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Dharmesh Jain

Publications and source records attributed to Dharmesh Jain.

25 records · Page 2Linked to original sources
arXiv2012

Free Energy of D_n Quiver Chern-Simons Theories

We apply the matrix model of Kapustin, Willett and Yaakov to compute the free energy of N=3 Chern-Simons matter theories with D_n quivers in the large N limit. We conjecture a general expression for the free energy that is explicitly invariant under Seiberg duality and show that it can be interpreted as a sum over certain graphs known as signed graphs. Through the AdS/CFT correspondence, this leads to a prediction for the volume of certain tri-Sasaki Einstein manifolds. We also study the unfolding procedure, which relates these D_n quivers to A_{2n-5} quivers. Furthermore, we consider the addition of massive fundamental flavor fields, verifying that integrating these out decreases the free energy in accordance with the F-theorem.

hep-th↗
arXiv2012

Darboux Coordinates and Instanton Corrections in Projective Superspace

By demanding consistency of the Legendre transform construction of hyperkähler metrics in projective superspace, we derive the expression for the Darboux coordinates on the hyperkähler manifold. We apply these results to study the Coulomb branch moduli space of 4D, N=2 super-Yang-Mills theory (SYM) on R^3 x S^1, recovering the results by GMN. We also apply this method to study the electric corrections to the moduli space of 5D, N=1 SYM on R^3 x T^2 and give the Darboux coordinates explicitly.

hep-th↗
arXiv2012

N=2 Super-Yang-Mills Theory from a Chern-Simons Action

We present a Chern-Simons action for N=2 Super-Yang-Mills theory (SYM) in 'full' N=2 superspace (hyperspace) augmented by coordinates of the internal SU(2) group and show that this action can be reduced to the usual SYM action in the Harmonic hyperspace. We also discover that the 'choice' of Harmonic hyperspace is not unique and under suitable conditions, further reduction to the well-known Projective hyperspace is possible.

hep-th↗
arXiv2010

On Projective Hoops: Loops in Hyperspace

We (re)derive the propagators and Feynman rules for the massless scalar and vector multiplets in N=2 Projective Superspace ('Projective Hyperspace'). With these, we are able to calculate both the divergent and finite parts of 2, 3 & 4-point functions at 1-loop for N=2 Super-Yang-Mills theory (SYM) explicitly in Projective Hyperspace itself. We find that effectively only the coupling constant needs to be renormalized unlike in the N=1 case where an independent wavefunction renormalization is also required. This feature is similar to that of the background field gauge, even though we are using ordinary Fermi-Feynman gauge. The computation of 1-hoop beta-function is then straightforward and matches with the known result. We also show that it receives no 2-hoops contributions. All these calculations provide an alternative proof of the finiteness of N=4 SYM.

hep-th↗
arXiv2009

Deriving Projective Hyperspace from Harmonic

We derive actions for projective N=2 superspace ("hyperspace") from those for harmonic hyperspace, including that for nonabelian Yang-Mills (a new result). The method uses Wick rotation of the sphere from complex conjugate coordinates to real, null ones, which can be treated as independent. The result can be considered "holographic" in that the dimension of the internal (R-symmetry) space is reduced from 2 to 1, by solving equations of motion or gauge conditions for dependence on the other coordinate. The auxiliary nature of the redundant dimension makes the hypergraph rules and evaluation almost identical.

hep-th↗
arXiv2006

Path integrals and wavepacket evolution for damped mechanical systems

Damped mechanical systems with various forms of damping are quantized using the path integral formalism. In particular, we obtain the path integral kernel for the linearly damped harmonic oscillator and a particle in a uniform gravitational field with linearly or quadratically damped motion. In each case, we study the evolution of Gaussian wavepackets and discuss the characteristic features that help us distinguish between different types of damping. For quadratic damping, we show that the action and equation of motion of such a system has a connection with the zero dimensional version of a currently popular scalar field theory. Furthermore we demonstrate that the equation of motion (for quadratic damping) can be identified as a geodesic equation in a fictitious two-dimensional space.

quant-ph↗