James Drummond
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Research Subjects
James Drummond has a total of 34 co-authors. Here are the top co-authors by number of shared publications:
- Ömer Gürdoğan
University of Southampton
11 shared publications - Hynek Paul
KU Leuven
8 shared publications - Jack Foster
University of Southampton
7 shared publications - Francesco Antonio Aprile
Department of Chemistry, Molecular Sciences Research Hub, Imperial College London, London, UK
6 shared publications - Georgios Papathanasiou
Deutsches Elektronen-Synchrotron DESY
5 shared publications - Rowan Wright
School of Physics and Astronomy University of Southampton SO17 1BJ Southampton UK
5 shared publications
Latest Publications
- Open Access
- 8 September 2026
- Published by Springer Nature in Journal of High Energy Physics
- Vol. 2026 (9) , 105
Singularities of massless scattering and cluster algebras
A bstract: Partial flag varieties arise in the context of massless scattering kinematics. They can be associated to both spinor-helicity variables and momentum twistor variables in two separate yet natural ways [1–3]. Here we report on evidence at five and six points that the cluster algebras associated to these partial flag varieties contain information relevant to non-dual conformal massless scattering amplitudes and related observables. At five points both spinor-helicity and momentum twistor cluster structures capture similar information about symbol alphabets. At six points we demonstrate that the momentum twistor structure captures a larger subset of the alphabet compared to the spinor-helicity one. We also observe that the associated cluster structures correctly predict the appearance of certain triples of symbol letters related to cluster mutation relations.
- 8 September 2026
- Published by Springer Nature in Journal of High Energy Physics
- Vol. 2026 (9) , 105
Open AccessSingularities of massless scattering and cluster algebras
A bstract: Partial flag varieties arise in the context of massless scattering kinematics. They can be associated to both spinor-helicity variables and momentum twistor variables in two separate yet natural ways [1–3]. Here we report on evidence at five and six points that the cluster algebras associated to these partial flag varieties contain information relevant to non-dual conformal massless scattering amplitudes and related observables. At five points both spinor-helicity and momentum twistor cluster structures capture similar information about symbol alphabets. At six points we demonstrate that the momentum twistor structure captures a larger subset of the alphabet compared to the spinor-helicity one. We also observe that the associated cluster structures correctly predict the appearance of certain triples of symbol letters related to cluster mutation relations.
- Open Access
Leading singularities of Wilson loop correlators from twistor Wilson loop diagrams
The leading singularities of one-loop scattering amplitudes in planar $\mathcal{N}=4$ super Yang-Mills theory are known to factorise into products of tree-level amplitudes, and this can be seen from a number of different perspectives e.g. generalised unitarity or on-shell diagrams. Here we investigate the leading singularities from the perspective of the Wilson loop expectation values to which these amplitudes are dual, in particular making use of the twistor Wilson loop formalism. We show that the factorisation of one-loop leading singularities of a null Wilson loop's expectation value into a product of tree-level objects is manifest at the level of twistor Wilson loop diagrams, and is a simple consequence of planarity, without appeal to e.g. unitarity on the amplitude side of the duality. We then use the same approach to derive compact formulae for the one-loop leading singularities of correlators of multiple light-like Wilson loop operators in terms of tree-level objects. Via the chiral box expansion, these formulae provide a simple route to writing down the $O(g^2)$ correlation function of any number of Wilson loops at any MHV degree.Open AccessLeading singularities of Wilson loop correlators from twistor Wilson loop diagrams
The leading singularities of one-loop scattering amplitudes in planar $\mathcal{N}=4$ super Yang-Mills theory are known to factorise into products of tree-level amplitudes, and this can be seen from a number of different perspectives e.g. generalised unitarity or on-shell diagrams. Here we investigate the leading singularities from the perspective of the Wilson loop expectation values to which these amplitudes are dual, in particular making use of the twistor Wilson loop formalism. We show that the factorisation of one-loop leading singularities of a null Wilson loop's expectation value into a product of tree-level objects is manifest at the level of twistor Wilson loop diagrams, and is a simple consequence of planarity, without appeal to e.g. unitarity on the amplitude side of the duality. We then use the same approach to derive compact formulae for the one-loop leading singularities of correlators of multiple light-like Wilson loop operators in terms of tree-level objects. Via the chiral box expansion, these formulae provide a simple route to writing down the $O(g^2)$ correlation function of any number of Wilson loops at any MHV degree. - Open Access
Light-like Wilson loops and the $\bar{Q}$-equation
In recent work we began a study of the correlators of multiple light-like Wilson loops in $\mathcal{N}=4$ super Yang-Mills theory, focussing primarily on tree-level calculations and, beyond tree-level, to the Abelian theory. Here we calculate $O(g^2)$ correlators of multiple light-like Wilson loops in the $SU(N)$ theory. We use the chiral box expansion and a study of the leading singularities of the loop integrand to arrive at integrated expressions for these objects. We then use the results of these calculations to verify that a natural generalisation of the $\bar{Q}$-equation, familiar from the study of single Wilson loops, holds in the $SU(N)$ theory. This $\bar{Q}$-equation should provide a valuable tool for the computation of multiple Wilson loop correlators at higher order in the coupling.Open AccessLight-like Wilson loops and the $\bar{Q}$-equation
In recent work we began a study of the correlators of multiple light-like Wilson loops in $\mathcal{N}=4$ super Yang-Mills theory, focussing primarily on tree-level calculations and, beyond tree-level, to the Abelian theory. Here we calculate $O(g^2)$ correlators of multiple light-like Wilson loops in the $SU(N)$ theory. We use the chiral box expansion and a study of the leading singularities of the loop integrand to arrive at integrated expressions for these objects. We then use the results of these calculations to verify that a natural generalisation of the $\bar{Q}$-equation, familiar from the study of single Wilson loops, holds in the $SU(N)$ theory. This $\bar{Q}$-equation should provide a valuable tool for the computation of multiple Wilson loop correlators at higher order in the coupling. - Open Access
Tropical symmetries of cluster algebras
We study tropicalisations of quasi-automorphisms of cluster algebras and show that their induced action on the g-vectors can be realized by tropicalising their action on the homogeneous $\hat{y}$ (or $\mathcal{X}$) variables of a chosen initial cluster. This perspective allows us to interpret the action on g-vectors as a change of coordinates in the tropical setting. Focusing on Grassmannian cluster algebras, we analyse tropicalisations of quasi-automorphisms in detail. We derive tropical analogues of the braid group action and the twist map on both g-vectors and tableaux. We introduce the notions of unstable and stable fixed points for quasi-automorphisms, which prove useful for constructing cluster monomials and non-real modules, respectively. As an application, we demonstrate that the counts of prime non-real tableaux with a fixed number of columns in $\mathrm{SSYT}(3, [9])$ and $\mathrm{SSYT}(4, [8])$, arising from the braid group action on stable fixed points, are governed by Euler's totient function. Furthermore, we apply our findings to scattering amplitudes in physics, providing a novel interpretation of the square root associated with the four-mass box integral via stable fixed points of quasi-automorphisms of the Grassmannian cluster algebra $\CC[\Gr(4,8)]$.Open AccessTropical symmetries of cluster algebras
We study tropicalisations of quasi-automorphisms of cluster algebras and show that their induced action on the g-vectors can be realized by tropicalising their action on the homogeneous $\hat{y}$ (or $\mathcal{X}$) variables of a chosen initial cluster. This perspective allows us to interpret the action on g-vectors as a change of coordinates in the tropical setting. Focusing on Grassmannian cluster algebras, we analyse tropicalisations of quasi-automorphisms in detail. We derive tropical analogues of the braid group action and the twist map on both g-vectors and tableaux. We introduce the notions of unstable and stable fixed points for quasi-automorphisms, which prove useful for constructing cluster monomials and non-real modules, respectively. As an application, we demonstrate that the counts of prime non-real tableaux with a fixed number of columns in $\mathrm{SSYT}(3, [9])$ and $\mathrm{SSYT}(4, [8])$, arising from the braid group action on stable fixed points, are governed by Euler's totient function. Furthermore, we apply our findings to scattering amplitudes in physics, providing a novel interpretation of the square root associated with the four-mass box integral via stable fixed points of quasi-automorphisms of the Grassmannian cluster algebra $\CC[\Gr(4,8)]$. - Open Access
Light-like Wilson loop correlators
It is well-known that the expectation values of null polygonal Wilson loops computed in planar \(\mathcal{N}=4\) super Yang-Mills theory are dual to MHV amplitudes in that theory, and moreover that the duality can be extended to higher helicity sectors through the introduction of super Wilson loops. In this first of a series of papers, we investigate the natural generalisation posed by correlation functions of multiple light-like loop operators, both in the bosonic case and in the case of super Wilson loops. Explicit calculations are presented in several cases and we verify that, in the Abelian theory, these objects obey a natural generalisation of the \(\bar{Q}\)-equation which relates different loop orders, kinematic configurations and Grassmann sectors.Open AccessLight-like Wilson loop correlators
It is well-known that the expectation values of null polygonal Wilson loops computed in planar \(\mathcal{N}=4\) super Yang-Mills theory are dual to MHV amplitudes in that theory, and moreover that the duality can be extended to higher helicity sectors through the introduction of super Wilson loops. In this first of a series of papers, we investigate the natural generalisation posed by correlation functions of multiple light-like loop operators, both in the bosonic case and in the case of super Wilson loops. Explicit calculations are presented in several cases and we verify that, in the Abelian theory, these objects obey a natural generalisation of the \(\bar{Q}\)-equation which relates different loop orders, kinematic configurations and Grassmann sectors. - Open Access
Singularities of massless scattering and cluster algebras
Partial flag varieties arise in the context of massless scattering kinematics. They can be associated to both spinor-helicity variables and momentum twistor variables in two separate yet natural ways. Here we report on evidence at five and six points that the cluster algebras associated to these partial flag varieties contain information relevant to non-dual conformal massless scattering amplitudes and related observables. At five points both spinor-helicity and momentum twistor cluster structures capture similar information about symbol alphabets. At six points we demonstrate that the momentum twistor structure captures a larger subset of the alphabet compared to the spinor-helicity one. We also observe that the associated cluster structures correctly predict the appearance of certain triples of symbol letters related to cluster mutation relations.
Open AccessSingularities of massless scattering and cluster algebras
Partial flag varieties arise in the context of massless scattering kinematics. They can be associated to both spinor-helicity variables and momentum twistor variables in two separate yet natural ways. Here we report on evidence at five and six points that the cluster algebras associated to these partial flag varieties contain information relevant to non-dual conformal massless scattering amplitudes and related observables. At five points both spinor-helicity and momentum twistor cluster structures capture similar information about symbol alphabets. At six points we demonstrate that the momentum twistor structure captures a larger subset of the alphabet compared to the spinor-helicity one. We also observe that the associated cluster structures correctly predict the appearance of certain triples of symbol letters related to cluster mutation relations.
- Open Access
- 2 November 2023
- Published by Springer Nature in Journal of High Energy Physics
- Vol. 2023 (11) , 1-38
Adjacency for scattering amplitudes from the Gröbner fan
Scattering amplitudes in planar $$ \mathcal{N} $$ = 4 super Yang-Mills theory exhibit singularities which reflect various aspects of the cluster algebras associated to the Grassmannians Gr(4, n) and their tropical counterparts. Here we investigate the potential origins of such structures and examine the extent to which they can be recovered from the Gröbner structure of the underlying Plücker ideals, focussing on the Grassmannians corresponding to finite cluster algebras.Starting from the Plücker ideal, we describe how the polynomial cluster variables are encoded in non-prime initial ideals associated to certain maximal cones of the positive tropical fan. Following [1] we show that extending the Plücker ideal by such variables leads to a Gröbner fan with a single maximal Gröbner cone spanned by the positive tropical rays. The associated initial ideal encodes the compatibility relations among the full set of cluster variables. Thus we find that the Gröbner structure naturally encodes both the symbol alphabet and the cluster adjacency relations exhibited by scattering amplitudes without invoking the cluster algebra at all.As a potential application of these ideas we then examine the kinematic ideal associated to non-dual conformal massless scattering written in terms of spinor helicity variables. For five-particle scattering we find that the ideal can be identified with the Plücker ideal for Gr(3, 6) and the corresponding tropical fan contains a number of non-prime ideals which encode all additional letters of the two-loop pentagon function alphabet present in various calculations of massless five-point finite remainders.- 2 November 2023
- Published by Springer Nature in Journal of High Energy Physics
- Vol. 2023 (11) , 1-38
Open AccessAdjacency for scattering amplitudes from the Gröbner fan
Scattering amplitudes in planar $$ \mathcal{N} $$ = 4 super Yang-Mills theory exhibit singularities which reflect various aspects of the cluster algebras associated to the Grassmannians Gr(4, n) and their tropical counterparts. Here we investigate the potential origins of such structures and examine the extent to which they can be recovered from the Gröbner structure of the underlying Plücker ideals, focussing on the Grassmannians corresponding to finite cluster algebras.Starting from the Plücker ideal, we describe how the polynomial cluster variables are encoded in non-prime initial ideals associated to certain maximal cones of the positive tropical fan. Following [1] we show that extending the Plücker ideal by such variables leads to a Gröbner fan with a single maximal Gröbner cone spanned by the positive tropical rays. The associated initial ideal encodes the compatibility relations among the full set of cluster variables. Thus we find that the Gröbner structure naturally encodes both the symbol alphabet and the cluster adjacency relations exhibited by scattering amplitudes without invoking the cluster algebra at all.As a potential application of these ideas we then examine the kinematic ideal associated to non-dual conformal massless scattering written in terms of spinor helicity variables. For five-particle scattering we find that the ideal can be identified with the Plücker ideal for Gr(3, 6) and the corresponding tropical fan contains a number of non-prime ideals which encode all additional letters of the two-loop pentagon function alphabet present in various calculations of massless five-point finite remainders. - Open Access
- 8 February 2023
- Published by Springer Nature in Journal of High Energy Physics
- Vol. 2023 (2) , 1-40
One-loop string amplitudes in AdS5×S5: Mellin space and sphere splitting
We study string corrections to one-loop amplitudes of single-particle operators $$ \mathcal{O} $$ p in AdS5×S5. The tree-level correlators in supergravity enjoy an accidental 10d conformal symmetry. Consequently, one observes a partial degeneracy in the spectrum of anomalous dimensions of double-trace operators and at the same time equality of many different correlators for different external charges pi=1,2,3,4. The one-loop contribution is expected to lift such bonus properties, and its precise form can be predicted from tree-level data and consistency with the operator product expansion.Here we present a closed-form Mellin space formula for $$ \left\langle {\mathcal{O}}_{p1}{\mathcal{O}}_{p2}{\mathcal{O}}_{p3}{\mathcal{O}}_{p4}\right\rangle $$ at order (α′)3, valid for arbitrary external charges pi. Our formula makes explicit the lifting of the bonus degeneracy among different correlators through a feature we refer to as ‘sphere splitting’. While tree-level Mellin amplitudes come with a single crossing symmetric kernel, which defines the pole structure of the AdS5× S5 amplitude, our one-loop amplitude naturally splits the S5 part into two separate contributions. The amplitude also exhibits a remarkable consistency with the corresponding flat space IIB amplitude through the large p limit.- 8 February 2023
- Published by Springer Nature in Journal of High Energy Physics
- Vol. 2023 (2) , 1-40
Open AccessOne-loop string amplitudes in AdS5×S5: Mellin space and sphere splitting
We study string corrections to one-loop amplitudes of single-particle operators $$ \mathcal{O} $$ p in AdS5×S5. The tree-level correlators in supergravity enjoy an accidental 10d conformal symmetry. Consequently, one observes a partial degeneracy in the spectrum of anomalous dimensions of double-trace operators and at the same time equality of many different correlators for different external charges pi=1,2,3,4. The one-loop contribution is expected to lift such bonus properties, and its precise form can be predicted from tree-level data and consistency with the operator product expansion.Here we present a closed-form Mellin space formula for $$ \left\langle {\mathcal{O}}_{p1}{\mathcal{O}}_{p2}{\mathcal{O}}_{p3}{\mathcal{O}}_{p4}\right\rangle $$ at order (α′)3, valid for arbitrary external charges pi. Our formula makes explicit the lifting of the bonus degeneracy among different correlators through a feature we refer to as ‘sphere splitting’. While tree-level Mellin amplitudes come with a single crossing symmetric kernel, which defines the pole structure of the AdS5× S5 amplitude, our one-loop amplitude naturally splits the S5 part into two separate contributions. The amplitude also exhibits a remarkable consistency with the corresponding flat space IIB amplitude through the large p limit. - Open Access
- 26 August 2022
- Published by Springer Nature in Journal of High Energy Physics
- Vol. 2022 (8) , 1-48
Two-loop supergravity on AdS5×S5 from CFT
We describe a construction of the two-loop amplitude of four graviton supermultiplets in AdS5×S5. We start from an ansatz for a preamplitude from which we generate the full amplitude under the action of a specific Casimir operator. The ansatz captures a recent ansatz of Huang and Yuan and we confirm their result through similar constraints. The form of the result suggests that all ambiguities are captured by the preamplitude which determines the result up to tree-level ambiguities only. We identify a class of four-dimensional ‘zigzag’ integrals which are perfectly adapted to describing the leading logarithmic discontinuity to all orders. We also observe that a bonus crossing symmetry of the preamplitude follows from the transformation properties of the Casimir operator. Combined with the zigzag integrals this allows us to construct a crossing symmetric function with the correct leading logarithmic discontinuities in all channels.From the two-loop result we extract an explicit expression for the two-loop correction to the anomalous dimensions of twist-four operators of generic spin which includes dependence on (alternating) nested harmonic sums up to weight three. We also revisit the prescription of the bulk-point limit of AdS amplitudes and show how it recovers the full flat-space amplitude, not just its discontinuity. With this extended notion of the bulk-point limit we reproduce the scale-dependent logarithmic threshold terms of type IIB string theory in flat-space.
- 26 August 2022
- Published by Springer Nature in Journal of High Energy Physics
- Vol. 2022 (8) , 1-48
Open AccessTwo-loop supergravity on AdS5×S5 from CFT
We describe a construction of the two-loop amplitude of four graviton supermultiplets in AdS5×S5. We start from an ansatz for a preamplitude from which we generate the full amplitude under the action of a specific Casimir operator. The ansatz captures a recent ansatz of Huang and Yuan and we confirm their result through similar constraints. The form of the result suggests that all ambiguities are captured by the preamplitude which determines the result up to tree-level ambiguities only. We identify a class of four-dimensional ‘zigzag’ integrals which are perfectly adapted to describing the leading logarithmic discontinuity to all orders. We also observe that a bonus crossing symmetry of the preamplitude follows from the transformation properties of the Casimir operator. Combined with the zigzag integrals this allows us to construct a crossing symmetric function with the correct leading logarithmic discontinuities in all channels.From the two-loop result we extract an explicit expression for the two-loop correction to the anomalous dimensions of twist-four operators of generic spin which includes dependence on (alternating) nested harmonic sums up to weight three. We also revisit the prescription of the bulk-point limit of AdS amplitudes and show how it recovers the full flat-space amplitude, not just its discontinuity. With this extended notion of the bulk-point limit we reproduce the scale-dependent logarithmic threshold terms of type IIB string theory in flat-space.
- Open Access
- 10 December 2021
- Published by Springer Nature in Journal of High Energy Physics
- Vol. 2021 (12) , 1-25
One-loop string corrections for AdS Kaluza-Klein amplitudes
We discuss the string corrections to one-loop amplitudes in AdS5×S5, focussing on their expressions in Mellin space. We present the leading (α′)3 corrections to the family of correlators $$ \left\langle {\mathcal{O}}_2{\mathcal{O}}_2{\mathcal{O}}_p{\mathcal{O}}_p\right\rangle $$ at one loop and begin the exploration of the form of correlators with multiple channels. From these correlators we extract some string corrections to one- loop anomalous dimensions of families of operators of low twist.- 10 December 2021
- Published by Springer Nature in Journal of High Energy Physics
- Vol. 2021 (12) , 1-25
Open AccessOne-loop string corrections for AdS Kaluza-Klein amplitudes
We discuss the string corrections to one-loop amplitudes in AdS5×S5, focussing on their expressions in Mellin space. We present the leading (α′)3 corrections to the family of correlators $$ \left\langle {\mathcal{O}}_2{\mathcal{O}}_2{\mathcal{O}}_p{\mathcal{O}}_p\right\rangle $$ at one loop and begin the exploration of the form of correlators with multiple channels. From these correlators we extract some string corrections to one- loop anomalous dimensions of families of operators of low twist.