## Introduction to the Swampland: The Distance Conjecture and Weak Gravity Conjecture

Notes based on the lectures by Eran Palti.

1) Constraining Effective Field Theories

2) The Weak Gravity Conjecture, Distance Conjecture, and the Parameter Space of M-theory

3) Testing the Weak Gravity Conjecture – Gauge Fields, Dp-branes, Type II Strings, and F-Theory / Heterotic Duality

4) The Distance Conjecture for Arbitrary Calabi-Yau Manifolds, the Emergence Proposal, and the de Sitter Conjecture

## Developing the String Worldsheet Theory

This paper serves to present a set of notes developed while self-studying bosonic string theory as a first-year undergraduate student. Organised as a dissertation, this paper was developed specifically for submission as part of my formal academic acceleration from a first-year undergraduate degree into a full-time research degree (MRes). The product of a rigorous review organised around the central motivation to rederive the whole of bosonic string theory from first principles, what follows is a summary overview of a selection of key concepts and methods. The paper follows Joseph Polchinski’s textbook ‘String Theory: An Introduction to the Bosonic String’, with guidance also from a list of supplementary texts.

## String Notes (Blog Series on Volumes 1 and 2 of Joseph Polchinski’s ‘String Theory’)

**A number of posts are broken due moving my blog to a new host. I am slowly revising these posts and fixing the LaTex. **

**1) Series Introduction**

First entry, including a list of supplementary texts

**2) Non-relativistic / Relativistic theory**

— The Non-relativistic String

— The Relativistic Free Point Particle

**3) Elementary String Action**

— The Nambu-Goto action for the relativistic string

— Equations of motion, Dp-branes, and the slope parameter [LaTex broken]

**4) Polyakov Action**

— Polyakov Action by way of General Relativity in m-dimensions [LaTex broken]

— Polyakov action – Symmetries, classical equivalence, equations of motion, and Virasoro constraints [LaTex broken]

— Symmetries of the Polyakov action (additional comments) [LaTex broken]

**5) Side notes for Chapter 1 in Polchinski**

— Energy-momentum tensor [LaTex broken]

— Hamiltonian formalism and Poisson brackets [LaTex broken]

— Fiducial Metric [LaTex broken]

**6) Light-cone Gauge**

— Enter into the Light-cone [LaTex broken]

— String action in the light-cone [LaTex broken]

— Equations of motion, wave equation, and centre of mass position for the free open string [LaTex broken]

— Virasoro operators (defined classically) [LaTex broken]

— Classical Mass of a String [LaTex broken]

**7) Free Bosonic String Spectrum**

— Quantum Strings (Introduction) [LaTex broken]

— Quantisation – the point particle case [LaTex broken]

— Light-cone Quantisation of the Free String [LaTex broken]

— String Mass and the Riemann Zeta Function [LaTex broken]

— Constructing the Hilbert Space of Single String States [LateX broken]

— The Virasoro Algebra, Plus an Introduction to the Central Charge [LaTex broken]

— Internal Excitations of a Free Open Bosonic String [LaTex broken]

— Closed String Spectrum [LaTex broken]

**8) Conformal Field Theory**

— Introduction to Conformal Field Theory

— Generators of Conformal Transformations

— Conformal Group in 2-dimensions

— Massless Scalars in Flat 2-dimensions

— Local Operators, the String Propagator, and Operator Product Expansions

— Further Introduction to Operator Product Expansions

— Ward Identities and Noether’s Theorem

— Ward Identities, Noether’s Theorem, and OPEs