**Elementary Particle physics and physics beyond the Standard Model**

__Origin of the Higgs boson__: The Higgs boson plays an important role in the Standard Model and provides a universal mechanism for particle masses. Theoretically it is required as the remnant of electroweak symmetry breaking (EWSB) that separates the weak forces from electromagnetism. Is the 125 GeV boson discovered at the LHC really the Higgs boson of the Standard Model? If so, why is its mass much smaller than the naively expected theoretical value?

__Top quark physics__: Is there any connection of EWSB to the mass of the top quark? We have been exploring Higgs and Top quark physics in beyond Standard Model (bSM) models. We have especially been exploring collider signatures of new physics contributions to Higgs and top quark observables, through polarization and jet substructure studies both at the Large Hadron Collider (LHC) and the proposed International Linear Collider (ILC).

__Understanding the proton spin__: We know that the proton has spin 1/2. How is this built up from the intrinsic spin of quarks and gluons and their orbital angular momentum? In a high energy collider experiment, if one polarizes one or both beams either longitudinally or in the transverse direction, what new information can one obtain about the structure of the nucleons and their interaction?

__Neutrino Physics__: What makes the neutrino masses a trillion times smaller than the EWSB scale? What new physics underlies their individual masses and mixings? Is one or more neutrino its own antiparticle? What is the mass hierarchy of the neutrinos? Is there any CP violation in the neutrino sector?

__Flavour Physics__: Both quarks and the leptons appear with identical gauge couplings across three generations, this is associated with a "flavour'' identity that is preserved by the strong and electromagnetic interactions. This flavour identity is violated in charge- current weak interactions and it also leads to a mixing between generations. What explains the masses and mixings of the fermions in the Standard Model? What are the CP violating parameters in their interactions and what connection does this have to the baryon asymmetry of the universe?
Unified Theories
The explanation for some of the theoretical issues with elementary particles can be found by invoking new symmetry principles. Historically, this has been an extremely fruitful direction. In addition, we would like a theory of fundamental particles that includes quantum gravity.

__Supersymmetric gauge theories__: Supersymmetry is a theoretically appealing quantum symmetry, that relates bosons and fermions. The problems faced by the standard Higgs can be reduced if nature is supersymmetric at the weak scale. Additionally, if we assume that the unequal participation of left handed and right handed particles in the weak force is only a low energy manifestation, we can construct left-right symmetric extended supersymmetric models. Can such extensions explain the origin of the matter vs. anti- matter asymmetry of the universe and the extremely low neutrino mass? Does one necessarily require a very high scale and a large gauge group like SO(10) for unification?

__Topological Quantum Field Theories and knot theory__: During the last three decades, we have seen topological quantum field theories playing a crucial role in providing a natural framework for the study of geometry and topology of three and four-dimensional manifolds. One of the challenging open problem is the classification of knots and links in three-manifolds. We have made significant progress on knot polynomials using Chern- Simons topological field theory and have distinguished many inequivalent knots.

__AdS-CFT correspondence__: The AdS-CFT correspondence or duality (also called “gauge- gravity correspondence”) is a powerful tool which enables computations of the strong coupling regime of gauge field theory using the weak-coupling limit of gravity or String Theory. Interestingly, Gopakumar-Vafa conjectured a similar correspondence between Chern-Simons field theory and topological string theory. This led to a flurry of activities resulting in connection between integer coefficients in the knot polynomials to the counting of stable states in string theory called BPS states. We have been working on string theory-gauge theory dualities to understand counting of BPS states as well as to obtain the transport properties like ratio of shear viscosity to entropy density as experimentally observed in the quark gluon plasma.
Astroparticle physics and early universe cosmology

__Matter-antimatter asymmetry__: Why is the mass of baryons in the universe today dominated by protons and neutrons, but not by their anti-particles? All the known forces preserve baryon number (B) and separately lepton number (L) at low energies. Yet theoretical arguments based on quantum “anomalies” show that only the combined number B-L should be preserved at high energies. However, violation of baryon number alone proves to be insufficient to generate a matter-antimatter asymmetry. Invoking extensions of Standard Model in the hot Big Bang Universe we have advanced explanations for the observed matter-anti-matter asymmetry. Specifically, topological defects occurring in extended gauge models, like cosmic strings and domain walls are shown to play a crucial role in these scenarios.

__Dark matter__: The evidence for dark matter is overwhelming from cosmology and astrophysics, yet we are clueless as to the particle nature of dark matter. What particle or particles are responsible for forming the dark matter which constitutes 20% of the energy budget of the universe? Do our extended models contain possible candidates that can be tested in the near future?

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