Study Notes

Double Field Theory


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

Pure Spinors


Developing the String Worldsheet Theory

1) The Bosonic String

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