arXiv subjects

Sachin Jain

Publications and source records attributed to Sachin Jain.

At least 19 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.

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arXiv2026

A Cosmological BCFW Bridge and Its Canonical Geometry

We build a BCFW-like recursion for cosmological correlators using the orthogonal Grassmannian. The key step is a bridge deformation that leaves all the Grassmannian constraints intact. The recursion relations are purely algebraic and avoid any spectral or radial integrals that usually appear in curved space. We obtain the gluon 4-point correlator using this bridge, producing two factorization poles, a total energy singularity coming from the three point building block, and a shifted energy singularity that emerges only after adding the two channels using recursion. We then show that the helicity stripped four-gluon correlator has the canonical form of a rectangle, where its boundaries represent various poles. We also describe the geometry of the gluon correlator in the Pfaffians as the natural coordinates in the Grassmannian. Using multiple deformation bridges, we also obtain the graviton four point correlator and observe a double-copy like relation at the level of the four point function, away from the physical cuts for each channel. We also extended the BCFW bridge formalism to the supersymmetric Grassmannian.

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arXiv2026

The Conformal Grassmannian: A Symplectic Bi-Grassmannian for $CFT_ 4$ Correlators

We introduce a formalism for conformal field theory in four dimensions: a symplectic bi-Grassmannian representation of CFT$_4$ Wightman correlators. Working in Klein space with off-shell spinor-helicity variables, we show that correlators of $\Delta = 2$ scalars and symmetric-traceless conserved currents are encoded by integrals over a pair of $n$-planes in a $2n$-dimensional symplectic vector space. These planes are constrained to be mutually symplectically orthogonal and aligned with the external kinematics. Conformal invariance, momentum conservation, and little-group covariance all follow geometrically from this structure. We derive all two- and three-point functions involving scalars, fermions, conserved currents, and stress tensors. As a non-trivial test, we show that the construction reproduces the full set of independent conformally invariant structures of $\langle JJJ\rangle$ and $\langle TTT\rangle$ in CFT$_4$. The resulting expressions are considerably more compact than their momentum-space counterparts. They also make manifest the double copy between Yang--Mills $\langle JJJ \rangle$ and Einstein-gravity $\langle TTT \rangle$. We further present a helicity-basis reformulation that makes the GL(1,R) and SL(2,R) weights of individual helicity components explicit. This basis also provides a natural starting point for a twistor-space formulation of the correlators.

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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.

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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.

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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.

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arXiv2025

AdS$_4$ Boundary Wightman functions in Twistor Space: Factorization, Conformal blocks and a Double Copy

We study real-time holographic four point Wightman functions involving scalars, photons, gluons and gravitons in the Poincare patch of AdS$_4$. We show that when the momenta of the middle two operators are spacelike, four-point exchange Wightman functions factorize into a product of three-point functions. This expression coincides with a Wightman conformal partial wave corresponding to the operator dual to the exchanged particle in the bulk. Further, we discuss and explicitly show how these results can be analytically continued to obtain Euclidean AdS correlators up to contact diagrams and avoid the need to perform any nested bulk point integrals in contrast to the traditional Witten diagram approach. We then translate our results to twistor space taking first steps towards a twistor space reformulation of four point Wightman functions. For conformally coupled scalars interacting with a cubic potential, we obtain a beautiful form for four and five point functions. For the interesting case of Yang-Mills theory and Einstein gravity, we derive a simple double copy relation. This is easiest to see when correlators are expressed in twistor space using Schwinger parameterization where the graviton correlator is simply the square of its gluon counterpart.

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arXiv2025

Hidden sectors of Chern-Simons Matter theories and Exact Holography

Chiral higher-spin gravity is a higher-spin extension of both self-dual Yang-Mills and self-dual gravity and is a unique local higher-spin gravity in four dimensions. Its existence implies that there are two closed subsectors in Chern-Simons matter theories. We make first steps in identifying these (anti-)chiral subsectors directly on the CFT side, which should result in a holographically dual pair where both sides are nontrivial, complete, yet exactly soluble. We also discuss closely related theories: self-dual Yang-Mills (SDYM) and self-dual gravity (SDGR) in the holographic context.

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arXiv2025

Direct Experimental Observation of Quantum Mpemba Effect without Bath Engineering

The quantum Mpemba effect refers to the phenomenon of a quantum system in an initial state, far away from equilibrium, relaxing much faster than a state comparatively nearer to equilibrium. We experimentally demonstrate that this highly counterintuitive effect can occur naturally during the thermalization of quantum systems. Considering dipolar relaxation as the dominant decoherence process, we theoretically derive the conditions that can lead to the Mpemba effect in nuclear spins. After experimentally preparing nuclear spin states dictated by those conditions, we observe the occurrence of the Mpemba effect when they are left to thermalize without any external control. We also experimentally observe the genuine quantum Mpemba effect during thermalization of nuclear spins. Our results establish that both these effects are natural in thermalization of quantum systems, and may show up without the need for any bath engineering.

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arXiv2025

Bootstrapping LSS perturbation theory beyond third order

Bootstrap techniques relying on the constraints imposed by Extended Galilean Invariance (EGI), have proved to be very useful in the context of perturbation theory of the Large Scale Structure (LSS). It has been formulated in both the Eulerian as well as Lagrangian space. While the Eulerian bootstrap formalism has been successfully applied to both tracer and matter kernels, the application of bootstrap methods in Lagrangian space has so far been restricted to matter. Up to third order, it has been shown that implementing EGI constraints in Eulerian space fully reproduces the bias expansion for tracers. Previous studies have demonstrated that time non-locality affects the bias expansion in a non-trivial way starting from fifth order. Motivated by this fact, we extend the bootstrap approach upto fifth order in both Eulerian and Lagrangian space and demonstrate that it fully captures the time non-local effects. For this, we generalize the Lagrangian bootstrap for tracers, and found that it agrees with the corresponding results obtained in Eulerian space. One of the major challenges in implementing EGI constraints in Eulerian space, is to systematically find out all the "spurious poles" and make them vanish. We have proposed a method that bypasses this difficulty making the procedure tractable at higher orders. From Lagrangian perspective, we have identified coefficients in the tracer kernel whose ratios are independent of tracer properties and may serve as direct probes of the underlying cosmology.

astro-ph.CO↗

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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arXiv2024

Inflationary non-Gaussianities in alpha vacua and consistency with conformal symmetries

We study the conformal invariance of inflationary non-Gaussianities associated with scalar fluctuations in a non-Bunch-Davies initial state, known as the $α$-vacuum, in single-field slow-roll inflation. The $α$-vacuum is a one-parameter family of states, including the Bunch-Davies one, that preserves the conformal symmetry of inflationary dynamics in a nearly de-Sitter space-time. Working within the leading slow-roll approximation, we compute the four-point scalar correlator (the trispectrum) in $α$-vacuum using the in-in formalism. We check that the conformal Ward identities are met between the three and four-point scalar $α$-vacua correlators. Surprisingly, this contrasts the previously reported negative result of the Ward identities being violated between the two and the three-point correlators. We have also extended the wave-functional method, previously used for correlators with Bunch-Davies initial condition, to compute the three and four-point scalar correlators in $α$-vacua. The results obtained from the wave-function method match the corresponding in-in results, adding further justification to our check of Ward identities with $α$-vacua correlators.

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arXiv2024

Time Non-locality in Dark Matter and LSS

We explore the intriguing phenomenon of time non-locality in the evolution of dark matter and Large Scale Structure (LSS). Recently in\,\cite{Donath:2023sav}, it was shown that time non-locality emerges in bias tracer fluctuations, which are $SO(3)$ scalars in real space, at fifth order in the perturbation expansion in dark matter overdensity. We demonstrate that by breaking the symmetry down to $SO(2)$, which is the case whenever line-of-sight effects become important, such as for flux fluctuations in the Lyman $\alpha$ forest, the temporal non-locality appears at the third order in expansion. Additionally, within the framework of EFTofLSS, we demonstrate that time non-locality manifests in the effective stress tensor of dark matter, which is a second rank tensor under $SO(3)$ transformations, again at the third order in dark matter overdensity. Furthermore, we highlight the effectiveness of the standard $\Pi$ basis\,\cite{Mirbabayi:2014zca} in handling time non-local operators.

astro-ph.CO↗

arXiv2024

Mapping Large N Slightly Broken Higher Spin (SBHS) theory correlators to Free theory correlators

We develop a systematic method to constrain any n-point correlation function of spinning operators in Large N Slightly Broken Higher Spin (SBHS) theories. As an illustration of the methodology, we work out the three point functions which reproduce the previously known results. We then work out the four point functions of spinning operators. We show that the correlation functions of spinning operators in the interacting SBHS theory take a remarkably simple form and that they can be written just in terms of the free fermionic and critical bosonic theory correlators. They also interpolate nicely between the results in these two theories. When expressed in spinor-helicity variables we obtain an anyonic phase which nicely interpolates between the free fermionic and critical bosonic results which makes 3D bosonization manifest. Further, we also obtain a form for five and higher point functions as well by performing a similar analysis.

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arXiv2024

Steady state correlation function beyond the standard weak coupling limit and consistency with KMS relation

Thermalization of a system when interacting with a thermal bath is an interesting problem. If a system eventually reaches a thermal state in the long time limit, it's expected that its density matrix would resemble the mean-force Gibbs state. Moreover, the correlation function must satisfy the Kubo-Martin-Schwinger (KMS) condition or equivalently the Fluctuation-Dissipation Relation (FDR). In this paper, we derive a formal expression for the non-Markovian two-point function within the context of the weak coupling limit. Using this expression, we explicitly compute the two-point function for specific models, demonstrating their adherence to the KMS. In addition, we have formulated a non-perturbative approach in the form of a self-consistent approximation that includes a partial resummation of perturbation theory. This approach can capture strong coupling phenomena while still relying on simple equations. Notably, we verify that the two-point function obtained through this method also satisfies the KMS condition.

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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.

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arXiv2023

Statistical Correlators and Tripartite Entanglement

It has recently been argued that among the various suggested measures of tripartite entanglement, the two particular measures, viz. the Concurrence Fill and the Genuine Multipartite Concurrence are the only 'genuine' tripartite entanglement measures based on certain suitably specified criteria. In this context, we show that these two genuine tripartite entanglement measures can be empirically determined for the two important classes of tripartite entangled states, viz. the generalized GHZ and the generalized W states using the derived relationships of these two measures with the observable statistical correlators like the Pearson correlator and mutual information. Such a formulated scheme would therefore provide for the first time the means to exactly quantify tripartite entanglement, crucial for the proper assessment of its efficacy as resource. We also point out two specific applications of this scheme, viz. a) Enabling empirical demonstration of the potentially significant feature of inequivalence between Concurrence Fill and Genuine Multipartite Concurrence in quantitatively assessing which of the two given tripartite states is more entangled than the other one. b) Enabling experimental detection of the recently predicted phenomenon of entanglement sudden death for a tripartite system.

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