Undergraduate Programme and Module Handbook 2024-2025

# Module MATH4271: Superstrings IV

## Department: Mathematical Sciences

### MATH4271: Superstrings IV

Type | Open | Level | 4 | Credits | 20 | Availability | Available in 2024/2025 | Module Cap | None. | Location | Durham |
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#### Prerequisites

- None

#### Corequisites

- Advanced Quantum Theory IV (MATH4061) OR Particle Theory (PHYS4181)

#### Excluded Combination of Modules

- None

#### Aims

- This module is an introduction to String Theory, including supersymmetry and Superstring Theory.
- To introduce superstring theory through its two-dimensional worldsheet conformal field theory.
- To quantise string theory and show that the superstring spectrum includes all elementary particles thus unifying the fundamental forces including gravity.

#### Content

- Classical String Theory.
- Quantisation of String worldsheet theory.
- String theory spectrum and spacetime interpretation.
- T-duality and D-branes.
- Supersymmetry.
- Superstring theory.

#### Learning Outcomes

Subject-specific Knowledge:

- Having studied the module students will know the basic principles of worldsheet (super)string theory.
- The relation between the (super)string worldsheet theory and spacetime fields which are de-scribed using quantum field theory in the corequisite modules.
- The concept of duality whereby apparently different theories are equivalent, with T-duality as an example.

Subject-specific Skills:

- Students will be able to apply a variety of advanced techniques in the area of string theory.
- Students will be able to how symmetries and constraints of the worldsheet theory lead, af-ter quantisation, to a specific spectrum with a spacetime interpretation.

Key Skills:

- The students will have developed the ability to operate in complex and specialised contexts close to the cutting edge of current research.

#### Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module

- Lectures demonstrate what is required to be learned and the application of the theory to practical examples.
- Subject material assigned for independent study develops the ability to acquire knowledge and understanding without dependence on lectures.
- Assignments for self-study develop problem-solving skills and enable students to test and develop their knowledge and understanding.
- Formatively assessed assignments provide practice in the application of logic and high level of rigour as well as feedback for the students and the lecturer on students' progress.
- The end-of-year examination assesses the knowledge acquired and the ability to solve predictable and unpredictable problems.

#### Teaching Methods and Learning Hours

Activity | Number | Frequency | Duration | Total/Hours | |
---|---|---|---|---|---|

Lectures | 42 | 2 per week in Michaelmas and Epiphany; 2 in Easter | 1 Hour | 42 | |

Problems Classes | 8 | Fortnightly in Michaelmas and Epiphany | 1 Hour | 8 | |

Preparation and Reading | 150 | ||||

Total | 200 |

#### Summative Assessment

Component: Examination | Component Weighting: 100% | ||
---|---|---|---|

Element | Length / duration | Element Weighting | Resit Opportunity |

End of year written examinations | 3 hours | 100% |

#### Formative Assessment:

Eight assignments to be submitted.

■ Attendance at all activities marked with this symbol will be monitored. Students who fail to attend these activities, or to complete the summative or formative assessment specified above, will be subject to the procedures defined in the University's General Regulation V, and may be required to leave the University