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Prof Sudipta Sarkar is visiting us for a week and delivering two scientific talks and one colloquium

Scientific talk

Title: Light rings of stationary spacetimes (Part I & II)

Abstract: The motion of light is affected by the geometry of the spacetime surrounding a compact object. This led to the existence of a circular null orbit called the photon sphere. As far as observational implications are concerned, the photon sphere further leads to the existence of an unobservable dark patch around the compact object, known as the shadow. The recent observation of black hole shadow by the Event Horizon telescope may give us valuable information about the physics of strong gravity.

In this talk, I will describe several recent results about the existence of a light ring surface around compact objects and how the observation can be used to constrain the possibility of ultracompact black hole mimickers.

Reference: Light rings of stationary spacetimes, Phys. Rev. D 104, 044019 (2021) [arxiv: 2107.07370]

Colloquium

Title: Towards Relativity: Einstein and His Compass

Abstract: The advent of special relativity resulted from intense scientific thinking spanning several decades. The history of relativity begins with the strive to understand motion, inertia, and light, which finally led to the Einsteinian revolution in 1905. In this seminar, I attempt to summarize the rich history of the theory of relativity; the emphasis would be to discuss the contributions of several physicists and mathematicians and the uniqueness of the approach taken by Einstein.

Time: 4 pm on 4th November 2022

Lectures Schwinger-Kyldesh formalism by Chandan Jana (MITP, South Africa)

1. Why is Schwinger-Keldysh a unified approach to describe physical systems?

-Adiabatic approximation in Feynman path-integral

-Complication in Matsubara technique

-Effective field theory by integrating out light degrees of freedom

2. Basics on Schwinger-Keldysh formalism

-SK path integral and contour

-Propagators and correlation functions

-Keldysh basis

3. Unitary QFT using Schwinger-Keldysh formalism

-Feynman rules, propagators, loops, unitarity

-Effective field theories

Lectures SPT phases by Abhisodh Prakash (ICTS-TIFR, Bangalore)

Lecture 1: All about the Haldane chain

I will start with a spin chain model with two phases- the trivial and Haldane phase. After briefly describing the essential properties of both phases and the critical theory, I will focus deep inside the Haldane phase and demonstrate the nature of robust boundary modes. I will then switch to a continuum description and recast the same results in this language. The non-trivial nature of the bulk is seen to arise in the form of a topological term, and the anomalous nature of the boundary is seen to arise in the form of a WZW term. I will end by emphasizing how bulk TQFTs and boundary anomalies are a repeating theme in this whole story.

References:

a. https://arxiv.org/pdf/1708.07192.pdf

b. https://mcgreevy.physics.ucsd.edu/talks/jm-SPT-FRIDAY.pdf

Lecture 2: Bosonic fixed-point models I- Hamiltonians

I will place the Haldane phase within a classification scheme involving projective representations. The classification of projective representations and thus 1+1 dim bosonic SPT phases can be shown to be related to the second group cohomology which I will define. This naturally leads to a conjecture that higher dimensional SPT phases are related to higher group cohomology groups which I will define. This conjecture can be proven by constructing an exactly solvable fixed-point lattice commuting-projector Hamiltonian for each phase using group cohomology data for which I will give the prescription. The anomalous nature of the boundary can also be understood via a 'descent procedure' that generalizes projective representations of 1+1 d.

References:

a. https://arxiv.org/abs/1106.4772

b. https://arxiv.org/abs/1409.5436

Lecture 3: Bosonic fixed-point models II- Path integrals

I will revisit the group cohomology models from a space-time perspective and construct fixed point partition functions. In addition to recovering the various interesting properties of the previous talk, we can also easily see the effect of background gauge fields- the free energy obtained by evaluating the partition function evaluates to the Dijkgraaf-Witten TQFT. This `topological response' to background gauge fields is a hallmark of all invertible phases. I will describe that this is well-known in the case of integer-quantum-Hall states whose topological response is encoded in the free-energy being the Chern-Simons action. This will segue us into fermions

References:

a. Max Metlitski's lectures in TASI 2019: https://physicslearning.colorado.edu/tasi/tasi_2019/tasi_2019.html

Lecture 4: Fermionic models and phases

I will use the example at the end of the previous talk to start a discussion of fermionic invertible phases. I will describe Kitaev's Majorana chain similar to how the Haldane chain was introduced - first via a Hamiltonian and then in the continuum. I will describe how, in the continuum, the partition function evaluates to the so-called Arf invariant, and the boundary consists of a mod-2 anomaly that has received attention in various works recently. I will state how these generalize to well-known bulk topological invariants (such as the theta term in 3+1 d) and boundary anomalies (of gapless fermions, APS index theorem etc).

References:

a. Max Metlitski's lectures in TASI 2019: https://physicslearning.colorado.edu/tasi/tasi_2019/tasi_2019.html

b. https://arxiv.org/abs/1508.04715

Lecture 5: The grand scheme of things

I will spend the first part of the lecture finishing any remaining material from the previous lecture. In the time remaining, using motivating examples, I will state the current understanding with regard to the classification of invertible phases- cobordism, generalized cohomology, spectral sequences etc. I will adjust the topics and amount of detail depending on the previous lectures and how they were received.

References:

a. https://arxiv.org/abs/1906.02892

b. https://arxiv.org/abs/1712.07950

Lectures on Black Hole mechanics by Sudipta Sarkar (IIT Gandhinagar)

Lecture 1: Schwarzschild Solution and Kruskal–Szekeres Diagram; Notion of Event Horizon, Cosmic Censorship; Killing horizon; Hawking Rigidity Theorem.

Lecture 2: Killing Horizon and Surface Gravity, Zeroth Law for Killing and Event horizon. Different proofs with or without the field equations. Generalization to higher curvature gravity.

Lecture 3: Raychaudhuri equation for Null hypersurface; Physical Process Law, Assumptions and criterion of validity.

Lecture 4: The second law, Hawking area theorem, General relativity & beyond, Relationship with holography.

Lecture 5: Cosmic Censorship, Weak and Strong version, Possible violation of Strong Cosmic censorship, Present status and future directions.

Each lecture will be about 1.5 hours of duration.

References:

1. Black hole thermodynamics: general relativity and beyond,

Sudipta Sarkar, arXiv:1905.04466

2. Black Holes, P. K. Townsend, arXiv:gr-qc/9707012

3. Book: The relativist Toolkit, Eric Poisson.

4. Book: General Relativity, Robert M. Wald.

Lectures on supersymmetric quantum mechanics by Diksha Jain (ICTP-SISSA)

Lecture 1: What is supersymmetric quantum mechanics (4th January 2021) - Classnote, Videolink

Lecture 2: Spontaneous breaking of supersymmetry and Witten index (7th January 2021) - Classnote, Videolink

Lecture 3: How does supersymmetry help us to solve the Hamiltonian system? (9th January 2021) - Classnote, Videolink

Lecture 4: Lagrangian formulation (12th January 2021) - Classnote, Videolink

Lecture 5: Supersymmetry and Dirac operator in target space (16th January 2021) - Classnote, Videolink

References:

1. Supersymmetry and quantum mechanics (hep-th/9405029)

2. MIT Physics 8.05: An Introduction to Supersymmetric Quantum Mechanics (link)