arXiv subjects

Arnab Priya Saha

Publications and source records attributed to Arnab Priya Saha.

15 recordsLinked to original sources

arXiv2026

Asymptotic expansion of cavity Quasi-Normal Modes in Schwarzschild de-Sitter black hole

We study large-overtone quasi-normal modes of a massive scalar field in a four-dimensional Schwarzschild de-Sitter black hole in the presence of a wall placed at the static sphere. Dirichlet boundary condition is imposed at the wall. At leading order the quasi-normal modes with large overtones scale as $n$ for $n\gg 1$ and are inversely proportional to the bouncing time. We analyze correction terms up to $n^{-1}$ order in the asymptotic expansion.

gr-qc↗

arXiv2026

Five-point partial waves, splitting constraints and hidden zeros

We introduce a partial-wave basis for the double residues of five-point tree amplitudes involving identical external scalar particles, decomposing them into exchanges of definite spin at each internal channel. We verify this basis using massive spinor-helicity building blocks and by matching the resulting partial-wave coefficients against the tree-level five-point Veneziano amplitude at fixed mass levels. As an application, we express five-point splitting constraints -- the reduction of the five-point amplitude to products of four-point amplitudes on special kinematic loci -- as linear relations among the five-point partial-wave coefficients. At low mass levels these constraints, together with spin truncation, fix the full five-point partial-wave data in terms of the four-point coefficients and imply simple compatibility conditions; remarkably, imposing two independent splitting loci also forces the residue to vanish on their intersection, making the associated hidden zero manifest in partial-wave space. We also show that once both channels allow spin-2 exchange a genuine kernel can remain, indicating the need for additional higher-point input to achieve complete rigidity.

hep-th↗

arXiv2026

A stringy dispersion relation for field theory

We derive a local, crossing symmetric dispersion relation (CSDR) for 2-2 scattering amplitudes with a parametric ambiguity motivated by string theory. Various limits of the parameter lead to the fixed-t, fixed-s, and other known CSDRs. We also present formulae for higher-subtracted cases. Several examples are discussed for illustration. In particular, for the Veneziano and the Virasoro-Shapiro amplitudes, we derive parametric series representations which manifest poles in all channels and converge everywhere. We then discuss applications of our formalism for bootstrapping weakly-coupled gravitational EFTs. We demonstrate that even in the presence of the graviton pole, one can derive bounds on the Wilson coefficients while working in the forward limit, with the parameter acting as the IR regulator instead. Finally, we derive series representations for multi-variable, totally symmetric generalisations of the Veneziano and Virasoro-Shapiro amplitudes that manifest poles in all the variables. This is a first step towards dispersion relations for n-particle scattering amplitudes.

hep-th↗

arXiv2024

Bootstrapping string models with entanglement minimization and Machine-Learning

We present a new approach to bootstrapping string-like theories by exploiting a local crossing symmetric dispersion relation and field redefinition ambiguities. This approach enables us to use mass-level truncation and to go beyond the dual resonance hypothesis. We consider both open and closed strings, focusing mainly on open tree-level amplitudes with integer-spaced spectrum, and two leading Wilson coefficients as inputs. Using entanglement minimization in the form of the minimum of the first finite moment of linear entropy or entangling power, we get an excellent approximation to the superstring amplitudes, including the leading and sub-leading Regge trajectories. We find other interesting S-matrices which do not obey the duality hypothesis, but exhibit a transition from Regge behaviour to power law behaviour in the high energy limit. Finally, we also examine Machine-Learning techniques to do bootstrap and discuss potential advantages over the present approach.

hep-th↗

arXiv2024

On-shell functions on the Coulomb branch of $\mathcal{N}=4$ SYM

We study on-shell functions in the kinematic space for the Coulomb branch of $\mathcal{N}=4$ SYM. We construct BCFW bridges that help us build bigger on-shell functions. As a consequence, we provide on-shell diagram formulations for BCFW shifts that correspond to various mass configurations. We will use this to calculate the quadruple cut for the one-loop amplitude on the Coulomb branch and maximal cuts for higher-loops. We make preliminary comments on finding the inequivalent set of on-shell functions for the Coulomb branch.

hep-th↗

arXiv2024

Field theory expansions of string theory amplitudes

Motivated by quantum field theory (QFT) considerations, we present new representations of the Euler-Beta function and tree-level string theory amplitudes using a new two-channel, local, crossing symmetric dispersion relation. Unlike standard series representations, the new ones are analytic everywhere except at the poles, sum over poles in all channels and include contact interactions, in the spirit of QFT. This enables us to consider mass-level truncation, which preserves all the features of the original amplitudes. By starting with such expansions for generalized Euler-Beta functions and demanding QFT like features, we single out the open superstring amplitude. We demonstrate the difficulty in deforming away from the string amplitude and show that a class of such deformations can be potentially interesting when there is level truncation. Our considerations also lead to new QFT-inspired, parametric representations of the Zeta function and $π$, which show fast convergence.

hep-th↗

arXiv2024

Loop Amplitudes in the Coulomb Branch of $\mathcal{N}=4$ Super-Yang-Mills Theory

We study four point planar loop amplitudes at an arbitrary point in the Coulomb branch of $\mathcal{N}=4$ super-Yang-Mills theory. We study two particle unitary cuts up to four loop order. We explicitly verify that bubble and triangle graphs do not contribute at one loop level and show that the results hold at higher loop level as well. We also write down an all loop recursion relation for two particle reducible graphs for four point amplitudes.

hep-th↗

arXiv2022

On-shell Supersymmetry and higher-spin amplitudes

We use on-shell Supersymmetry to constrain the three-point function of two massless particles and one massive particle in 3+1 dimensions. We use this information to write down the tree-level four-point function of massless particles for $\mathcal{N}=1$, $2$ and $4$ theories. In particular, we derive the expressions for four-photon/gluon amplitudes with massive higher spin exchange in theories with $\mathcal{N}=4$ Supersymmetry in 3+1 dimensions.

hep-th↗

arXiv2022

Scattering Amplitudes and BCFW in $\mathcal{N}=2^{\ast}$ Theory

We use massive spinor helicity formalism to study scattering amplitudes in $\mathcal{N}=2^*$ super-Yang-Mills theory in four dimensions. We compute the amplitudes at an arbitrary point in the Coulomb branch of this theory. We compute amplitudes using projection from $\mathcal{N}=4$ theory and write three point amplitudes in a convenient form using special kinematics. We then compute four point amplitudes by carrying out massive BCFW shifts of the amplitudes. We find some of the shifted amplitudes have a pole at $z=\infty$. Taking the residue at $z=\infty$ into account ensures little group covariance of the final result.

hep-th↗

arXiv2021

One-loop integrand from generalised scattering equations

Generalised bi-adjoint scalar amplitudes, obtained from integrations over moduli space of punctured $\mathbb{CP}^{k-1}$, are novel extensions of the CHY formalism. These amplitudes have realisations in terms of Grassmannian cluster algebras. Recently connections between one-loop integrands for bi-adjoint cubic scalar theory and $\mathcal{D}_n$ cluster polytope have been established. In this paper using the $\text{Gr}\left(3,6\right)$ cluster algebra, we relate the singularities of $\left(3,6\right)$ amplitude to four-point one-loop integrand in the bi-adjoint cubic scalar theory through the $\mathcal{D}_{4}$ cluster polytope. We also study factorisation properties of the $(3,6)$ amplitude at various boundaries in the worldsheet.

hep-th↗

arXiv2021

Double Soft Theorem for Generalised Biadjoint Scalar Amplitudes

We study double soft theorem for the generalised biadjoint scalar field theory whose amplitudes are computed in terms of punctures on $\mathbb{CP}^{k-1}$. We find that whenever the double soft limit does not decouple into a product of single soft factors, the leading contributions to the double soft theorems come from the degenerate solutions, otherwise the non degenerate solutions dominate. Our analysis uses the regular solutions to the scattering equations. Most of the results are presented for $k=3$ but we show how they generalise to arbitrary $k$. We have explicit analytic results, for any $k$, in the case when soft external states are adjacent.

hep-th↗

arXiv2020

Proof of the Classical Soft Graviton Theorem in D=4

Classical subleading soft graviton theorem in four space-time dimensions determines the gravitational wave-form at late and early retarded time, generated during a scattering or explosion, in terms of the four momenta of the ingoing and outgoing objects. This result was `derived' earlier by taking the classical limit of the quantum soft graviton theorem, and making some assumptions about how to deal with the infrared divergences of the soft factor. In this paper we give a direct proof of this result by analyzing the classical equations of motion of gravity coupled to matter. We also extend the result to the electromagnetic wave-form generated during scattering of charged particles, and present a new conjecture on subsubleading corrections to the gravitational wave-form at early and late retarded time.

hep-th↗

arXiv2019

Modified celestial amplitude in Einstein gravity

In this paper we evaluate the modified celestial amplitude for gravitons and gluons, as defined in arXiv:1801.10171[hep-th]. We find that the modified (tree) amplitude is finite for gravitons in Einstein gravity. The modified amplitude behaves like correlation function of operators inserted at various points of null-infinity in the Minkowski space-time. Therefore, unlike the standard celestial amplitudes, these are three dimensional objects. We also show that this amplitude admits conformal soft factorization recently studied in the literature.

hep-th↗

arXiv2017

Double Soft Limit of Graviton Amplitude from the Cachazo-He-Yuan Formalism

We present a complete analysis for double soft limit of graviton scattering amplitude using the formalism proposed by Cachazo, He and Yuan. Our results agree with that obtained via BCFW recursion relations in arXiv:1504.05558. In addition we find precise relations between degenerate and nondegenerate solutions of scattering equations with local and nonlocal terms in the soft factor.

hep-th↗

arXiv2016

Double Soft Theorem for Perturbative Gravity

Following up on the recent work of Cachazo, He and Yuan \cite{arXiv:1503.04816 [hep-th]}, we derive the double soft graviton theorem in perturbative gravity. We show that the double soft theorem derived using CHY formula precisely matches with the perturbative computation involving Feynman diagrams. In particular, we find how certain delicate limits of Feynman diagrams play an important role in obtaining this equivalence.

hep-th↗