arXiv subjects

Shounak De

Publications and source records attributed to Shounak De.

17 recordsLinked to original sources

arXiv2026

Higher-Spin Correlators in dS

We study momentum-space correlators in minimal higher-spin gravity in $\mathrm{dS}_4$ using its holographic vector-model description. Connected $n$-point functions in this model are represented by three-dimensional one-loop integrals and are rational functions of the boundary kinematics. We show that the four-point function displays a nontrivial geometric feature: its physical singularity is governed by a Ptolemy relation for the dual momentum quadrilateral. At five points, the pentagon integral introduces an apparent leading Landau singularity, which we show is spurious and disappears once the Gram constraint is imposed. We derive a representation of the five-point function free of spurious singularities and organized in terms of graph-theoretic building blocks. We then verify the conformal invariance of these correlators and discuss their behavior in the soft, collapsed, and Ptolemy limits. This structure suggests a combinatorial bootstrap for higher-spin correlators at general multiplicity, in which conformal invariance and the physical singularities emerge from the underlying graph combinatorics.

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arXiv2026

The Vasiliev Grassmannian

We express the scalar four-point function of minimal Vasiliev higher-spin gravity in de Sitter space as an integral over the orthogonal Grassmannian OGr(4,8). The full crossing-symmetric Vasiliev Grassmannian correlator is given by $(S^2+T^2+U^2)/(STU)$, where $S$, $T$, $U$ are the Grassmannian Mandelstam variables. Remarkably, this has the same form as the field-theory limit of the Veneziano amplitude, despite arising from the opposite, tensionless limit of an infinite massless higher-spin tower. We verify the formula by evaluating the Grassmannian contour integral and matching it to the momentum-space result, and analyze its singularities and residues directly in Grassmannian space.

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arXiv2025

De Sitter Light-Ray Operators

In this work, we initiate the study of light-ray operators in four-dimensional de Sitter space focusing on null integrals of the stress tensor. In Minkowski space, the null integral of the stress tensor unifies several ostensibly different constructions, functioning simultaneously as the energy flux operator, the angular contribution to a conserved charge, the averaged null energy operator, and the light transform of the stress tensor. However, we show that the de Sitter analogs of these various interpretations do not necessarily coincide but rather lead to distinct, observer-dependent light-ray operators. We construct four such de Sitter analogs and analyze their matrix elements in a free, conformally coupled scalar theory, showing that they exhibit the expected symmetry and positivity properties.

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arXiv2025

Hidden Zeros of the Cosmological Wavefunction

Motivated by the recent discovery of hidden zeros in particle and string amplitudes, we characterize zeros of individual graph contributions to the cosmological wavefunction of a scalar field theory. We demonstrate that these contributions factorize near these zeros for all tree graphs and provide evidence that this extends to loop graphs as well. We explicitly construct polytopal realizations of the relevant graph associahedra and show that the cosmological zeros have natural geometric and physical interpretations. As a byproduct, we establish an equivalence between the wavefunction coefficients of chain graphs and flat-space Tr$(\phi^3)$ amplitudes, enabling us to leverage the cosmological zeros to uncover the recently discovered hidden zeros of colored amplitudes.

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arXiv2024

A physical basis for cosmological correlators from cuts

Significant progress has been made in our understanding of the analytic structure of FRW wavefunction coefficients, facilitated by the development of efficient algorithms to derive the differential equations they satisfy. Moreover, recent findings indicate that the twisted cohomology of the associated hyperplane arrangement defining FRW integrals overestimates the number of integrals required to define differential equations for the wavefunction coefficient. We demonstrate that the associated dual cohomology is automatically organized in a way that is ideal for understanding and exploiting the cut/residue structure of FRW integrals. Utilizing this understanding, we develop a systematic approach to organize compatible sequential residues, which dictates the physical subspace of FRW integrals for any $n$-site, $\ell$-loop graph. In particular, the physical subspace of tree-level FRW wavefunction coefficients is populated by differential forms associated to cuts/residues that factorize the integrand of the wavefunction coefficient into only flat space amplitudes. After demonstrating the validity of our construction using intersection theory, we develop simple graphical rules for cut tubings that enumerate the space of physical cuts and, consequently, differential forms without any calculation.

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arXiv2024

From Feynman diagrams to the amplituhedron: a gentle review

In this article we review, for a mathematical audience, the computation of (tree-level) scattering amplitudes in Yang-Mills theory in detail, in order to bridge the gap in understanding of the subject between mathematicians and physicists. In particular we demonstrate explicitly how the same formulas for six-particle NMHV helicity amplitudes are obtained from summing Feynman diagrams and from computing the canonical form of the $n=6, k=1, m=4$ amplituhedron.

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arXiv2024

Surfaceology for Colored Yukawa Theory

Arkani-Hamed and collaborators have recently shown that scattering amplitudes for colored theories can be expressed as integrals over combinatorial objects simply constructed from surfaces decorated by kinematic data. In this paper we extend the curve integral formalism to theories with colored fermionic matter and present a compact formula for the all-loop, all-genus, all-multiplicity amplitude integrand of a colored Yukawa theory. The curve integral formalism makes certain properties of the amplitudes manifest and repackages non-trivial numerators into a single combinatorial object. We also present an efficient formula for $L$-loop integrated amplitudes in terms of a sum over $2^L$ combinatorial determinants.

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arXiv2024

On unitarity of the Coon amplitude

The Coon amplitude is a one-parameter deformation of the Veneziano amplitude. We explore the unitarity of the Coon amplitude through its partial wave expansion using tools from $q$-calculus. Our analysis establishes manifest positivity on the leading and sub-leading Regge trajectories in arbitrary spacetime dimensions $D$, while revealing a violation of unitarity in a certain region of $(q,D)$ parameter space starting at the sub-sub-leading Regge order. A combination of numerical studies and analytic arguments allows us to argue for the manifest positivity of the partial wave coefficients in fixed spin and Regge asymptotics.

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arXiv2023

Scalar-Graviton Amplitudes and Celestial Holography

We compute scattering amplitudes involving one massive scalar and two, three, or four gravitons. We show that when the conformal dimension of the massive scalar is set to zero, the resulting celestial correlators depend {\it only} on the coordinates of the gravitons. Such correlators of gravitons are well-defined and do not suffer from divergences associated with the Mellin transform of usual graviton amplitudes. Moreover, they are non-distributional and take the form of standard CFT correlators. We show that they are consistent with the usual OPEs but the statement of the soft theorem is modified.

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arXiv2023

Dual resonant amplitudes from Drinfel'd twists

We postulate the existence of a family of dual resonant, four-point tachyon amplitudes derived using invertible coproduct maps called Drinfel'd twists. A sub-family of these amplitudes exhibits well-defined ultraviolet behaviour, namely in the fixed angle high-energy and Regge scattering regimes. This discovery emerges from a systematic study of the set of observables that can be constructed out of $q$-deformed worldsheet CFTs with the underlying conformal group being the quantum group $SU(1,1)_q$. We conclude our analysis by discussing the possibility (or the lack thereof) of known $q$-deformations of the Veneziano amplitude as an observable in such theories, in particular, the Coon amplitude.

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arXiv2023

Cosmology meets cohomology

The cosmological polytope and bootstrap programs have revealed interesting connections between positive geometries, modern on-shell methods and bootstrap principles studied in the amplitudes community with the wavefunction of the Universe in toy models of FRW cosmologies. To compute these FRW correlators, one often faces integrals that are too difficult to evaluate by direct integration. Borrowing from the Feynman integral community, the method of (canonical) differential equations provides an efficient alternative for evaluating these integrals. Moreover, we further develop our geometric understanding of these integrals by describing the associated \emph{relative} twisted cohomology. Leveraging recent progress in our understanding of relative twisted cohomology in the Feynman integral community, we give an algorithm to predict the basis size and simplify the computation of the differential equations satisfied by FRW correlators.

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arXiv2022

Correlators of Four Light-Ray Operators in CCFT

Building on results in arXiv:2203.04255, we compute the correlator of four gluon light-ray operators in celestial CFT. We find that it is described by Fox H-functions and generalized I-functions of multiple variables. We also analyze light-ray correlators for a scalar amplitude involving the exchange of a massive scalar.

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arXiv2020

Beyond-Newtonian dynamics of a planar circular restricted three-body problem with Kerr-like primaries

The dynamics of the planar circular restricted three-body problem with Kerr-like primaries in the context of a beyond-Newtonian approximation is studied. The beyond-Newtonian potential is developed by using the Fodor-Hoenselaers-Perjés procedure. An expansion in the Kerr potential is performed and terms up-to the first non-Newtonian contribution of both the mass and spin effects are included. With this potential, a model for a test particle of infinitesimal mass orbiting in the equatorial plane of the two primaries is examined. The introduction of a parameter, $ε$, allows examination of the system as it transitions from the Newtonian to the beyond-Newtonian regime. The evolution and stability of the fixed points of the system as a function of the parameter $ε$ is also studied. The dynamics of the particle is studied using the Poincaré map of section and the Maximal Lyapunov Exponent as indicators of chaos. Intermediate values of $ε$ seem to be the most chaotic for the two cases of primary mass-ratios ($=0.001,0.5$) examined. The amount of chaos in the system remains higher than the Newtonian system as well as for the planar circular restricted three-body problem with Schwarzschild-like primaries for all non-zero values of $ε$.

gr-qc↗

arXiv2020

Gravity dual of Navier-Stokes equation in a rotating frame through parallel transport

The fluid-gravity correspondence documents a precise mathematical map between a class of dynamical spacetime solutions of the Einstein field equations of gravity and the dynamics of its corresponding dual fluid flows governed by the Navier-Stokes (NS) equations of hydrodynamics. This striking connection has been explored in several dynamics-based approaches and has surfaced in various forms over the past four decades. In a recent construction, it has been shown that the manifold properties of geometric duals are in fact intimately connected to the dynamics of incompressible fluids, thus bypassing the conventional on-shell standpoints. Following such a prescription, we construct the geometrical description that effectively captures the dynamics of an incompressible NS fluid with respect to a uniformly rotating frame. We propose the gravitational dual(s) described by bulk metric(s) in $(p+2)$-dimensions such that the equations of parallel transport of an appropriately defined bulk velocity vector field when projected onto an induced timelike hypersurface require that the incompressible NS equation of a fluid relative to a uniformly rotating frame be satisfied at the relevant perturbative order in $(p+1)$-dimensions. We argue that free fluid flows on manifold(s) described by the proposed metric(s) can be effectively considered as an equivalent theory of non-relativistic viscous fluid dynamics with respect to (w.r.t) a uniform rotating frame. We also present suggestive insights as to how space-time rotation parameters encode information pertaining to the inertial effects in the corresponding fluid dual.

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arXiv2019

Effective metric in fluid-gravity duality through parallel transport: a proposal

The incompressible Navier-Stokes (NS) equation is known to govern the hydrodynamic limit of essentially any fluid and its rich non-linear structure has critical implications in both mathematics and physics. The employability of the methods of Riemannian geometry to the study of hydrodynamical flows has been previously explored from a purely mathematical perspective. In this work, we propose a bulk metric in $(p+2)$-dimensions with the construction being such that the induced metric is flat on a timelike $r = r_c$ (constant) slice. We then show that the equations of {\it parallel transport} for an appropriately defined bulk velocity vector field along its own direction on this manifold when projected onto the flat timelike hypersurface requires the satisfaction of the incompressible NS equation in $(p+1)$-dimensions. Additionally, the incompressibility condition of the fluid arises from a vanishing expansion parameter $θ$, which is known to govern the convergence (or divergence) of a congruence of arbitrary timelike curves on a given manifold. In this approach Einstein's equations do not play any role and this can be regarded as an {\it off-shell} description of fluid-gravity correspondence. We argue that {\it our metric effectively encapsulates the information of forcing terms in the governing equations as if a free fluid is parallel transported on this curved background}. We finally discuss the implications of this interesting observation and its potentiality in helping us to understand hydrodynamical flows in a probable new setting.

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arXiv2019

Quantum gravity as an emergent phenomenon

There ought to exist a reformulation of quantum theory which does not depend on classical time. To achieve such a reformulation, we introduce the concept of an atom of space-time-matter (STM). An STM atom is a classical non-commutative geometry, based on an asymmetric metric, and sourced by a closed string. Different such atoms interact via entanglement. The statistical thermodynamics of a large number of such atoms gives rise, at equilibrium, to a theory of quantum gravity. Far from equilibrium, where statistical fluctuations are large, the emergent theory reduces to classical general relativity. In this theory, classical black holes are far-from-equilibrium low entropy states, and their Hawking evaporation represents an attempt to return to the (maximum entropy) equilibrium quantum gravitational state.

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arXiv2018

Fluid description of gravity on a timelike cut-off surface: beyond Navier-Stokes equation

Over the past few decades, a host of theoretical evidence have surfaced that suggest a connection between theories of gravity and Navier-Stokes (NS) equation of fluid dynamics. It emerges out that gravity theory can be treated as some kind of fluid on a particular surface. Motivated by the work carried out by Bredberg et al (JHEP 1207, 146 (2012)) \cite{Bredberg:2011jq}, our paper focuses on including certain modes to the metric which are consistent with the so called hydrodynamic scaling and discuss the consequences, one of which appear in the form of Damour Navier Stokes (DNS) equation with the incompressibility condition. We also present an alternative route to the results by considering the metric as a perturbative expansion in the hydrodynamic scaling parameter $ε$ and with a specific gauge choice, thus modifying the metric. It is observed that the inclusion of certain modes in the metric corresponds to the solution of Einstein's equations in presence of a particular type of matter in the spacetime. This analysis reveals that gravity has both the NS and DNS description not only on a null surface, but also on a timelike surface. So far we are aware of, this analysis is the first attempt to illuminate the possibility of presenting the gravity dual of DNS equation on a timelike surface. In addition, an equivalence between the hydrodynamic expansion and the near-horizon expansion has also been studied in the present context.

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