arXiv subjects

Adithya A Rao

Publications and source records attributed to Adithya A Rao.

5 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

$\mathbb{R}$eal Ambitwistors & Massive Twistors for CFT$_4$

We develop a real twistor-space formulation of four-dimensional CFT Wightman correlators. We write the conformal generators and little-group constraints in ambitwistor space. The quadric condition $Z\cdot W$=0 arises naturally from the little-group constraints. We then solve for both the parity-even and parity-odd correlators in the ambitwistor variables. We further establish the connection between the ambitwistor correlators and the ones in the helicity-basis Grassmannian via a half-Fourier transform, and also develop the Penrose transform to recover the corresponding position-space correlators. We notice that for correlators with multiple tensor structures, the Penrose transform yields the full space of conformally invariant structures, but regularizing the associated Schwinger integrals selects the physical correlator. Finally, starting from the covariant Grassmannian formulation, we construct massive twistors that make the little-group symmetries manifest and develop their Penrose transform, which again reproduces the correct position-space correlators.

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↗

arXiv2024

Gribov Problem and Stochastic Quantization

The standard procedure for quantizing gauge fields is the Faddeev-Popov quantization, which performs gauge fixing in the path integral formulation and introduces additional ghost fields. This approach provides the foundation for calculations in quantum Yang-Mills theory. However, in 1978, Vladimir Gribov showed that the gauge-fixing procedure was incomplete, with residual gauge copies (called Gribov copies) still entering the path integral even after gauge fixing. These copies impact the infrared behavior of the theory and modify gauge-dependent quantities, such as gluon and ghost propagators, as they represent redundant integrations over gauge-equivalent configurations. Furthermore, their existence breaks down the Faddeev-Popov prescription at a fundamental level. To partially resolve this, Gribov proposed restricting the path integral to the Gribov region, which alters the gluon propagator semiclassically in a way that points to gluon confinement in the Yang-Mills theory. In this thesis, we comprehensively study the Gribov problem analytically. After reviewing Faddeev-Popov quantization, the BRST symmetry of the complete Lagrangian and the Gribov problem in depth, we detail Gribov's semi-classical resolution involving restriction of the path integral to the Gribov region, outlining its effects on the theory. Further, we elucidate stochastic quantization prescription for quantizing the gauge fields. This alternate quantization prescription hints towards a formalism devoid of the Gribov problem, making it an interesting candidate for quantizing and studying the non-perturbative regime of gauge theories.

hep-th↗

arXiv2023

Interacting tachyonic scalar field II

The existence of dark energy is essential to explain the cosmic accelerated expansion. We consider a homogenous interacting tachyonic scalar field as a possible candidate for the dynamical dark energy. The interaction between the tachyonic field and matter can be gauged to be linear in the energy density of matter (or the tachyonic field) and Hubble's parameter. We estimate the rate of expansion, the age of the universe, the evolution of energy density of matter and tachyonic field, and the coupling strength of the interaction for a spatially flat ($k=0$) universe. We observed that the upper limit of coupling strength is 1, and it is the same whether the interaction term depends on the energy density of matter or the energy density of tachyonic scalar field.

gr-qc↗