arXiv subjects

Shruti Paranjape

Publications and source records attributed to Shruti Paranjape.

At least 19 recordsLinked to original sources

arXiv2026

Cluster Bootstrap for Cosmological Correlators

We show that cosmological wavefunction coefficients associated with $n$-site chain and loop graphs for a cubic scalar theory in de Sitter spacetime have symbol alphabets given by subsets of $A_{2n{-}2}$ and $B_{2n{-}1}$ cluster variables, respectively, and satisfy the associated cluster adjacency properties. The key step in proving this is identifying a precise connection between graph "tubings" that appear in the kinematic flow equation and polygon "triangulations" that encode the combinatorics of cluster compatibility. Our results imply that cosmological wavefunction coefficients in a general power-law FRW cosmology satisfy cluster adjacency to all orders in the $ε$ expansion around the de Sitter limit. We use this information as bootstrap input to show that de Sitter symbols for $n \leq 4$ are uniquely determined by simple physical constraints.

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arXiv2026

Bound States in Perturbative Quantum Gravity with Hydrogen-like Degeneracy

Recent results in the study of gravitational scattering amplitudes indicate that some highly-symmetric relativistic systems may exactly conserve a version of the Laplace-Runge-Lenz (LRL) vector in two-body bound states. We make a systematic study, in the context of a generic EFT of long-range interactions due to the exchange of massless mediator particles of spins 0, $\frac{1}{2}$, 1, $\frac{3}{2}$, 2, of the conditions for the conservation of a hidden LRL vector; both classically (no orbital precession) and quantum mechanically (hydrogen-like degeneracy of bound states). The calculations require several new technical developments including the extension of relativistic post-Minkowskian potential matching to quantum corrections and the incorporation of long-range forces due to the exchange of pairs of massless fermions. We find that while classically the absence of precession is a generic property of a large class of models, including Kaluza-Klein theories, with vector and scalar exchanges, maintaining the degeneracy quantum mechanically requires a surprising cancellation between gravitons and 6 Majorana gravitinos, hinting at a special role for $\mathcal{N}=6$ supergravity.

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arXiv2026

Multi-Loop Negative Geometries

Scattering amplitudes in planar ${\cal N}=4$ supersymmetric Yang-Mills theory are dual to expectation values of null polygonal Wilson loops. The Amplituhedron provides a geometric construction for the all-loop integrand as the canonical form on the geometric region in the Grassmannian defined by a certain set of inequalities. For a closely related object, the logarithm of the scattering amplitude, the integrand is reproduced in a similar way using negative geometries. When integrated over all loop momenta except one, the result is infrared (IR) finite and equal to the expectation value of a certain Wilson loop with a Lagrangian insertion. At four points, this quantity, ${\cal F}(g,z)$ only depends on a single cross ratio $z$ and the 't Hooft coupling $g$. At weak coupling, it is known up to three loops from perturbative Wilson loop computations and at strong coupling through the AdS/CFT correspondence at leading order. In this paper, we explore this object further through the lens of the Amplituhedron and negative geometries, which provide very natural IR finite building blocks. We perform an explicit three-loop computation of all negative geometries and show that the number of internal cycles in the diagram is closely linked to the depth of polylogarithms. We calculate the cusp anomalous dimension $Γ_{\rm cusp}$ by integrating ${\cal F}(g,z)$ over $z$. We show that the higher-cycle diagrams are suppressed if we consider separate odd and even zeta contributions. Furthermore, we focus on certain convergent infinite series of one-cycle diagrams, perform all-loop order resummations of such contributions, and discuss various features of the result.

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arXiv2026

Landau Analysis of One-Cycle Negative Geometries

We use geometric Landau analysis to determine the singularity structure of four-point, one-cycle negative geometries in $\mathcal{N}=4$ super-Yang-Mills theory, which represent certain contributions to the logarithm of the four-point amplitude or equivalently the normalized quadrangular Wilson loop with a Lagrangian insertion. By analyzing the relevant Landau diagrams recursively, we prove that this quantity has singularities only at $z=-1,0$ and $\infty$ to all loop orders. This represents a first step towards obtaining a non-perturbative resummation for this quantity at next-to-leading order in the expansion over cycles.

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arXiv2025

Split-Helicity Tree Amplitudes and Flag Cluster Algebras

Recent work has uncovered a connection between the symbol letters of general massless scattering and (permutations of) cluster variables of partial flag varieties. In this paper we explore the cluster adjacency of tree-level gluon amplitudes, specifically focusing on split-helicity amplitudes which can be written in closed form in terms of zigzag diagrams. We check in several cases, and conjecture in general, that the poles in each term satisfy cluster adjacency under a set of permutations that is built from arc permutations of the corresponding zigzag.

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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$(ϕ^3)$ amplitudes, enabling us to leverage the cosmological zeros to uncover the recently discovered hidden zeros of colored amplitudes.

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arXiv2025

Smooth Splitting and Zeros from On-Shell Recursion

We describe a new approach to understanding the origins of recently discovered "hidden zeros" and "smooth splitting" of tree-level amplitudes in $\text{Tr}ϕ^3$, Non-Linear Sigma Model (NLSM), Yang-Mill-Scalar (YMS) and the special Galileon. Introducing a new type of linear shift in kinematic space we demonstrate that the mysterious splitting formulae follow from a simple contour integration argument in the style of on-shell recursion. The argument makes use of only standard notions of tree-level factorization on propagators, but assumes improved UV behavior in the form of the absence of a residue at infinity. In the case of $\text{Tr}ϕ^3$ and NLSM this is proven by identifying our shift as a special case of a more general construction called a $g$-vector shift; in the case of YMS it remains an unproven conjecture. This recursive perspective leads to numerous new results: we derive generalizations of the splitting formulae on more relaxed near-zero kinematics, including interesting new kinematic limits in which the amplitude splits into a triple-product; we also demonstrate that the uncolored special Galileon model has improved UV scaling and hence also splits. We also investigate the possible realization of hidden zeros in four dimensions. The conditions under which the dimensionality constraints are compatible with zero kinematics is investigated in detail for $\text{Tr}ϕ^3$ and YMS; for the latter we find they can be realized only with certain restrictions on external helicity states. The realizable 4d zeros are proven by a similar recursive argument based on BCFW and is found to generalize to a new class of intrinsically 4d "helicity zeros" present in all sectors of YM and also gravity.

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arXiv2025

Large deformations of Tr($Φ^3$) and the world at infinity

The amplitudes of the non-linear sigma model can be obtained from those of Tr($Φ^3$) theory by sending the kinematic (Mandelstam) variables to infinity in a certain direction. In this paper we characterize the behavior of Tr($Φ^3$) amplitudes under a general class of large kinematic shifts called $g$-vector shifts. The objects that live in this world at infinity retain certain key amplitude-like properties, most notably factorization, and admit descriptions in terms of polytopes, but they are not generally amplitudes of any cognizable theory. We identify particular $g$-vector shifts that lead at infinity to mixed amplitudes involving two pions and any number of scalars, allowing us to provide polytopal descriptions of these amplitudes.

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arXiv2024

Uniqueness of MHV Gravity Amplitudes

We investigate MHV tree-level gravity amplitudes as defined on the spinor-helicity variety. Unlike their gluon counterparts, the gravity amplitudes do not have logarithmic singularities and do not admit Amplituhedron-like construction. Importantly, they are not determined just by their singularities, but rather their numerators have interesting zeroes. We make a conjecture about the uniqueness of the numerator and explore this feature from a more mathematical perspective. This leads us to a new approach for examining adjoints. We outline steps of our proposed proof and provide computational evidence for its validity in specific cases.

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arXiv2024

Thermalization and non-monotonic entanglement growth in an exactly solvable model

We study quantum quenches and subsequent non-equilibrium dynamics of free Dirac fermions in 1+1 spacetime dimensions using time dependent mass. The final state is a normalized boundary state which is called generalized Calabrese-Cardy (gCC) state and the system thermalizes to a generalized Gibb's Ensemble(GGE). We can also tune the initial states so that the final states are exact Calabrese-Cardy (CC) state and special gCC states. The system in the CC state thermalizes to a Gibb's ensemble. We derive closed-form analytic expressions for the growth of entanglement entropy of subsystems consisting of arbitrary number of disjoint intervals in CC state. We show that the entanglement entropy of a single interval grows monotonically before saturation. In case of certain gCC states, for particular charges, the entanglement entropy of a single interval grows non-monotonically when the effective chemical potential is increased beyond a critical value. We argue that the non-monotonic growth of entanglement entropy is due to increase in long range correlation and decrease in short range correlation at early times.

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arXiv2024

Hidden Amplitude Zeros From Double Copy

Recently, Arkani-Hamed et al. proposed the existence of zeros in scattering amplitudes in certain quantum field theories including the cubic adjoint scalar theory Tr($ϕ^3$), the $SU(N)$ non-linear sigma model (NLSM) and Yang-Mills (YM) theory. These hidden zeros are special kinematic points where the amplitude vanishes and factorizes into a product of lower-point amplitudes, similar to factorization near poles. In this letter, we show a close connection between the existence of such zeros and color-kinematics duality. In fact, all zeros can be derived from the Bern-Carrasco-Johansson (BCJ) relations. We also show that these zeros extend via the Kawai-Lewellen-Tye (KLT) relations to special Galileon amplitudes and their corrections, evincing that these hidden zeros are also present in permutation-invariant amplitudes.

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arXiv2024

Supersymmetric Massive Gravity

We initiate a systematic study of the self-interactions of a massive spin-2 "graviton" consistent with up to $\mathcal{N}=4$ supersymmetry. Using a recently developed massive on-shell superspace formalism, we construct the most general set of cubic massive graviton amplitudes in a form with all supersymmetry and Lorentz invariance manifest. We find that for $\mathcal{N}\geq 3$ supersymmetry, the family of consistent interactions coincide with those of the ghost-free dRGT model. For $\mathcal{N}=4$ (maximal) supersymmetry there is a single consistent cubic interaction which coincides with the unique structure required for the absence of asymptotic superluminality. Additionally, we discuss the structure of interactions in the high-energy limit, connections to supersymmetric Galileons and the possibility of a supersymmetric massive double copy.

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arXiv2023

Loops of Loops Expansion in the Amplituhedron

We study a novel geometric expansion for scattering amplitudes in the planar sector of N=4 super Yang-Mills theory, in the context of the Amplituhedron which reproduces the all-loop integrand as a canonical differential form on the positive geometry. In a paper by Arkani-Hamed, Henn and one of the authors, it was shown that this result can be recast in terms of negative geometries with a certain hierarchy of loops (closed cycles) in the space of loop momenta, represented by lines in momentum twistor space. One can then calculate an all-loop order result in the approximation where only tree graphs in the space of all loops are considered. Furthermore, using differential equation methods, it is possible to calculate and resum integrated expressions and obtain strong coupling results. In this paper, we provide a more general framework for the loops of loops expansion and outline a powerful method for the determination of differential forms for higher-order geometries. We solve the problem completely for graphs with one internal cycle, but the method can be used more generally for other geometries.

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arXiv2023

Gravity Amplitudes From Double Bonus Relations

In this letter we derive new expressions for tree-level graviton amplitudes in $\mathcal{N}=8$ supergravity from BCFW recursion relations combined with new types of bonus relations. These bonus relations go beyond the famous $1/z^2$ behavior under a large BCFW shift, and use knowledge about certain zeroes of graviton amplitudes in collinear kinematics. This extra knowledge can be used in the context of global residue theorems by writing the amplitude in a special form using canonical building blocks. In the NMHV case these building blocks are dressed one-loop leading singularities, the same objects that appear in the expansion of Yang-Mills amplitudes, where each term corresponds to an $R$-invariant. Unlike other approaches, our formula is not an expansion in terms of cyclic objects and does not manifest color-kinematics duality, but rather preserves the permutational symmetry of its building blocks. We also comment on the possible connection to Grassmannian geometry and give some non-trivial evidence of such structure for graviton amplitudes.

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arXiv2023

Scalar BCJ Bootstrap

In this letter, we study tree-level scattering amplitudes of scalar particles in the context of effective field theories. We use tools similar to the soft bootstrap to build an ansatz for cyclically ordered amplitudes and impose the Bern-Carrasco-Johansson (BCJ) relations as a constraint. We obtain a set of BCJ-satisfying amplitudes as solutions to our procedure, which can be thought of as special higher-derivative corrections to SU(N) non-linear sigma model amplitudes satisfying BCJ relations to arbitrary multiplicity at leading order. The surprising outcome of our analysis is that BCJ conditions on higher-point amplitudes impose constraints on lower-point amplitudes, and they relate coefficients at different orders in the derivative expansion. This shows that BCJ conditions are much more restrictive than soft limit behavior, allowing only for a very small set of solutions.

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arXiv2022

Non-planar BCFW Grassmannian Geometries

In this paper, we study non-adjacent BCFW recursion relations and their connection to positive geometry. For an adjacent BCFW shift, the $n$-point N$^k$MHV tree-level amplitude in ${\cal N}=4$ SYM theory is expressed as a sum over planar on-shell diagrams, corresponding to canonical dlog forms on the cells in the positive Grassmannian $G_+(k,n)$. Non-adjacent BCFW shifts naturally lead to an expansion of the amplitude in terms of a different set of objects, which do not manifest the cyclic ordering and the hidden Yangian symmetry of the amplitude. We show that these terms can be interpreted as dlog forms on the non-planar Grassmannian geometries, generalizing the cells of the positive Grassmannian $G_+(k,n)$ to a larger class of objects which live in $G(k,n)$. We focus mainly on the case of NMHV amplitudes and discuss in detail the Grassmannian geometries. We also propose an alternative way to calculate the associated on-shell functions and dlog forms using an intriguing connection between Grassmannian configurations and the geometry in the kinematical space.

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arXiv2021

Generalizations of the Double-Copy: the KLT Bootstrap

We formulate a new program to generalize the double-copy of tree amplitudes. The approach exploits the link between the identity element of the KLT algebra and the KLT kernel, and we demonstrate how this leads to a set of KLT bootstrap equations that the double-copy kernel has to satisfy (in addition to locality constraints). We solve the KLT bootstrap equations perturbatively to find the most general higher-derivative corrections to the 4- and 5-point field theory KLT kernel. The new kernel generalizes the string KLT kernel and its associated monodromy relations. It admits new color-structures in the effective theories it double-copies. It provides distinct generalized KK and BCJ relations for the left and right single-color theories and is in that sense a heterotic-type double-copy. We illustrate the generalized double-copy in detail for 4d Yang-Mills theory with higher-derivative corrections that produce dilaton-axion-gravity with local operators up order $\nabla^{10} R^4$. Finally, we initiate a search for new double-copy kernels.

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arXiv2021

Electromagnetic Duality and D3-Brane Scattering Amplitudes Beyond Leading Order

We use on-shell methods to study the non-supersymmetric and supersymmetric low-energy S-matrix on a probe D3-brane, including both the 1-loop contributions of massless states as well as the effects of higher-derivative operators. Our results include: (1) A derivation of the duality invariance of Born-Infeld electrodynamics as the dimensional oxidation of the group of spatial rotations transverse to a probe M2-brane; this is done using a novel implementation of subtracted on-shell recursion. (2) The first explicit loop-level BCJ double-copy in a non-gravitational model, namely the calculation of the 4-point self-dual amplitude of non-supersymmetric Born-Infeld. (3) From previous results for $n$-point self-dual 1-loop BI amplitudes and the conjectured dimension-shifting relations in Yang-Mills, we obtain an explicit all-multiplicity, at all orders in $ε$, expression for the 1-loop integrand of the MHV sector of $\mathcal{N}=4$ DBI. (4) For all $n>4$, the explicitly integrated duality-violating 1-loop amplitudes (self-dual and next-to-self-dual in pure BI as well as MHV in $\mathcal{N}=4$ DBI) are shown to be removable at $\mathcal{O}(ε^0)$ by adding finite local counterterms; we propose that this may be true more generally at 1-loop order. (5) We find that in non-supersymmetric Born-Infeld, not all finite local counterterms needed to restore electromagnetic duality can be constructed using the double-copy with higher-derivative corrections, suggesting a fundamental tension between electromagnetic duality and color-kinematics duality at loop-level. Finally we comment on oxidation of duality symmetries in supergravity and the parallels it has to the M2-brane to D3-brane oxidation demonstrated in this paper.

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