I am part of the Fundamental Theory Group: Particle and Gravitational Physics at the Department of Physics at Syracuse University.

My current research mostly focuses on constructing supersymmetric field theories on a Euclidean spacetime lattice preserving exact supersymmetry. I am working with Prof. Simon Catterall in the High Energy Theory group of the physics department at Syracuse University.

I am also interested in noncommutative geometry, and have worked on quantum field theories on the noncommutative spacetime called the Moyal plane.

Exact Lattice Supersymmetry from Topological Twisting

Recently there has been much progress in formulating supersymmetric field theories on a spacetime lattice using new ideas such as topological twisting and orbifold projection. My current research with Prof. Catterall focuses on constructing a class of lattice models which maintain one or more super-symmetries exactly at non-zero lattice spacing using the method of topological twisting.

The basic idea of twisting is to use a subalgbra of the supersymmetry algebra to constrain the effective lattice action and thus to protect the theory from the dangerous supersymmetry violating counter terms. The target theory in the continuum is reformulated in terms of twisted fields. The fermionic and bosonic fields of the theory are decomposed in terms of representations of a twisted rotational symmetry which is the diagonal subgroup of the Euclidean Lorentz symmetry and the R-symmetry of the theory. Twisting produces a nilpotent scalar supercharge Q and the supersymmetric action can generically be written in a form S = Q (something).

The twisted sixteen supercharge theory serves as tool to explore the connection between gauge theory and string/supergravity models. The twisted lattice formulation of the gauge theory may help us to learn more about the nonperturbative aspects of the dual string/supergravity theories. Currently we are focusing on observing phase transitions in thermal gauge theories through Monte Carlo simulation.

Quantum Fields on Noncommutative Spacetime

At energy scales close to the Planck scale, the quantum nature of spacetime is expected to become important. Arguments based on Heisenberg's uncertainty principle and Einstein's theory of classical gravity suggest that spacetime has a noncommutative structure at such small length scales.

The noncommutative algebra of functions called the Moyal plane models such a spacetime. With Prof. Balachandran and collaborators in the High Energy Theory Group, I have shown that the discrete symmetry of space reflection called parity (P) is broken in non-abelian gauge theories with matter fields on the noncommutative spacetime. This in turn contributes to the violation of the fundamental symmetry called CPT. This can give rise to possible experimental signals such as particle and anti-particle mass difference, (g-2) difference between a particle and its anti-particle etc.

These theories break rotational symmetry and it may give rise to a preferred direction in the Universe. We have shown that spacetime noncommutativity gives rise to a vector that breaks rotational symmetry. Effects due to this may be observed in the Cosmic Microwave Background (CMB) radiation.

Topological Sectors of Field Theories and Cosmology

Topologically stable solutions of field theoretic models appear in the context of topological defects in cosmology. Topological defects, such as magnetic monopoles, vortices (cosmic strings), domain walls etc., can be produced in our universe when it passed through a series of phase transitions while cooling down to the present temperature of around 2.7K.

I have collaborated with Prof. S. G. Rajeev (University of Rochester) on certain little Higgs models with symmetry breaking SU(N) -> SO(N), where N is the rank of the gauge group. For N > 3, we have shown that these models admit topologically stable solitons that may contribute to cosmological dark matter. We have constructed a spherically symmetric soliton and estimated its mass in the case of SU(5) -> SO(5). Its lower bound is found to be around 10 TeV. This particle could be a fermion of boson depending on the nature of the underlying field theory.