Atul Sharma
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Research Subjects
Atul Sharma has a total of 27 co-authors. Here are the top co-authors by number of shared publications:
- Tim Adamo
University of Edinburgh
14 shared publications - Lionel Mason
The Mathematical Institute, University of Oxford, Woodstock Road, Oxford OX2 6GG, United Kingdom
11 shared publications - Eduardo Casali
Universidade de São Paulo
6 shared publications - David Skinner
University of Cambridge
4 shared publications - Diandian Wang
Harvard University
4 shared publications - Wei Bu
University of Edinburgh
4 shared publications
Latest Publications
- Open Access
- 25 August 2026
- Published by Springer Nature in Journal of High Energy Physics
- Vol. 2026 (8) , 202
Chiral holography
A bstract: Using twistor string theory, we engineer a gravitational holographic dual of the self-dual sector of $$ \mathcal{N} $$ = 4 super Yang-Mills theory. This provides a top-down example of holography at zero ’t Hooft coupling. Our holographic dictionary operates at the level of D-branes wrapping twistor lines and generalizes the D-instanton prescription used to compute scattering amplitudes. As an application, we study the correlators of determinant operators that act as generating functions of half-BPS operators in the self-dual theory. We show that these correlators are dual to configurations of giant gravitons in the bulk.- 25 August 2026
- Published by Springer Nature in Journal of High Energy Physics
- Vol. 2026 (8) , 202
Open AccessChiral holography
A bstract: Using twistor string theory, we engineer a gravitational holographic dual of the self-dual sector of $$ \mathcal{N} $$ = 4 super Yang-Mills theory. This provides a top-down example of holography at zero ’t Hooft coupling. Our holographic dictionary operates at the level of D-branes wrapping twistor lines and generalizes the D-instanton prescription used to compute scattering amplitudes. As an application, we study the correlators of determinant operators that act as generating functions of half-BPS operators in the self-dual theory. We show that these correlators are dual to configurations of giant gravitons in the bulk. - Open Access
- 9 March 2026
- Published by IOP Publishing in Classical and Quantum Gravity
- Vol. 43 (5) , 055005
Graviton scattering on self-dual black holes
The computation of gravitational wave scattering on black hole spacetimes is an extremely hard problem, typically requiring approximation schemes that either treat the black hole perturbatively or are only amenable to numerical techniques. In this paper, we consider linearised gravitational waves (or gravitons) scattering on the self-dual analogue of a black hole: namely, the self-dual Taub-NUT (SDTN) metric. Using the hidden integrability of the self-dual sector, we solve the linearised Einstein equations on these self-dual black hole backgrounds exactly in terms of simple, explicit quasi-momentum eigenstates. Using a description of the SDTN metric and its gravitons in terms of twistor theory, we obtain an explicit formula, exact in the background, for the tree-level maximal helicity violating (MHV) graviton scattering amplitude at arbitrary multiplicity, with and without spin. This is obtained from the description of the MHV amplitudes in terms of the perturbation theory of a chiral sigma model whose target is the twistor space of the background. The incorporation of spin effects on these backgrounds is a straightforward application of the Newman–Janis shift. We also demonstrate that the holomorphic collinear splitting functions in the self-dual background are equal to those in flat space so that the celestial symmetry algebra is undeformed.
- 9 March 2026
- Published by IOP Publishing in Classical and Quantum Gravity
- Vol. 43 (5) , 055005
Open AccessGraviton scattering on self-dual black holes
The computation of gravitational wave scattering on black hole spacetimes is an extremely hard problem, typically requiring approximation schemes that either treat the black hole perturbatively or are only amenable to numerical techniques. In this paper, we consider linearised gravitational waves (or gravitons) scattering on the self-dual analogue of a black hole: namely, the self-dual Taub-NUT (SDTN) metric. Using the hidden integrability of the self-dual sector, we solve the linearised Einstein equations on these self-dual black hole backgrounds exactly in terms of simple, explicit quasi-momentum eigenstates. Using a description of the SDTN metric and its gravitons in terms of twistor theory, we obtain an explicit formula, exact in the background, for the tree-level maximal helicity violating (MHV) graviton scattering amplitude at arbitrary multiplicity, with and without spin. This is obtained from the description of the MHV amplitudes in terms of the perturbation theory of a chiral sigma model whose target is the twistor space of the background. The incorporation of spin effects on these backgrounds is a straightforward application of the Newman–Janis shift. We also demonstrate that the holomorphic collinear splitting functions in the self-dual background are equal to those in flat space so that the celestial symmetry algebra is undeformed.
- Open Access
Chiral holography
Using twistor string theory, we engineer a gravitational holographic dual of the self-dual sector of $\mathcal{N}=4$ super Yang-Mills theory. This provides a top-down example of holography at zero 't Hooft coupling. Our holographic dictionary operates at the level of D-branes wrapping twistor lines and generalizes the D-instanton prescription used to compute scattering amplitudes. As an application, we study the correlators of determinant operators that act as generating functions of half-BPS operators in the self-dual theory. We show that these correlators are dual to configurations of giant gravitons in the bulk.Open AccessChiral holography
Using twistor string theory, we engineer a gravitational holographic dual of the self-dual sector of $\mathcal{N}=4$ super Yang-Mills theory. This provides a top-down example of holography at zero 't Hooft coupling. Our holographic dictionary operates at the level of D-branes wrapping twistor lines and generalizes the D-instanton prescription used to compute scattering amplitudes. As an application, we study the correlators of determinant operators that act as generating functions of half-BPS operators in the self-dual theory. We show that these correlators are dual to configurations of giant gravitons in the bulk. - Open Access
- 12 September 2025
- Published by IOP Publishing in Classical and Quantum Gravity
- Vol. 42 (19)
S-algebra in Gauge Theory: Twistor, Spacetime and Holographic Perspectives
The celestial $S$-algebra arose from a reinterpretation of collinear limits of the Yang-Mills S-matrix as OPEs in celestial holography. It was subsequently represented via asymptotic charge aspects defined in the Yang-Mills radiative phase space defined at null infinity on the one hand, and via a twisted holography vertex algebra construction in twistor space on the other. Here we first identify it with the traditional symmetry algebra of self-dual Yang-Mills theory as an integrable system via its hierarchies of conserved quantities and associated flows; the self-dual phase space can be canonically identified with that of full Yang-Mills at null infinity $\scri$. We derive the associated canonical generators from the twistor space action, identifying two infinite towers of charges corresponding to the two gluon helicities. These expressions are translated into spacetime data at null infinity using twistor integral formulae. Examining the charge algebra at spacelike infinity reveals the vertex algebras studied in the context of twisted holography. Our discussion extends directly to the celestial $\text{LHam}(\C^2)$ symmetries of self-dual gravity. This analysis provides a unified framework for celestial symmetries, connecting twistor, spacetime, and holographic approaches and culminating in a nonlinear extrapolate dictionary for self-dual gauge theory.- 12 September 2025
- Published by IOP Publishing in Classical and Quantum Gravity
- Vol. 42 (19)
Open AccessS-algebra in Gauge Theory: Twistor, Spacetime and Holographic Perspectives
The celestial $S$-algebra arose from a reinterpretation of collinear limits of the Yang-Mills S-matrix as OPEs in celestial holography. It was subsequently represented via asymptotic charge aspects defined in the Yang-Mills radiative phase space defined at null infinity on the one hand, and via a twisted holography vertex algebra construction in twistor space on the other. Here we first identify it with the traditional symmetry algebra of self-dual Yang-Mills theory as an integrable system via its hierarchies of conserved quantities and associated flows; the self-dual phase space can be canonically identified with that of full Yang-Mills at null infinity $\scri$. We derive the associated canonical generators from the twistor space action, identifying two infinite towers of charges corresponding to the two gluon helicities. These expressions are translated into spacetime data at null infinity using twistor integral formulae. Examining the charge algebra at spacelike infinity reveals the vertex algebras studied in the context of twisted holography. Our discussion extends directly to the celestial $\text{LHam}(\C^2)$ symmetries of self-dual gravity. This analysis provides a unified framework for celestial symmetries, connecting twistor, spacetime, and holographic approaches and culminating in a nonlinear extrapolate dictionary for self-dual gauge theory. - Open Access
S-algebra in Gauge Theory: Twistor, Spacetime and Holographic Perspectives
The celestial $S$-algebra arose from a reinterpretation of collinear limits of the Yang-Mills S-matrix as OPEs in celestial holography. It was subsequently represented via asymptotic charge aspects defined in the Yang-Mills radiative phase space defined at null infinity on the one hand, and via a twisted holography vertex algebra construction in twistor space on the other. Here we first identify it with the traditional symmetry algebra of self-dual Yang-Mills theory as an integrable system via its hierarchies of conserved quantities and associated flows; the self-dual phase space can be canonically identified with that of full Yang-Mills at null infinity $\mathscr{I}$. We derive the associated canonical generators from the twistor space action, identifying two infinite towers of charges corresponding to the two gluon helicities. These expressions are translated into spacetime data at null infinity using twistor integral formulae. Examining the charge algebra at spacelike infinity reveals the vertex algebras studied in the context of twisted holography. Our discussion extends directly to the celestial LHam$(\mathbb{C}^2)$ symmetries of self-dual gravity. This analysis provides a unified framework for celestial symmetries, connecting twistor, spacetime, and holographic approaches and culminating in a nonlinear extrapolate dictionary for self-dual gauge theory.Open AccessS-algebra in Gauge Theory: Twistor, Spacetime and Holographic Perspectives
The celestial $S$-algebra arose from a reinterpretation of collinear limits of the Yang-Mills S-matrix as OPEs in celestial holography. It was subsequently represented via asymptotic charge aspects defined in the Yang-Mills radiative phase space defined at null infinity on the one hand, and via a twisted holography vertex algebra construction in twistor space on the other. Here we first identify it with the traditional symmetry algebra of self-dual Yang-Mills theory as an integrable system via its hierarchies of conserved quantities and associated flows; the self-dual phase space can be canonically identified with that of full Yang-Mills at null infinity $\mathscr{I}$. We derive the associated canonical generators from the twistor space action, identifying two infinite towers of charges corresponding to the two gluon helicities. These expressions are translated into spacetime data at null infinity using twistor integral formulae. Examining the charge algebra at spacelike infinity reveals the vertex algebras studied in the context of twisted holography. Our discussion extends directly to the celestial LHam$(\mathbb{C}^2)$ symmetries of self-dual gravity. This analysis provides a unified framework for celestial symmetries, connecting twistor, spacetime, and holographic approaches and culminating in a nonlinear extrapolate dictionary for self-dual gauge theory. - Open Access
Chiral higher-spin theories from twistor space
We reformulate chiral higher-spin Yang-Mills and gravity on $\mathbb{R}^4$ as 'CR-holomorphic' theories of Chern-Simons type; in the most general case, these are Moyal deformed to become non-commutative. They are defined on the space of non-projective twistors of unit length. These spaces carry $S^7$, $S^3\times \mathbb{R}^4$ or AdS$_{3+4}$ metrics but are also endowed with a Cauchy-Riemann structure, an odd-dimensional analogue of a complex structure, with respect to which the theories are holomorphic. They are circle bundles over standard projective twistor spaces and the higher spin fields arise naturally as Kaluza-Klein modes. We give a perturbative analysis to identify the spectrum and three-point vertices on spacetime and, for flat space, in momentum space. These vertices can have helicities $(+++)$, $(++-)$ or $(+--)$, but are nevertheless all of $\overline{\text{MHV}}$ type in the sense that they are supported on momenta with proportional anti-self-dual spinors. On reduction to spacetime, there are higher valence vertices but these appear to be a gauge artifact. Further generalizations are discussed.Open AccessChiral higher-spin theories from twistor space
We reformulate chiral higher-spin Yang-Mills and gravity on $\mathbb{R}^4$ as 'CR-holomorphic' theories of Chern-Simons type; in the most general case, these are Moyal deformed to become non-commutative. They are defined on the space of non-projective twistors of unit length. These spaces carry $S^7$, $S^3\times \mathbb{R}^4$ or AdS$_{3+4}$ metrics but are also endowed with a Cauchy-Riemann structure, an odd-dimensional analogue of a complex structure, with respect to which the theories are holomorphic. They are circle bundles over standard projective twistor spaces and the higher spin fields arise naturally as Kaluza-Klein modes. We give a perturbative analysis to identify the spectrum and three-point vertices on spacetime and, for flat space, in momentum space. These vertices can have helicities $(+++)$, $(++-)$ or $(+--)$, but are nevertheless all of $\overline{\text{MHV}}$ type in the sense that they are supported on momenta with proportional anti-self-dual spinors. On reduction to spacetime, there are higher valence vertices but these appear to be a gauge artifact. Further generalizations are discussed. - 17 April 2025
- Published by IOP Publishing in Journal of Physics A: Mathematical and Theoretical
- Vol. 58 (16) , 165401
No-boundary state for Klein space
Analytic continuation from (3, 1) signature Minkowski to (2, 2) signature Klein space has emerged as a useful tool for the understanding of scattering amplitudes and flat space holography. Under this continuation, past and future null infinity merge into a single boundary ( J ) which is the product of a null line with a (1, 1) signature torus. The Minkowskian S -matrix continues to a Kleinian S -vector which in turn may be represented by a Poincaré-invariant vacuum state | C ⟩ in the Hilbert space built on J . | C ⟩ contains all information about S in a novel, repackaged form. We give an explicit construction of | C ⟩ in a Lorentz/conformal basis for a free massless scalar. J separates into two halves J ± which are the asymptotic null boundaries of the regions timelike and spacelike separated from the origin. | C ⟩ is shown to be a maximally entangled state in the product of the J ± Hilbert spaces.
- 17 April 2025
- Published by IOP Publishing in Journal of Physics A: Mathematical and Theoretical
- Vol. 58 (16) , 165401
No-boundary state for Klein space
Analytic continuation from (3, 1) signature Minkowski to (2, 2) signature Klein space has emerged as a useful tool for the understanding of scattering amplitudes and flat space holography. Under this continuation, past and future null infinity merge into a single boundary ( J ) which is the product of a null line with a (1, 1) signature torus. The Minkowskian S -matrix continues to a Kleinian S -vector which in turn may be represented by a Poincaré-invariant vacuum state | C ⟩ in the Hilbert space built on J . | C ⟩ contains all information about S in a novel, repackaged form. We give an explicit construction of | C ⟩ in a Lorentz/conformal basis for a free massless scalar. J separates into two halves J ± which are the asymptotic null boundaries of the regions timelike and spacelike separated from the origin. | C ⟩ is shown to be a maximally entangled state in the product of the J ± Hilbert spaces.
- Open Access
- 8 February 2025
- Published by Springer Nature in Letters in Mathematical Physics
- Vol. 115 (1) , 1-32
Gluon scattering on the self-dual dyon
The computation of scattering amplitudes in the presence of non-trivial background gauge fields is an important but extremely difficult problem in quantum field theory. In even the simplest backgrounds, obtaining explicit formulae for processes involving more than a few external particles is often intractable. Recently, it has been shown that remarkable progress can be made by considering background fields which are chiral in nature. In this paper, we obtain a compact expression for the tree-level, maximal helicity violating (MHV) scattering amplitude of an arbitrary number of gluons in the background of a self-dual dyon. This is a Cartan-valued, complex gauge field sourced by a point particle with equal electric and magnetic charges and can be viewed as the self-dual version of a Coulomb field. Twistor theory enables us to manifest the underlying integrability of the self-dual dyon, trivializing the perturbative expansion in the MHV sector. The formula contains a single position-space integral over a spatial slice, which can be evaluated explicitly in simple cases. As an application of the formula, we show that the holomorphic collinear splitting functions of gluons in the self-dual dyon background are un-deformed from a trivial background, meaning that holomorphic celestial OPE coefficients and the associated chiral algebra are similarly un-deformed. We also comment on extensions of our MHV formula to the full tree-level gluon S-matrix.
- 8 February 2025
- Published by Springer Nature in Letters in Mathematical Physics
- Vol. 115 (1) , 1-32
Open AccessGluon scattering on the self-dual dyon
The computation of scattering amplitudes in the presence of non-trivial background gauge fields is an important but extremely difficult problem in quantum field theory. In even the simplest backgrounds, obtaining explicit formulae for processes involving more than a few external particles is often intractable. Recently, it has been shown that remarkable progress can be made by considering background fields which are chiral in nature. In this paper, we obtain a compact expression for the tree-level, maximal helicity violating (MHV) scattering amplitude of an arbitrary number of gluons in the background of a self-dual dyon. This is a Cartan-valued, complex gauge field sourced by a point particle with equal electric and magnetic charges and can be viewed as the self-dual version of a Coulomb field. Twistor theory enables us to manifest the underlying integrability of the self-dual dyon, trivializing the perturbative expansion in the MHV sector. The formula contains a single position-space integral over a spatial slice, which can be evaluated explicitly in simple cases. As an application of the formula, we show that the holomorphic collinear splitting functions of gluons in the self-dual dyon background are un-deformed from a trivial background, meaning that holomorphic celestial OPE coefficients and the associated chiral algebra are similarly un-deformed. We also comment on extensions of our MHV formula to the full tree-level gluon S-matrix.
- Open Access
- 30 August 2024
- Published by American Physical Society (APS) in Physical Review Letters
- Vol. 133 (9) , 091603
Celestial Dual for Maximal Helicity Violating Amplitudes
It is shown that a 2D conformal field theory consisting of a central charge Liouville theory, a chiral level one, rank Kac-Moody algebra, and a weight free fermion holographically generate 4D maximal helicity violating tree-level scattering amplitudes. The correlators of this 2D conformal field theory give directly the 4D leaf amplitudes associated to a single hyperbolic slice of flat space. The 4D celestial amplitudes arise in a large- and semiclassical large- limit, according to the holographic dictionary, as a translationally invariant combination of leaf amplitudes. A step in the demonstration is showing that the semiclassical limit of Liouville correlators are given by contact 3D anti–de Sitter Witten diagrams.- 30 August 2024
- Published by American Physical Society (APS) in Physical Review Letters
- Vol. 133 (9) , 091603
Open AccessCelestial Dual for Maximal Helicity Violating Amplitudes
It is shown that a 2D conformal field theory consisting of a central charge Liouville theory, a chiral level one, rank Kac-Moody algebra, and a weight free fermion holographically generate 4D maximal helicity violating tree-level scattering amplitudes. The correlators of this 2D conformal field theory give directly the 4D leaf amplitudes associated to a single hyperbolic slice of flat space. The 4D celestial amplitudes arise in a large- and semiclassical large- limit, according to the holographic dictionary, as a translationally invariant combination of leaf amplitudes. A step in the demonstration is showing that the semiclassical limit of Liouville correlators are given by contact 3D anti–de Sitter Witten diagrams. - Open Access
- 15 July 2024
- Published by Springer Nature in Journal of High Energy Physics
- Vol. 2024 (7) , 1-18
Celestial leaf amplitudes
Celestial amplitudes may be decomposed as weighted integrals of AdS3-Witten diagrams associated to each leaf of a hyperbolic foliation of spacetime. We show, for the Kleinian three-point MHV amplitude, that each leaf subamplitude is smooth except for the expected light-cone singularities. Moreover, we find that the full translationally-invariant celestial amplitude is simply the residue of the pole in the leaf amplitude at the point where the total conformal weights of the gluons equals three. This full celestial amplitude vanishes up to light-cone contact terms, as required by spacetime translation invariance, and reduces to the expression previously derived by Mellin transformation of the Parke-Taylor formula.
- 15 July 2024
- Published by Springer Nature in Journal of High Energy Physics
- Vol. 2024 (7) , 1-18
Open AccessCelestial leaf amplitudes
Celestial amplitudes may be decomposed as weighted integrals of AdS3-Witten diagrams associated to each leaf of a hyperbolic foliation of spacetime. We show, for the Kleinian three-point MHV amplitude, that each leaf subamplitude is smooth except for the expected light-cone singularities. Moreover, we find that the full translationally-invariant celestial amplitude is simply the residue of the pole in the leaf amplitude at the point where the total conformal weights of the gluons equals three. This full celestial amplitude vanishes up to light-cone contact terms, as required by spacetime translation invariance, and reduces to the expression previously derived by Mellin transformation of the Parke-Taylor formula.