My physics research mainly focuses on string theory and supergravity. String theory provides a consistent description of quantum gravity. Supergravity is a supersymmetric extension of gravity; whose solutions provide consistent backgrounds for the quantum propagation of strings. Supergravity theories exist in various dimensions and they are, more often than not, connected by a web of various dualities and reductions. The mother theory of all these is eleven-dimensional supergravity, an extremely simple theory. As simple as it is, imposing supersymmetry reveals a plethora of elegant geometric structure. The connection between supersymmetry and geometric structure is a recurrent theme in my research.

Here is a list of some of the research I worked on, notes on the different topics of supervised study as well as my own ideas that I worked on in my free time.

- MS Thesis: D-Branes and AdS/CFT
- Canonical Gravity: Hamiltonian Formalism Of General Relativity.
- BS Thesis: Smeared Potential Model.
- Course Project: Measuring Mean Lifetime of Muon
- Course Project: Propagation of Thermal Diffusive Waves in a Metal by Fourier Analysis
- Entanglement in QFT and Holography.
- Black holes in General Relativity.

## D-Branes and AdS/CFT:

**Master Dissertation with Dr. Babar Qureshi:** [Downloads As PDF]

It has been conjectured that a quantum gravity system in (d+1)-dimensional spacetime can be described by the degrees of freedom living on the d-dimensional boundary of this spacetime. This is the holographic principle. In this thesis, I’ve derived one particular realization of this principle known as the AdS-CFT correspondence which relates type-IIB superstring theory in anti de-Sitter space (AdS) with a Super Yang-Mills theory on the Minkowskian boundary of AdS. This duality was originially put forward by Maldacena in 1997 and is the most well understood example of holography. Then I’ve used the correspondence to study the correlation functions of gravity and gauge theories which turned out to be the same on both sides of the duality.

I was to study all the prerequisites for this, which included having knowledge of string theory and have some working knowledge of supergravity. This was quite a gargantuan task but it solidified my interest in studying String Theory as an approach to Quantum Gravity.

## Hamiltonian Formalism of General Relativity

**Independent Research with Dr. Syed Moeez Hassan:**

This was to study Canonical gravity, a framework that uses Dirac’s method for constrained Hamiltonian systems, to derive the Hamiltonian for General Relativity, and then quantize it. In canonical gravity one usually reduces the system by symmetry arguments and then solves these Hamiltonians to get “wave functions” for the universe. This comes under Quantum Cosmology.

My job was to derive the ADM formalism and then expressed the Einstein’s Field equations as a constrained Hamiltonian system in terms of new variables, called the ADM variables after Arnowitt, Deser, Miser, and their canonically conjugate momenta.

## Smeared Potential Model:

**BS Thesis with Dr. Bilal Masud:**

My Undergraduate Final Year Project was centered around improving the Hamiltonian of mesons in a relativized quark model with chromodynamics by including relativistic effects and smearing motion. The second phase incorporates simulation of running coupling constant of QCD which require the deep insights of unified quark model and universal one-gluon-exchange-plus-linear-confinement potential. Through this project, I learned about various crucial ingredients of Quantum Chromodynamics, such as the strong, weak, and electromagnetic meson couplings.

**Course Projects**

**Measuring Mean Lifetime of Muon**

The formation of muons was studied from primary cosmic rays and measured its mean lifetime value experimentally which was close enough to the theoretical one. During this project, I learned a great deal of mathematical and physical concepts whose elegance I utterly appreciated: non-Gaussian distributions, nonlinear fitting, formation and decaying of subatomic particles, basics of Standard Model and some useful equipment including scintillator detectors, NIM module, Picoscope, TAC, MCA and photomultiplier tubes. The results were summarized in a **lab report**.

**Propagation of Thermal Diffusive Waves in a Metal by Fourier Analysis**

A temperature wave propagates along a long thin bar of a metallic sample when subjected to periodic heating. In this way it is demonstrated that there is no wave nature in these improperly called thermal waves by showing that they do not transport energy and its propagation properties can be used to determine the thermal diffusivity of the material. The results were summarized in a **lab report**.

## COMP 4801: Computational Physics Lab

**C# Simulations**

Simulated the following systems in C# language:

- Solar System.
- ECGM and Diffusion-Limited Aggregation (DLA) Cluster Growth Models.
- Mean-Field Theory (MFT).
- Ising Monte Carlo Method.