’. Palti’s five lectures were supported by his most recent and impressive 200 page review paper on the …

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# Notes on the Swampland (2): Weak Gravity Conjecture, Distance Conjecture, and the Parameter Space of M-theory

The following collection of notes is based on a series of lectures that I attended by Eran Palti at SiftS 2019 at Universidad Autonoma de Madrid. The theme of the lecture series was 'String Theory and the Swampland'. Palti's five lectures were supported by his most recent and impressive 200 page review paper on the …

Continue reading Notes on the Swampland (2): Weak Gravity Conjecture, Distance Conjecture, and the Parameter Space of M-theory