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# Supersymmetry and Extra Dimensions

## Module PH2250

This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.

### Module version of SS 2019

There are historic module descriptions of this module. A module description is valid until replaced by a newer one.

Whether the module’s courses are offered during a specific semester is listed in the section Courses, Learning and Teaching Methods and Literature below.

available module versions
SS 2021SS 2019SS 2017

### Basic Information

PH2250 is a semester module in German or English language at Master’s level which is offered in summer semester.

This module description is valid to WS 2020/1.

If not stated otherwise for export to a non-physics program the student workload is given in the following table.

300 h 60 h 10 CP

Responsible coordinator of the module PH2250 in the version of SS 2019 was Patrick Vaudrevange.

### Content, Learning Outcome and Preconditions

#### Content

This lecture introduces supersymmetric theories in four and more dimensions. The basis of this course lies in the understanding of the supersymmetry algebra and its representations with N=1 or more supersymmetry generators. The following topics are covered:

- mathematical foundation: Grassmann variables

- supersymmetry algebra and its representations: chirale superfields, vector superfields

- superfields and superspace as an extension of fields and space

- supersymmetric theories in four dimensions: superpotential and Kähler potential

- non-renormalization theorems

- overview on supergravity, introduction of supergravity as local supersymmetry

- supersymmetry-breaking using F- und D-terms

- the MSSM: particle spectrum, symmetries and interactions

- extra dimensions and Kaluza-Klein compactification

- spinors and supersymmetry in extra dimensions

#### Learning Outcome

After successful completion of the module the students are able to:

1. understand recent literaure on supersymmetric theories.
2. follow talks on supersymmetric extensions of the Standard Model.
3. learn extended theories, like "Grand Unified Theories" in extra dimensions and string theory.

#### Preconditions

No preconditions in addition to the requirements for the Master’s program in Physics.

### Courses, Learning and Teaching Methods and Literature

#### Learning and Teaching Methods

The mathematical and theoretical foundations are introduced carefully and well motivated. Several examples and explicit calculations are used to deepen the insight and to illustrate the content. The main concepts are repeated at the beginning of each lecture and discussed with the students. Thus the students are able to explain and apply the learned physics knowledge independently.

#### Media

• black board
• repetitions at the beginning of each lecture using beamer-presentations

#### Literature

"Cambridge Lectures on Supersymmetry and Extra Dimensions"
by Fernando Quevedo, Sven Krippendorf, Oliver Schlotterer
see https://arxiv.org/abs/1011.1491

### Module Exam

#### Description of exams and course work

There will be an oral exam of 25 minutes duration. Therein the achievement of the competencies given in section learning outcome is tested exemplarily at least to the given cognition level using comprehension questions and sample calculations.

For example an assignment in the exam might be:

• How does a chiral superfield transform under a supersymmetry transformation?
• How does one write down a supersymmetric Lagrangian?
• How does the scalar potential look like when supersymmetry is broken spontaneously?

In the exam no learning aids are permitted.

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