## PHY 440: Introduction to String Theory

3 credits | Prerequisites: PHY 304

### Course rationale

Quantum Field Theory (QFT) and General Relativity (GR) are two of the pillars of modern physics. While QFT is based on Quantum Mechanics, GR is a classical theory. The program of quantizing gravity is challenging, mainly due to the non-normalizable feature of GR. String Theory follows a different path. In String Theory, the fundamental object is a relativistic string. Quantization of this string gives rise to different quanta one of which can be interpreted as a graviton, the quantum of gravity. Therefore, it can be said that String Theory is a candidate for quantum theory of gravity. This course introduces the basic concepts of String Theory.

### Course content

Gravity and Electromagnetism in Different Dimensions: review of special relativity, classical electrodynamics, electrodynamics in various dimension, review of general relativity, gravitation and the Planck length, Nonrelativistic Strings: review of Lagrangian mechanics, equation of motion for transverse oscillations, boundary conditions, frequencies of transverse oscillation; Relativistic Point Particle: action, equation of motion, reparameterization invariance, relativistic particle with electric charge; Relativistic Strings: area functional, reparameterization invariance, Nambu-Goto string action, equation of motion, gauge condition, tension and energy, motion of the end-points, choosing a particular parameterization, physical interpretation of the equation of motion, wave equation and constraints, open string, cusps; World-sheet Current: charge conservation, symmetry and Noether’s theorem, conserved current on the word-sheet, momentum current, Lorentz symmetry and associated current, slope parameter; Light-cone Quantization: a class of choices for world sheet time and space, wave equation and constraint, light-cone solution of the equation of motion, review of different particles of QFT, light-cone quantum particle, light-cone momentum operators, and Lorentz generators; Relativistic Quantum Open Strings: light-cone Hamiltonian and commutators, canonical commutators, strings as harmonic oscillators, Lorentz generators, state space, tachyons; Relativistic Quantum Closed Strings: mode expansion and commutation relation, Virasoro operators and algebra, closed string state, string coupling and the dilaton, twisted string and the orbifold; Introduction to Superstrings: anticommutating variables and Grassmann numbers, world-sheet fermions, Neveu-Schwarz sector, Ramond sector, counting states, open and closed superstrings; Introduction to D-branes: Dp-branes and boundary conditions, quantizing open strings on Dp-branes, open strings between Dp-branes, strrings between Dp and Dq branes.

### Course objectives

- Understand the problem of quantizing gravity.
- Analyze string action and equation of motion.
- Use light-cone quantization to solve the string equation of motion.
- Quantize relativistic open and closed strings.
- Familiarize with superstring theory

### References

- A First Course in String Theory (2nd edition) by Barton Zwiebach
- String Theory, Vol 1 by Joseph Polchinski
- String Theory and M-theory: a Modern Introduction by Becker, Becker, Schwarz
- Basic Concepts of String Theory by Blumenhagen, Lust, Theisen