Graduate Opportunities
The Fields, Strings, and Gravity group, as well as other areas of theoretical and mathematical physics (covered in the QMAP center), will potentially be taking on students each year. Interested students should apply to the physics (or math) graduate program. Details relating to the application procedure for physics be found at Physics Graduate Application. Students admitted to the physics department need to satisfy various course and progression requirements for advancement to candidacy. Individual faculty may have additional requirements for taking on a student (e.g., a trial project).
The group expects students to be familiar with the workings of Quantum Field Theory, Gravity, and elements of String Theory. The former two topics are covered under the current Physics department courses PHY 230A, 230B, 230C, and 260, respectively.
FSG Graduate Courses
Each year we offer two FSG courses:
- Physics 232: Topics in String Theory
- Physics 233: Topics in Geometry and Physics
Current and past offerings are listed below:
Academic year 2024-2025
1. Topics in String Theory (Winter 2025): The AdS/CFT correspondence (Mukund Rangamani)
The course will cover the basics of perturbative string theory. We will discuss the worldsheet construction of both bosonic and superstring theories. Topics to be covered include covariant and BRST quantizations, open string boundary conditions and D-branes, T-duality, etc.
Pre-requisite: basic knowledge of quantum field theory (PHY 230A and B or equivalent) and general relativity and black holes (PHY 260 or equivalent)
2. Advanced topics in Geometry & Physics (Spring 2025): Black holes (Veronika Hubeny)
The course will cover advanced topics in black holes, describing various exact solutions in across dimensions, their causal structure, and an introduction to black hole thermodynamics.
Pre-requisite: knowledge of classical general relativity (Physics 260 or equivalent)
Academic year 2023-2024
1. Topics in String Theory (Fall 2023): Superstring theory (Mukund Rangamani)
The course will cover string scattering, and non-perturbative aspects superstring theory. I will assume familiarity with the covariant worldsheet description of the bosonic and RNS superstrings (open and closed). We will discuss string scattering amplitudes, non-perturbative effects, compactifications, etc.
Pre-requisite: basic knowledge of quantum field theory (PHY 230A and B or equivalent) and general understanding of worldsheet string theory.
Academic year 2022-2023
1. Topics in String Theory (Spring 2023): A modern introduction to worldsheet string theory (Mukund Rangamani)
The course will cover the basics of perturbative string theory. We will discuss the worldsheet construction of both bosonic and superstring theories. Topics to be covered include covariant and BRST quantizations, open string boundary conditions and D-branes, T-duality, etc.
Pre-requisite: basic knowledge of quantum field theory (PHY 230A and B or equivalent) and general relativity and black holes (PHY 260 or equivalent)
2. Advanced topics in Geometry & Physics (Spring 2023): Black holes (Veronika Hubeny)
The course will cover advanced topics in black holes, describing various exact solutions in across dimensions, their causal structure, and an introduction to black hole thermodynamics.
Pre-requisite: knowledge of classical general relativity (Physics 260 or equivalent)
Academic year 2021-2022
1. Topics in String Theory (Winter 2022): The AdS/CFT correspondence (Mukund Rangamani)
The course will introduce the basic ideas behind the AdS/CFT correspondence and describe various applications. Topics to be covered include, large N field theories, motivation for the correspondence from D-brane dynamics, and developing the basic dictionary between the CFT and gravitational dynamics in AdS spacetimes (correlation functions, Wilson loops, entanglement entropy, etc). The second half of the course will focus on applications of the correspondence to understanding QCD dynamics (AdS/QCD), phases of compressible phases of matter (AdS/CMT), hydrodynamics (fluid/gravity), and the physics of black holes and quantum gravity (bulk reconstruction via entanglement).
Pre-requisite: basic knowledge of quantum field theory (PHY 230A and B or equivalent) and general relativity and black holes (PHY 260 or equivalent)
2. Advanced topics in Geometry & Physics (Winter 2022): Global aspects of spacetimes (Veronika Hubeny)
The course will cover classic results on global structures of spacetimes, singularity theorems in classical general relativity in the first part of the course. The second part will focus on developments related to the generalized second law, quantum focussing conjectures, and recent proofs of energy theorems for quantum fields in curved spacetime.
Pre-requisite: knowledge of classical general relativity (PHY 260 or equivalent)
Academic year 2020-2021
1. Topics in String Theory (Spring 2021): Superstring Theory (Jaroslav Trnka)
The course will continue from Spring 2020 with superstring theory and non-perturbative aspects of string theory.
Pre-requisite: quantum field theory and basics of bosonic string theory.
2. Advanced topics in Geometry & Physics (Spring 2021): Black holes (Veronika Hubeny)
The course will cover advanced topics in black holes, describing various exact solutions in across dimensions, their causal structure, and an introduction to black hole thermodynamics.
Pre-requisite: knowledge of classical general relativity (Physics 260 or equivalent)
Academic year 2019-2020
1. Topics in String Theory (Spring 2020): Bosonic Strings (Jaroslav Trnka)
The course will describe the basics of bosonic string theory.
Pre-requisite: quantum field theory.
Academic year 2018-2019
1. Black holes (Winter 2019): Veronika Hubeny
The course will cover advanced topics in black holes, describing various exact solutions in across dimensions, their causal structure, and an introduction to black hole thermodynamics.
Pre-requisite: knowledge of classical general relativity (Physics 260 or equivalent)
2. Topics in String Theory (Spring 2019): Jaroslav Trnka
The course will describe the computation of string scattering amplitudes.
Pre-requisite: quantum field theory and basics of bosonic and superstring theory.
Academic year 2017-2018
1. Advanced General Relativity (Winter 2018): Veronika Hubeny
The course will cover classic results on global structures of spacetimes, singularity theorems in classical general relativity in the first part of the course. The second part will focus on developments related to the generalized second law, quantum focussing conjectures, and recent proofs of energy theorems for quantum fields in curved spacetime.
Pre-requisite: knowledge of classical general relativity (PHY 260 or equivalent)
2. Conformal Field Theory (Winter 2018): Mukund Rangamani
The course will analyze quantum field theories exhibiting conformal symmetries in various dimensions. Topics to be covered include, representations of the conformal algebra, constraints from the symmetry on physical observables, physical applications in the theory of critical phenomena. Much of the focus will be on two dimensional systems, though we will touch upon higher dimensional CFTs and superconformal theories.
Pre-requisite: basic knowledge of quantum field theory (PHY 230A and B or equivalent)
3. Superstrings and D-branes (Spring 2018): Jaroslav Trnka
The course will describe the perturbative worldsheet theory of superstrings building partly on the technology from the CFT course. Topics to covered include quantization and superstring spectrum, low energy dynamics in terms of supergravity and D-branes. The later part of the course will focus on D-brane dualities and M-theory.
Pre-requisite: quantum field theory and basics of bosonic string theory
Academic year 2016-2017
1. Black holes (Winter 2017): Veronika Hubeny
The course will cover advanced topics in black holes, describing various exact solutions in across dimensions, their causal structure, and an introduction to black hole thermodynamics.
Pre-requisite: knowledge of classical general relativity (Physics 260 or equivalent)
2. String Theory (Winter 2017): Jaroslav Trnka
The course will describe the perturbative worldsheet theory of bosonic string. Topics to covered include quantization and the string spectrum for open and closed strings, and the low energy dynamics in terms of general relativity.
Pre-requisite: basic knowledge of quantum field theory (PHY 230A and B or equivalent)
3. QFT and Representation Theory (Winter 2017): Tudor Dimofte
The course will mathematical aspects of QFT, focusing on topological field theories. Topics to be covered include supersymmetric quantum mechanics, (2,2) theories in 2d, and 3d N=2 and N=4 theories.
Pre-requisite: basic knowledge of quantum field theory (PHY 230A and B or equivalent)
4. The AdS/CFT correspondence (Spring 2017): Mukund Rangamani
The course will introduce the basic ideas behind the AdS/CFT correspondence and describe various applications. Topics to be covered include, large N field theories, motivation for the correspondence from D-brane dynamics, and developing the basic dictionary between the CFT and gravitational dynamics in AdS spacetimes (correlation functions, Wilson loops, entanglement entropy, etc). The second half of the course will focus on applications of the correspondence to understanding QCD dynamics (AdS/QCD), phases of compressible phases of matter (AdS/CMT), hydrodynamics (fluid/gravity), and the physics of black holes and quantum gravity (bulk reconstruction via entanglement).
Pre-requisite: basic knowledge of quantum field theory (PHY 230A and B or equivalent) and general relativity and black holes (PHY 260 or equivalent)