arXiv subjects

Dhruva K. S.

Publications and source records attributed to Dhruva K. S..

4 recordsLinked to original sources

arXiv2026

The $\mathcal{N}=1$ Super-Grassmannian for CFT$_3$ and a Foray on AdS and Cosmological Correlators

We construct a Super-Grassmannian integral representation for $n-$point functions in $\mathcal{N}=1$ SCFT$_3$. In this formalism, conformal invariance, supersymmetry, and special superconformal invariance are implemented manifestly through (operator-valued) delta function constraints. An important feature of this framework is the fact that we obtain simple algebraic relations among component correlators, which enable us to determine any component correlator in terms of just one of the component correlators. In particular, this formalism enables us to construct (A)dS$_4$ boundary correlators with contact diagrams from those that receive contributions purely from particle exchanges. We illustrate this by determining the (A)dS$_4$ Yang-Mills gluon four-point function from its gluino counterpart. Further, we establish the flat-space limit in super-space, finding a perfect agreement with existing flat-space results.

hep-th↗

arXiv2026

Super-Grassmannians for $\mathcal{N}=2$ to $4$ SCFT$_3$: From AdS$_4$ Correlators to $\mathcal{N}=4$ SYM scattering Amplitudes

We construct a Super-Grassmannian for $n-$point functions in $\mathcal{N}=2$ to $4$ SCFT$_3$. The constraints imposed by super-conformal invariance and $R-$symmetry are completely manifest in this formalism through (operator-valued) delta functions. We test our formalism in $\mathcal{N}=2$ and $\mathcal{N}=4$ AdS$_4$ super Yang-Mills theories. In the $\mathcal{N}=2$ case, for instance, we reproduce the four-gluon correlator using the four-point scalar correlator as input. For $\mathcal{N}=4$, we construct the super-operator in two distinct ways. In one approach, the super-operator has a lowest component of spin zero and includes all states up to spin two. In the other approach, we build the super-operator in a CPT self-conjugate manner, which contains only operators with spin zero, spin half, and spin one mimicking flat space $\mathcal{N}=4$ SYM super-field constructions. The latter construction is particularly interesting, as it matches directly with the $\mathcal{N}=4$ SYM amplitudes in the flat space limit, thereby demonstrating the non-triviality and usefulness of our framework. It is interesting to note that the $R-$symmetry group enhances from $SO(\mathcal{N})$ to $SU(\mathcal{N})$ in the flat space limit.

hep-th↗

arXiv2025

A Supertwistor Formalism for $\mathcal{N}=1,2,3,4\;\text{SCFT}_3$

We develop a manifest supertwistor space formalism for three dimensional $\mathcal{N}=1, 2,3,4$ superconformal field theories. This formalism simultaneously makes manifest the supersymmetry, conformal invariance and conservation. We solve two and three point correlators of (half) integer spin conserved supercurrents using the graded supergroup generators. Apart from the superconformal generators, we find that the superhelicity operators are necessary to fix their functional form in this setup. The superhelicity operators can be recast into first order Euler equations which besides the standard polynomial solutions, also admit weak solutions that are distributional in nature. They play an important role in the case of three point functions, where the super-correlator takes the form of a product of delta functions. Interestingly, we find that these super-correlators are extremely simple, elegant and uniform for all spins and for all $\mathcal{N}\leq4$, which resemble the non supersymmetric correlators where the twistors are replaced with appropriately defined supertwistors.

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arXiv2025

3D Conformal Field Theory in Twistor Space

The aim of this paper is to study three dimensional Lorentzian conformal field theories in twistor space. We formulate the conformal Ward identities and solve for two and three point Lorentzian Wightman functions. We found that the Helicity operators apart from the conformal generators play an important role in fixing their functional form. The equations take the form of first order Euler equations which in addition to the usual solutions that are polynomials, also possess weak solutions which are distributional in nature. All of these play an important role in our analysis. For instance, in the case of three point functions, the distributional solutions are indeed the ones realized by the CFT correlators. We also extend our analysis to parity odd Wightman functions which take an interesting form in twistor space. We verify our results by systematically analyzing the corresponding Wightman functions in momentum space and spinor helicity variables and matching with the twistor results via a half-Fourier transform.

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