with Prof.Sujay Ashok & Prof.Alok Laddha

  • BMS Group & Soft theorems

    We know that the work by Christodoulu and Kleinermann on global properties of ASFT spacetimes (Asymptotical Flat spacetimes) laid the foundation to Strominger's boundary counditions (arXiv: 1312.2229). The existance of a symmetry group (BMS Group) on the ASFT implies the existence of inifnitely many conserved quantities defined on $\mathscr{I}^$. If we consider quantum ward identities corresponding to these conserved quantities in classical gravitation scattering, it gives rise to the well known Weibnberg's soft theorems. (arXiv: 1401.7026)

    However, there have been many variations of the notion of BMS in literature as a semi direct product of Supertranslations (angle dependent translations) on the 2-sphere at $\mathscr{I}^$ along with Lorentz transformations. There have been other variations as Generalized BMS = semi-direct product of supertranslations and Local Conformal Transfomations, Extended BMS = semi-direct product of supertranslations and Differomophism on the 2-sphere. The idea of extended BMS was proposed by Prof. Alok Laddha et al. (arXiv: 1408.2228). I was working on understanding these symmetries and their relation to subleading soft graviton theorems.

Reading Projects

Topics studied.

  • BCFW Recursion Relations

    Spinors, helicity and representations. The spinor helicity formalism and its representation free and Lorentz invariant description of scattering amplitudes. Explicitly used them in calculation of scattering amplitudes in Yukawa theory and n-gluon tree amplitudes in Yang-Mills (Parke-Taylor). The construction of BCFW, its usage and its application for the proof of Parke-Taylor formula.

    Reading was primarily from Elvang's paper (arXiv: 1308.1697) on 'Scattering Ampltidues' and BCFW's paper (arXiv: 0501052) on 'Direct Proof Of Tree-Level Recursion Relation In Yang-Mills Theory'.

  • Renormalization, Regularization & Beta functions

    I predominantly read about classification of divergences arising in $\phi^4$ theories, using $n-$PI reducible & irreducible diagrams and superficial degrees of divergence. Regularization to compute the exact form of infinities at loop level in scattering amplitidues. The infinites arising as simple poles upon dimensional regularization. Loop corrections by adding counter terms upto $O(w)$. Bare and renormalized parameters, running coupling constants. The relation between, energy scale, coupling paramters and the $\beta$ function, Landua point, scheme independence of renormalization. Quantization in non-Abelian gauge theories, gauge fixing, faddeev-popov ghosts. Computation of one loop corrections and counter terms in Yang-mills, QED. Coulping of QED becomes strong at high energy scales, Yang-mills asymptotically free at large energy scales. Ward identities and BRST symmetry, BRST symmetry as a cohomology to reduce formal fock space $\mathcal{F}$ to physical hilbert space \mathcal{H}.

    Reading was primarily from Pierre Ramod's Field Theory: A Modern Primer and notes by Dr.Kaplunovsky.

  • Introduction to Supersymmetry

    Why are we interested in symmetries, Wigner's theorem, irreducible representations as particles, representation theory of the Lorentz (spinors) and Poincaré group. The spinor algebra, conventions, manipulation and its representation.The no-go theorems of Coleman-Mandula and its extension by Haag-Lopuszanski-Sohnius Theorem. The supersymmetry algebra, superchargers in particular, $\mathcal{N}=1$ and $\mathcal{N}=2$ algebra, its massive and massless representations. Properties of the algebra, such as manifestly positive energy states, superpartners have equal mass,and degrees of freedom on bosonic and fermionic states.

    Reading was primarily from lecture notes by Bertolini, Argyres and Arguiro and from the following books, 'Introduction to Supersymmetry' by Wiedeman and 'Introduction to Supersymmetry & Supergravity' by Wess & Bagger.

  • Topological Solitons & Monoples in non-Abelian Gauge theories

    Manifolds, Langrangians on curved spaces, solving for EOM on manifolds, Spontaenous Symmetry breaking in various theories, Gldstone's theorem. In particular, Higg's field, Higg's boson and the Higg's mechanism, Introduction to Homotopy theory, homotopy groups, theorems of $\pi_n(Y)$ and $\pi_2(G/H) as a subgroup of $pi_1(H)$. SOlitons and kinks in $\phi^4$ and sine-gordon theory. Mathematical understanding of Gauge theory, topolgoical degree, monopoles in $SU(2)$ Gauge theory of Yang-mills on Eucledian & 4-D flat manifolds.

    Reading was primarily from 'Topological Solitons' by Nicholas Manton.

  • Non-Abelian Gauge Theories

    Noether's theorem, internal symmetries, gauge fields, the covariant derivative,gauge field from the comparator local invariance of comparator implies existance of $F_{\mu\nu}$, gauge boson, minimal coupling prescription. Lagrangian of $SU(2)$ and arbitrary $SU(n)$ Yang-mills theory. The $SU(N)$ internal symmetry as a lie group generated by a lie algebra $\mathfrank{su(n)}$. The explcit form of gauge fields and field strength tensor in these theories.

    Reading was primarily from 'An introduction to Quantum Field Theory' by Peskin & Shroeder and 'Quantum Field Theory' by Mark Srednicki.

  • Novel black hole bound states and entropy

    A reading project I undertook after self studying the preminilaries from Dirac's General Theory of Relativity. This project required very little understanding of GR. It was primarily Self Adjoint Analysis of Laplacian operator on a restricted domain for finding the bound state solutions of the time-independent Schroedinger Schrödinger's Equation.

    The primary reference was 'Self-Adjoint extensions of Quantum Mechanics' by Gitman.

  • Entropic Gravity

    This was a self reading project. I tried to understand the works on the much debated results of Eric Verlinde on Gravity as an emergent theory 1001.0785. This was disproved by Matt Visser in 1108.5240. However, Prof. Padmandabhan's approach to emergent gravity was consideraly different 1410.6285. I had formulated a few questions and got them clarified over email from the authors.


August 2013 - April 2016


Some material which might be useful to anyone.