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Nikhil Kalyanapuram

Publications and source records attributed to Nikhil Kalyanapuram.

At least 19 recordsLinked to original sources
arXiv2026

Nonlinear Tellegen limit

The Tellegen limit is the fundamental electromagnetic stability bound on magnetoelectric media. We show that nonlinear magnetoelectric coupling gives rise to a new Tellegen limit, which we term the nonlinear Tellegen limit. Unlike the linear Tellegen limit, which is fixed by material parameters, the nonlinear Tellegen limit is field-tunable -- a static electric or magnetic field drives the system toward electromagnetic instability at a material-specific critical field determined by the magnetic point group symmetry. The approach to this limit is accompanied by a field-tunable Faraday rotation that grows linearly with the applied field and is bounded from above by a universal maximum set by the nonlinear Tellegen limit -- beyond which the medium becomes electromagnetically unstable. We demonstrate the nonlinear Tellegen limit and the field-space stability phase diagram in two magnetically ordered material systems -- a d-wave altermagnet and an M-type hexagonal ferrite -- showing that the symmetry of the magnetic point group governs both the structure of the nonlinear magnetoelectric tensor and the resulting electromagnetic instability.

cond-mat.mtrl-sci↗
arXiv2023

Gauge-Invariant Double-Copies via Recursion

We prove that all tree-level amplitudes in pure (super-)gravity can be expressed as term-wise, gauge-invariant double-copies of those of pure (super-)Yang-Mills obtained via BCFW recursion. These representations are far from unique: varying the recursive scheme leads to a wide variety of distinct, but equally valid representations of gravitational amplitudes, all realized as double-copies.

hep-th↗
arXiv2023

Prescriptive Unitarity and Rigidity at Two Loops

We elaborate upon and consolidate various recent developments focusing on the triality of questions offered by issues of basis building, unitarity and non-polylogarithmicity in quantum field theory, specifically for planar two loops. The interplay between the dual questions of setting up bases of integrands and accurately preparing a complete set of cuts to secure correct \emph{ansätze} of loop integrands expanded thereby is enriched by the appearance of non-polylogarithmic structures, first seen in planar two loops in the form of elliptic polylogarithms. We strengthen this by presenting an extended discussion of a new method of building bases, classifying loop integrands by power counting, or their behaviour in the ultraviolet and studying a convenient, albeit manifestly non-canonical set of cuts of full rank. By studying cut equations derived from poorly chosen contours in loop momentum space, the question of finding morally good sets of cuts to accommodate ellipticity at two loops is forced upon us. We discuss a generalization of the notion of a leading singularity in this case -- something we call an elliptic leading singularity -- a concept which only makes reference to the underlying geometry of the elliptic curve. We also expand upon the task of constructing master integrand bases that neatly distinguish between elliptic and ordinary polylogs. This stratification of the basis -- where each master is either pure elliptic or polylog -- is carried out by drawing on an expanded basis at two loops, the so-called triangle power counting basis. In the course of developing such a master integrand basis, we emphasize the importance of choosing, intelligently, spanning sets of cuts, and writing down integrand numerators dual to these cuts that are diagonal -- or prescriptive -- with regard to these choices, to highlight the conceptual and technical simplifications arising therefrom.

hep-th↗
arXiv2022

The Stratification of Rigidity

We show that a master integrand basis exists for all planar, two-loop amplitudes in massless four-dimensional theories which is fully stratified by rigidity -- with each integrand being either pure and strictly polylogarithmic or (pure and) strictly elliptic-polylogarithmic, with each of the later involving a single elliptic curve. Such integrands can be said to have definite rigidity.

hep-th↗
arXiv2021

Holographic Representations of Supertranslation Eigenstates

We construct by direct computation holographic presentations of supertranslation vacua given a set of supermomenta. To do this, we make use of two-dimensional dual models recently discovered by the author, which encode soft dynamics of gravity at leading order. In particular, the two-dimensional models are used to define soft currents, of which the supertranslation vacua are eigenstates. Operationally, the eigenstates are determined by the bare vacuum state dressed by exponential operators that generalize the dressing due to Faddeev and Kulish.

hep-th↗
arXiv2021

Infrared and Holographic Aspects of the $S$-Matrix in Gauge Theory and Gravity

Soft theorems in gauge theory and gravity encode the universal properties of scattering amplitudes as the zero frequency limit of one or more external states is approached. When the participating particles are treated in the massless limit, the soft theorems are known to depend only on the directions of the states on null infinity. Leveraging this fact, we develop dual two-dimensional descriptions of soft theorems, recasting them as Ward identities of such dual models on the celestial sphere. This is done by first postulating putative holographic representations of the hard scattering amplitudes and dressing the asymptotic operators with appropriate two-dimensional analogues of the Wilson line. The soft theorems are then recovered by inserting currents that generate the Ward identities of the dual models. In addition to providing naturally holographic representations of the soft theorems, we see that it becomes possible to develop presentations of the asymptotic symmetries associated to these theorems entirely in terms of the dual two-dimensional fields. In the course of carrying out this analysis for soft theorems at leading order and beyond, we find that the two-dimensional dual description of soft theorems may be directly inferred by drawing analogies with the existing framework of asymptotic symmetry charges. We find that the soft charges generating the asymptotic symmetries can be brought into correspondence with dual two-dimensional currents, while the two-dimensional Wilson loops can be related to the hard parts of the conserved charges. Consequently, we rewrite the triality of asymptotic symmetries, soft theorems and conserved charges directly in the language of a class of two-dimensional theories.

hep-th↗
arXiv2021

The Holographic Soft $S$-Matrix in QED and Gravity

At leading order, the $S$-matrices in QED and gravity are known to factorise, providing unambiguous determinations of the parts divergent due to infrared contributions. The soft $S$-matrices defined in this fashion are shown to be defined entirely in terms of $2$ dimensional models on the celestial sphere, involving two real scalar fields, allowing us to express the soft $S$-matrices for real as well as virtual divergences as two dimensional correlation functions. We discuss what this means for finding holographic representations of scattering amplitudes in QED and gravity and comment on simple double copy structures that arise during the analysis.

hep-th↗
arXiv2021

Gauge and Gravity Amplitudes on the Celestial Sphere

The analytic structures of scattering amplitudes in gauge theory and gravity are examined on the celestial sphere. The celestial amplitudes in the two theories - computed by employing a regulated Mellin transform - can be compared at low multiplicity. It is established by direct computation that up to five external particles, the double copy relations of Kawai, Lewellen and Tye continue to hold identically, modulo certain multiplicative factors which are explicitly determined. Supersymmetric representations of the amplitudes are utilized throughout, manifesting the double copy structure between $\mathcal{N}=4$ super Yang-Mills and $\mathcal{N}=8$ supergravity on the celestial sphere.

hep-th↗
arXiv2021

Soft Gravity by Squaring Soft QED on the Celestial Sphere

We recast the soft $S$-matrices on the celestial sphere as correlation functions of certain $2$-dimensional models of topological defects. In pointing out the double copy structure between the soft photon and soft graviton cases, we arrive at a putative classical double copy between the corresponding topological models and a rederivation of gauge invariance and the equivalence principle as Ward identities of the $2$-dimensional theories.

hep-th↗
arXiv2021

On Chiral Splitting and the Ambitwistor String

Scattering amplitudes computed by superstring perturbation theory are known to holomorphically split into chiral half integrands at fixed internal loop momentum. It is established by direct computation that upon reduction to the ordinary moduli space, the chiral half integrands of the superstring match those computed by the ambitwistor string in the limit of zero tension ($α'\rightarrow\infty$). Subtleties that arise at higher genus due to the nonprojectedness of the supermoduli space are considered and arguments as to their resolution are furnished.

hep-th↗
arXiv2021

Prescriptive Unitarity with Elliptic Leading Singularities

We investigate the consequences of elliptic leading singularities for the unitarity-based representations of two-loop amplitudes in planar, maximally supersymmetric Yang-Mills theory. We show that diagonalizing with respect to these leading singularities ensures that the integrand basis is term-wise pure (suitably generalized, to the elliptic multiple polylogarithms, as necessary). We also investigate an alternative strategy based on diagonalizing a basis of integrands on differential forms; this strategy, while neither term-wise Yangian-invariant nor pure, offers several advantages in terms of complexity.

hep-th↗
arXiv2020

Geometric Recursion from Polytope Triangulations and Twisted Homology

A geometric approach to understanding recursion relations for scattering amplitudes is developed. We achieve this by studying intersection numbers of triangulated accordiohedra presented as hyperplane arrangements. The cancellation of spurious divergences is subsequently realized as a topological no-boundary condition.

hep-th↗
arXiv2020

On Polytopes and Generalizations of the KLT Relations

We combine the technology of the theory of polytopes and twisted intersection theory to derive a large class of double copy relations that generalize the classical relations due to Kawai, Lewellen and Tye (KLT) . To do this, we first study a generalization of the scattering equations of Cachazo, He and Yuan. While the scattering equations were defined on $\mathcal{M}_{0,n}$ - the moduli space of marked Riemann spheres - the new scattering equations are defined on polytopes known as accordiohedra, realized as hyperplane arrangements. These polytopes encode as patterns of intersection the scattering amplitudes of generic scalar theories. The twisted period relations of such intersection numbers provide a vast generalization of the KLT relations. Differential forms dual to the bounded chambers of the hyperplane arrangements furnish a natural generalization of the Bern-Carrasco-Johansson (BCJ) basis, the number of which can be determined by counting the number of solutions of the generalized scattering equations. In this work the focus is on a generalization of the BCJ expansion to generic scalar theories, although we use the labels KLT and BCJ interchangeably.

hep-th↗
arXiv2020

Positive Geometries for all Scalar Theories from Twisted Intersection Theory

We show that accordiohedra furnish polytopes which encode amplitudes for all massive scalar field theories with generic interactions. This is done by deriving integral formulae for the Feynman diagrams at tree level and integrands at one loop level in the planar limit using the twisted intersection theory of convex realizations of the accordiohedron polytopes.

hep-th↗
arXiv2020

Stokes Polytopes and Intersection Theory

Intersection numbers of Stokes polytopes living in complex projective space are computed using the techniques employed to find the inverse string KLT matrix elements in terms of intersection numbers of associahedra. To do this requires an appropriate convex realization of Stokes polytopes in $\mathbb{CP}^{n}$ loaded with suitable generalizations of the Koba-Nielsen factor. The procedure is carried out explicitly for the lower point cases and the prescription for the generic higher point cases is laid out as well. The intersection numbers are identified as scattering amplitudes corresponding to a theory the coupling constants of which are determined entirely in terms of the combinatorial weights of the Stokes polytopes. A parameter $α'$ having units of length is used to define the intersection numbers in a manner that yields the amplitudes of $ϕ^4$ theory to leading order when the limit of vanishing $α'$ limit is taken. Most importantly, we contrast this method of understanding quartic vertices with previous string-theoretic attempts to obtain quartic interaction amplitudes and highlight the advantages offered.

hep-th↗