arXiv subjects

Deep Mazumdar

Publications and source records attributed to Deep Mazumdar.

8 recordsLinked to original sources

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

Unitarity, Recursion and Soft Limits in (EA)dS through Dressing

Using the recently developed framework in which cosmological correlators in (E)AdS are represented as flat-space amplitudes dressed by auxiliary propagators, we show that several structural properties of the cosmological observables have a direct flat-space origin. We derive cosmological cutting rules for spinning correlators from the flat-space optical theorem, obtain the cosmological tree theorem from the Feynman tree theorem, and uplift BCFW recursion relations to (E)AdS via dressing. We also show that flat-space soft theorems reproduce the soft limits of (E)AdS correlators, and find indications of an emergent universal structure in subleading soft limits. These results provide evidence that key features of cosmological correlators can be systematically understood as dressed manifestations of flat-space physics.

hep-th↗

arXiv2026

Cosmological Cutting Rules from Flat-Space Unitarity via Dressing

Using cosmological dressing rules, we uplift flat-space unitarity cuts to discontinuity relations for dS/EAdS observables. In this representation, Cutkosky delta functions map directly to "Disc" operations in the exchanged energy variable. This provides a transparent diagram by diagram origin of cosmological cutting rules. We illustrate this with explicit examples at tree level and one loop for conformally coupled scalars.

hep-th↗

arXiv2025

Super-Penrose $\And$ Witten Transforms for SCFT$_3$

The study of three dimensional CFT correlators in twistor space has recently garnered a significant interest. Conformal symmetry acts linearly in the twistor space, which streamlines the analysis. Moreover, twistors provide a connection to the position and momentum space through the Penrose and Witten transforms, respectively. In this work, we develop the supersymmetric versions of Penrose and Witten transforms for three dimensional superconformal field theories for $\mathcal{N}=1\;\textrm{to}\;4$. We derive two and three point functions in the position and momentum superspace for the $\mathcal{N}=1$ scenario using these transforms. Extending this setup to higher supersymmetries turns out to be a simple extension of the $\mathcal{N}=1$ case, which aligns with the inherent simplicity of supertwistors.

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.

hep-th↗

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.

hep-th↗

arXiv2024

$n$-point functions in Conformal Quantum Mechanics: A Momentum Space Odyssey

In this paper, we study the implications of conformal invariance in momentum space for correlation functions in quantum mechanics. We find that three point functions of arbitrary operators can be written in terms of the $_2 F_1$ hypergeometric function. We then show that generic four-point functions can be expressed in terms of Appell's generalized hypergeometric function $F_2$ with one undetermined parameter that plays the role of the conformal cross ratio in momentum space. We also construct momentum space conformal partial waves, which we compare with the Appell $F_2$ representation. We test our expressions against free theory and DFF model correlators, finding an exact agreement. We then analyze five, six, and all higher point functions. We find, quite remarkably, that $n$-point functions can be expressed in terms of the Lauricella generalized hypergeometric function, $E_A$, with $n-3$ undetermined parameters, which is in one-to-one correspondence with the number of conformal cross ratios. This analysis provides the first instance of a closed form for generic momentum space conformal correlators in contrast to the situation in higher dimensions. Further, we show that the existence of multiple solutions to the momentum space can be attributed to the Fourier transforms of the various possible time orderings. Finally, we extend our analysis to theories with $\mathcal{N}=1,2$ supersymmetry, where we find that the constraints due to the superconformal ward identities are identical to identities involving hypergeometric functions.

hep-th↗

arXiv2023

A Foray on SCFT$_3$ via Super Spinor-Helicity and Grassmann Twistor Variables

In this paper, we develop a momentum super space formalism for $\mathcal{N}=1,2$ superconformal field theories in three dimensions. First, we solve for super-correlators in the usual momentum superspace variables. However, we found that expressing quantities in super space spinor helicity variables greatly simplifies the analysis. Further, by performing a "half" Fourier transform of the Grassmann coordinates which is analogous to the Twistor transform, an even more remarkable simplification occurs. Using these formalism, we first compute all three point correlation functions involving conserved super-currents with arbitrary spins in $\mathcal{N}=1,2$ theories. We discover interesting double copy relations in $\mathcal{N}=1$ super-correlators. Also, we discovered super double copy relations that take us from $\mathcal{N}=1$ to $\mathcal{N}=2$ super-correlators. We also comment on the connection of our results with the flat space super amplitudes in one higher dimension.

hep-th↗