Are perturbative superstring amplitudes for massless external states just an $\textit{α}$ dressing of super-Yang-Mills/supergravity? This is the case at tree level, where the worldsheet correlators at $\textit{n}$ points can be written in a natural worldsheet basis, such that the kinematic coefficients are BCJ numerators of super-Yang-Mills/supergravity amplitudes, with the non-trivial $\textit{α}$ dependence carried only by the Koba-Nielsen factor. Motivated by this construction, we present for the first time a complete worldsheet basis of one-loop superstring correlators at $\textit{n}$ points. All the kinematic coefficients associated to non-cusp basis elements are identified with pieces of one-loop BCJ numerators of super-Yang-Mills/supergravity. This determines the superstring correlators up to 15 points in terms of field theory. Starting at 16 points (modular weight 12), the worldsheet basis may include cusp forms, which vanish in the field-theory degeneration, such that the associated coefficients cannot be fixed in this manner. Therefore, the one-loop answer to our initial question is determined, at high multiplicity, by whether the coefficients of cusp basis elements vanish or not. As a by-product of our construction, we present new constraints on the field-theory limit that result from string modularity. These are expressed as additional relations among one-loop BCJ numerators in maximal super-Yang-Mills/supergravity starting at 6 points.

United Kingdom

Ricardo Monteiro

Lecheng Ren

Superstring amplitudes from the field-theory limit: an $\textit{n}$-point map at one loop

We find a direct map that determines moduli-space integrands for one-loop superstring amplitudes in terms of field-theory loop integrands in the BCJ form. The latter can be computed using efficient unitarity methods, so our map provides an alternative to worldsheet CFT techniques. This construction is a one-loop higher-point analogue of a recent conjecture for the three-loop four-point superstring amplitude. Based on the one-loop chiral-splitting representation, we show how all the coefficients of an ansatz for the superstring can be identified with field-theory BCJ numerators, up to at least 7-point amplitudes. Moreover, we obtain partial results for all higher-point amplitudes. The monodromy constraints associated to chiral splitting play a crucial role in determining coefficients of the ansatz that, naively, are not fixed by the field-theory limit. Taking a field-theory perspective, our ansatz for the superstring implies by construction the existence of one-loop BCJ numerators at any multiplicity.

Thailand

Yvonne Geyer

Jiachen Guo

Superstring amplitudes from BCJ numerators at one loop

Self-dual Yang-Mills and Einstein gravity in Euclidean AdS are useful toy models because they can be described by simple scalar Lagrangians exhibiting a new manifestation of the colour/kinematics duality, as recently shown by two of the authors. In this paper, we clarify how the self-dual sectors fit into the full theories. In particular, we explicitly construct the light-cone action for Yang-Mills theory and Einstein gravity in AdS in terms of positive and negative helicity fields, where we are able to pinpoint the self-dual sector as expected. We then show that the boundary correlators of these theories take a remarkably simple form in terms of Feynman diagrams in half of flat space, acted on by certain differential operators. We also analyse their soft limits and show that they exhibit Weinberg-like soft factors, where the soft pole which appears in scattering amplitudes is replaced by a derivative with respect to the energy.

Chandramouli Chowdhury

George Doran

Arthur Lipstein

Silvia Nagy

India

Kajal Singh

Light-cone actions and correlators of self-dual theories in AdS

We investigate the integrability anomalies arising in the self-dual sectors of gravity and Yang-Mills theory, focusing on their connection to both the chiral anomaly and the trace anomaly. The anomalies in the self-dual sectors generate the one-loop all-plus amplitudes of gravitons and gluons, and have recently been studied via twistor constructions. On the one hand, we show how they can be interpreted as an anomaly of the chiral U(1) electric-magnetic-type duality in the self-dual sectors. We also note the similarity, for the usual fermionic chiral anomaly, between the 4D setting of self-dual Yang-Mills and the 2D setting of the Schwinger model. On the other hand, the anomalies in the self-dual theories also resemble the trace anomaly, sharing the same type of non-local effective action. We highlight the role of a Weyl-covariant fourth-order differential operator familiar from the trace anomaly literature, which (i) explains the conformal properties of the one-loop amplitudes, and (ii) indicates how this story may be extended to non-trivial spacetime backgrounds, e.g. with a cosmological constant. Moving beyond the self-dual sectors, and focusing on the gravity case, we comment on an intriguing connection to the two-loop ultraviolet divergence of pure gravity, whereby cancelling the anomaly at one-loop eliminates the two-loop divergence for the simplest helicity amplitudes.

Sweden

Sam Wikeley

On the anomaly interpretation of amplitudes in self-dual Yang-Mills and gravity

We revisit the question of whether classical general relativity obeys, beyond the linearised order, an analogue of the global U(1) electric-magnetic duality of Maxwell theory, with the Riemann tensor playing the role analogous to the field strength. Following contradictory claims in the literature, we present a simple gauge-invariant argument that the duality does not hold. The duality condition is the conservation of the helicity charge. Scattering amplitudes of gravitons in general relativity, and of gluons in Yang-Mills theory, violate this selection rule already at tree level. Indeed, the maximally-helicity-violating (MHV) amplitudes are famous for their simplicity. The duality in the linearised theories is, therefore, broken by the interactions. In contrast, the tree-level scattering amplitudes in duality-invariant theories of non-linear electromagnetism are known to obey helicity conservation. While the duality is not a symmetry of the full theory of general relativity, it does hold within a sector of the solution space, including vacuum type D solutions, where the duality is known to rotate between mass and NUT charge.

No U(1) ‘electric-magnetic’ duality in Einstein gravity

Recent works have explored how scattering amplitudes in quantum self-dual Yang-Mills theory and self-dual gravity can be interpreted as resulting from an anomaly, as first proposed by W. Bardeen. We study this problem in the light-cone-gauge formulation of the theories. Firstly, we describe how the infinite tower of symmetries associated to classical integrability can be quantum corrected, exhibiting the one-loop anomaly. Secondly, we present quantum-corrected light-cone Lagrangians worthy of the simplicity of the amplitudes, building on recent works describing the anomaly in twistor space. Finally, we discover an unexpected BCJ-like double copy for the (loop-integrated) amplitudes, distinct from the well-known BCJ double copy for the loop integrands.

Ricardo Stark-Muchão

Anomaly and double copy in quantum self-dual Yang-Mills and gravity

We study the connection of Moyal deformations of self-dual gravity and self-dual Yang-Mills theory to chiral higher-spin theories, and also to deformations of operator algebras in celestial holography. The relation to Moyal deformations illuminates various aspects of the structure of chiral higher-spin theories. For instance, the appearance of the self-dual kinematic algebra in all the theories considered here leads via the double copy to vanishing tree-level scattering amplitudes. Regarding celestial holography, the Moyal deformation of self-dual gravity was recently shown to lead to the loop algebra of W ∧, and we obtain here the analogous deformation of a Kac-Moody algebra corresponding to Moyal-deformed self-dual Yang-Mills theory. We also introduce the celestial algebras for various chiral higher-spin theories.

From Moyal deformations to chiral higher-spin theories and to celestial algebras

We study celestial chiral algebras appearing in celestial holography, using the light-cone gauge formulation of self-dual Yang-Mills theory and self-dual gravity, and explore also a deformation of the latter. The recently discussed w 1+∞  algebra in self-dual gravity arises from the soft expansion of an area-preserving diffeomorphism algebra, which plays the role of the kinematic algebra in the colour-kinematics duality and the double copy relation between the self-dual theories. The W 1+∞  deformation of w 1+∞  arises from a Moyal deformation of self-dual gravity. This theory is interpreted as a constrained chiral higher-spin gravity, where the field is a tower of higher-spin components fully constrained by the graviton component. In all these theories, the chiral structure of the operator-product expansion exhibits the colour-kinematics duality: the implicit ‘left algebra’ is the self-dual kinematic algebra, while the ‘right algebra’ provides the structure constants of the operator-product expansion, ensuring its associativity at tree level. In a scattering amplitudes version of the Ward conjecture, the left algebra ensures the classical integrability of this type of theories. In particular, it enforces the vanishing of the tree-level amplitudes via the double copy.

Celestial chiral algebras, colour-kinematics duality and integrability

Recent work has shown how on-shell three-point amplitudes in gauge theory and gravity, representing the coupling to massive particles, correspond in the classical limit to the curvature spinors of linearised solutions. This connection, made explicit via the KMOC formalism in split metric signature, turns the double copy of scattering amplitudes into the double copy of classical solutions. Here, we extend this framework to the universal massless sector of supergravity, which is the complete double copy of pure gauge theory. Our extension relies on a Riemann-Cartan curvature incorporating the dilaton and the B-field. In this setting, we can determine the most general double copy arising from the product of distinct gauge theory solutions, say a dyon and   <math> <msqrt> <mtext>Kerr</mtext> </msqrt> </math>  $$ \sqrt{\mathrm{Kerr}} $$ . This gives a double-copy interpretation to gravity solutions of the type Kerr-Taub-NUT-dilaton-axion. We also discuss the extension to heterotic gravity. Finally, we describe how this formalism for the classical double copy relates to others in the literature, namely (i) why it is an on-shell momentum space analogue of the convolutional prescription, and (ii) why a straightforward prescription in position space is possible for certain vacuum solutions.

Donal O’Connell

David Veiga

Matteo Sergola

NS-NS spacetimes from amplitudes

A characteristic value formulation of the Weyl double copy leads to an asymptotic formulation. We find that the Weyl double copy holds asymptotically in cases where the full solution is algebraically general, using rotating STU supergravity black holes as an example. The asymptotic formulation provides clues regarding the relation between asymptotic symmetries that follows from the double copy. Using the C-metric as an example, we show that a previous interpretation of this gravity solution as a superrotation has a single copy analogue relating the appropriate Liénard-Wiechert potential to a large gauge transformation.