arXiv subjects

Henriette Elvang

Publications and source records attributed to Henriette Elvang.

At least 19 recordsLinked to original sources

arXiv2026

String Theory from Maximal Supersymmetry

We explore the space of non-gravitational, maximally supersymmetric, planar 4d effective field theories (EFTs) that have $\mathcal{N}=4$ super Yang-Mills (SYM) at leading order. In the weakly-coupled regime, we examine the combined constraints of $\mathcal{N}=4$ supersymmetry and $SU(4)$ R-symmetry together with the requirement of standard tree-level factorization on the massless poles of the 4-, 5-, and 6-point EFT scattering amplitudes. When imposing a parity condition on the 6-scalar amplitudes, we find highly nontrivial nonlinear constraints on the 4-point Wilson coefficients. When these novel constraints are combined with positivity, the resulting bounds on the 4-point Wilson coefficients converge to the values of the open string Veneziano amplitude. Our results strongly suggest that supersymmetry, R-symmetry, the parity requirement on the 6-scalar amplitudes, and positivity are sufficient to single out this unique UV completion at tree level. Our findings, moreover, highlight the power of higher-point amplitudes in constraining EFT data and imply that the space of consistent quantum field theories is even more restricted than previously suggested by causality or swampland-based approaches.

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arXiv2026

Gravitational Effective Theories with Maximal Supersymmetry and a Peculiar Parity

We study the space of four-dimensional ultraviolet completions for $\mathcal{N}=8$ supergravity that are described at low energies by weakly-coupled effective field theories (EFTs) with maximal supersymmetry and $\mathrm{SU}(4)\times\mathrm{SU}(4)$ R-symmetry. We show that tree-level factorization of the 4-, 5-, and 6-point EFT scattering amplitudes, together with a certain ``peculiar parity'' condition, leads to nonlinear constraints on the 4-point Wilson coefficients. This peculiar parity is a property that can only be imposed on a subset of scalar amplitudes. Combining the nonlinear constraints with positivity, we find that the allowed region of 4-point Wilson coefficients is reduced to a non-convex domain with two sharp corners: one being the closed superstring Virasoro--Shapiro amplitude, the other an infinite spin tower amplitude exchanging states of every spin at the same mass. We show both numerically and analytically that requiring a finite number of states near the first mass level leaves only the Virasoro--Shapiro amplitude.

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arXiv2025

Splitting Regions and Shrinking Islands from Higher Point Constraints

We study constraints from higher-point amplitudes on $2 \to 2$ scattering in the context of effective field theory (EFT) using the perturbative numerical S-matrix bootstrap. Specifically, we investigate the class of weakly coupled EFTs with amplitudes that obey the hidden zero and split conditions that are known to hold both for Tr($Φ^3$) theory and for certain string tree amplitudes, including at 4-point the beta function. Requiring the splitting condition for the 5-point amplitude not only fixes nearly all its contact terms, but it also imposes non-linear constraints among the 4-point EFT Wilson coefficients. When included in the bootstrap, the resulting allowed region consistent with positivity is no longer convex but is restricted to a smaller non-convex region - which has a sharp corner near the string beta function! Assuming the absence of an infinite spin tower at the mass gap, the allowed region bifurcates into a trivial region (with states only above a chosen cutoff) and an island that continues to shrink around the string as more constraints are included in the bootstrap. The numerics indicate that in the absence of single-mass infinite spin towers the string beta function is the unique 4-point amplitude compatible with hidden zero and the 5-point splitting constraints. The analysis provides a prototype example for how features of higher-point amplitudes constrain the bootstrap of 4-point amplitudes.

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arXiv2024

Bootstrapping Extremal Scalar Amplitudes With and Without Supersymmetry

We re-examine positivity bounds on the $2\to2$ scattering of identical massless real scalars with a novel perspective on how these bounds can be used to constrain the spectrum of UV theories. We propose that the entire space of consistent weakly-coupled (and generically non-supersymmetric) UV amplitudes is determined as a convex hull of the massive scalar amplitude and a one-parameter family of scalarless "extremal amplitudes" parameterized by the ratio of the masses of the two lightest massive states. Further, we propose that the extremal amplitudes can be constructed from a similar one-parameter set of maximally supersymmetric amplitudes, leading to the surprising possibility that the S-matrix bootstrap with maximal supersymmetry may be sufficient to determine the entire allowed space of four-point amplitudes! Finally, we show that minimal spectrum input reduces the allowed space of Wilson coefficients to small islands around the open string Dirac-Born-Infeld tree amplitude and the closed string Virasoro-Shapiro amplitude.

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arXiv2024

Corners and Islands in the S-matrix Bootstrap of the Open Superstring

We bootstrap the Veneziano superstring amplitude in 10 dimensions from the bottom-up. Starting with the most general maximally supersymmetric Yang-Mills EFT, we input information about the lowest-lying massive states, which we assume contribute via tree-level exchanges to the 4-point amplitude. We show the following: (1) if there is only a single state at the lowest mass, it must be a scalar. (2) Assuming a string-inspired gap between the mass of this scalar and any other massive states, the allowed region of Wilson coefficients has a new sharp corner where the Veneziano amplitude is located. (3) Upon fixing the next massive state to be a vector, the EFT bounds have a one-parameter family of corners; these would correspond to models with linear Regge trajectories of varying slopes, one of which is the open superstring. (4) When the ratio between the massive scalar coupling and the $\text{tr}\, F^4$ coefficient is fixed to its string value, the spin and mass of the second massive state is determined by the bootstrap and the Veneziano amplitude is isolated on a small island in parameter space. Finally, we compare with other recent bootstraps approaches, both the pion model and imposing Regge-inspired maximal spin constraints.

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arXiv2023

Flattening of the EFT-Hedron: Supersymmetric Positivity Bounds and the Search for String Theory

We examine universal positivity constraints on $2 \to 2$ scattering in 4d planar $N=4$ supersymmetric Yang-Mills theory with higher-derivative corrections. We present numerical evidence that the convex region of allowed Wilson coefficients (the ``EFT-hedron'') flattens completely along about one-third of its dimensions when an increasing number of constraints on the spectral density from crossing-symmetry are included. Our analysis relies on the formulation of the positivity constraints as a linear optimization problem, which we implement using two numerical solvers, SDPB and CPLEX. Motivated by the flattening, we propose a novel partially resummed low-energy expansion of the $2 \to 2$ amplitude. As part of the analysis, we provide additional evidence in favor of the conjecture [1] that the Veneziano amplitude is the only amplitude compatible with both S-matrix bootstrap constraints and string monodromy.

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arXiv2023

Bootstrapping the String KLT Kernel

We show that a generalized version of the 4-point string theory KLT double-copy map is the most general solution to the minimal-rank double-copy bootstrap in effective field theory. This follows from significant restrictions of the 4-point map resulting from the 6-point bootstrap analysis. The generalized 4-point double-copy map is defined by a function with only two parameters times a simple function that is symmetric in $s,t,u$. The two parameters can be interpreted as independent choices of $α'$, one for each of the two sets of amplitudes double-copied with the map. Specifically, each of those two sets of amplitudes must obey either the string monodromy relations or the field theory KK & BCJ relations; there are no other options. We propose a closed form of the new double-copy map that interpolates between the original KLT string double-copy and the open & closed string period integrals. The construction clarifies the "single-valued projection" property of the Riemann zeta-function values for the 4-point string theory double copy.

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arXiv2022

Emergence of String Monodromy in Effective Field Theory

String monodromy is a set of linear relations among open string tree amplitudes with different orderings of the vertex operators. In this Letter, we show how these intrinsically stringy relations emerge in low-energy effective field theory from the assumptions of locality and the field theory Kleiss-Kuijf (KK) and Bern-Carrasco-Johansson (BCJ) relations. Specifically, we study the bi-adjoint scalar model effective field theory (BAS EFT). We impose the field theory KK and BCJ relations on one of the two color-orderings of the BAS EFT amplitudes and show that the second color-ordering has an emergent set of linear relations that, as checked at 4-point to 36-derivative order, are exactly the monodromy relations. The 4-point results depend on a delicate interplay between consistent factorization of 6-point BAS EFT amplitudes and the 6-point KK BCJ conditions. As a consequence of the analysis, the 4-point Z-theory tree amplitudes are bootstrapped up to a symmetric function in $s,t,u$ whose simple exponentiated form has free parameters that capture all the odd zeta values when matched to Z-theory.

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arXiv2022

Snowmass White Paper: the Double Copy and its Applications

The double copy is, in essence, a map between scattering amplitudes in a broad variety of familiar field and string theories. In addition to the mathematically rich intrinsic structure, it underlies a multitude of active research directions and has a range of interesting applications in quantum, classical and effective field theories, including broad topics such as string theory, particle physics, astrophysics, and cosmology. This Snowmass white paper provides a brief introduction to the double copy, its applications, current research and future challenges.

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arXiv2021

On Extended Supersymmetry of 4d Galileons and 3-Brane Effective Actions

We use on-shell amplitude methods to systematically analyze the possibility of extended supersymmetry for 4d Galileon models, expanding on previous $\mathcal{N}=1$ results. Assuming spins $\le 1$, we prove that there exists no $\mathcal{N}=4$ supersymmetric extension of any 4d Galileons. Thus the Galileons cannot be part of the effective action of a single flat maximally supersymmetric D3-brane, and that explains why such terms do not appear in the $α'$-expansion of the abelian open superstring amplitude. For $\mathcal{N}=2$ Galileons, we show that the complex scalar $Z = ϕ+ i χ$ of the vector supermultiplet cannot have $ϕ$ and $χ$ both enjoy enhanced shift symmetry; instead, $χ$ can at best be an $R$-axion with constant shift symmetry. Using the soft bootstrap, we demonstrate that the quartic DBI-Galileon is incompatible with $\mathcal{N}=2$ supersymmetry. A similar analysis performed at 7-point shows that a 2-parameter family of $\mathcal{N}=2$ supersymmetric quintic Galileons coupled with DBI passes the soft bootstrap. Finally, we show how supersymmetric coup\-lings between Galileons and gravitons arise in generalizations of our constructions, and we conclude with a discussion of Galileons and DBI-Galileons in the context of UV-completability vs.~the Swampland.

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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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arXiv2020

Bootstrap and Amplitudes: A Hike in the Landscape of Quantum Field Theory

This article is an introduction to two currently very active research programs, the Conformal Bootstrap and Scattering Amplitudes. Rather than attempting full surveys, the emphasis is on common ideas and methods shared by these two seemingly very different programs. In both fields, mathematical and physical constraints are placed directly on the physical observables in order to explore the landscape of possible consistent quantum field theories. We give explicit examples from both programs: the reader can expect to encounter boiling water, ferromagnets, pion scattering, and emergent symmetries on this journey into the landscape of local relativistic quantum field theories. The first part is written for a general physics audience. The second part includes further details, including a new on-shell bottom-up reconstruction of the $\mathbb{CP}^1$ model with the Fubini-Study metric arising from re-summation of the $n$-point interaction terms derived from amplitudes.

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arXiv2019

All-Multiplicity One-Loop Amplitudes in Born-Infeld Electrodynamics from Generalized Unitarity

We initiate a study of non-supersymmetric Born-Infeld electrodynamics in 4d at the quantum level. Explicit all-multiplicity expressions are calculated for the purely rational one-loop amplitudes in the self-dual ($++\ldots+$) and next-to-self-dual ($-+\ldots+$) helicity sectors. Using a supersymmetric decomposition, $d$-dimensional unitarity cuts of the integrand factorize into tree-amplitudes in a 4d model of Born-Infeld photons coupled to a massive complex scalar. The two-scalar tree-amplitudes needed to construct the Born-Infeld integrand are computed using two complimentary approaches: (1) as a double-copy of Yang-Mills coupled to a massive adjoint scalar with a dimensionally reduced form of Chiral Perturbation Theory, and (2) by imposing consistency with low-energy theorems under a reduction from 4d to 3d and T-duality. The Born-Infeld integrand is integrated in $d=4-2ε$ dimensions at order $\mathcal{O}(ε^0)$ using the dimension-shifting formalism. We comment on the implications for electromagnetic duality in quantum Born-Infeld theory.

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arXiv2018

Soft Bootstrap and Supersymmetry

The soft bootstrap is an on-shell method to constrain the landscape of effective field theories (EFTs) of massless particles via the consistency of the low-energy S-matrix. Given assumptions on the on-shell data (particle spectra, linear symmetries, and low-energy theorems), the soft bootstrap is an efficient algorithm for determining the possible consistency of an EFT with those properties. The implementation of the soft bootstrap uses the recently discovered method of soft subtracted recursion. We derive a precise criterion for the validity of these recursion relations and show that they fail exactly when the assumed symmetries can be trivially realized by independent operators in the effective action. We use this to show that the possible pure (real and complex) scalar, fermion, and vector exceptional EFTs are highly constrained. Next, we prove how the soft behavior of states in a supermultiplet must be related and illustrate the results in extended supergravity. We demonstrate the power of the soft bootstrap in two applications. First, for the N= 1 and N=2 CP^1 nonlinear sigma models, we show that on-shell constructibility establishes the emergence of accidental IR symmetries. This includes a new on-shell perspective on the interplay between N=2 supersymmetry, low-energy theorems, and electromagnetic duality. We also show that N=2 supersymmetry requires 3-point interactions with the photon that make the soft behavior of the scalar O(1) instead of vanishing, despite the underlying symmetric coset. Second, we study Galileon theories, including aspects of supersymmetrization, the possibility of a vector-scalar Galileon EFT, and the existence of higher-derivative corrections preserving the enhanced special Galileon symmetry. This is addressed by soft bootstrap and by application of double-copy/KLT relations applied to higher-derivative corrections of chiral perturbation theory.

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arXiv2017

On the Supersymmetrization of Galileon Theories in Four Dimensions

We use on-shell amplitude techniques to study the possible $\mathcal{N}=1$ supersymmetrizations of Galileon theories in 3+1 dimensions, both in the limit of decoupling from DBI and without. Our results are that (1) the quartic Galileon has a supersymmetrization compatible with Galileon shift symmetry ($ϕ\to ϕ+c + b_μx^μ$) for the scalar sector and an ordinary shift symmetry ($ψ\to ψ+ ξ$) for the fermion sector, and it is unique at least at 6th order in fields, but possibly not beyond; (2) the enhanced "special Galileon" symmetry is incompatible with supersymmetry; (3) there exists a quintic Galileon with a complex scalar preserving Galileon shift symmetry; (4) one cannot supersymmetrize the cubic and quintic Galileon while preserving the Galileon shift symmetry for the complex scalar; and (5) for the quartic and quintic Galileon, we present evidence for a supersymmetrization in which the real Galileon scalar is partnered with an R-axion to form a complex scalar which only has an ordinary shift symmetry.

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arXiv2016

Soft Photon and Graviton Theorems in Effective Field Theory

Extensions of the photon and graviton soft theorems are derived in 4d local effective field theories with massless particles of arbitrary spin. We prove that effective operators can result in new terms in the soft theorems at subleading order for photons and subsubleading order for gravitons. The new soft terms are unique and we provide a complete classification of all local operators responsible for such modifications. We show that no local operators can modify the subleading soft graviton theorem. The soft limits are taken in a manifestly on-locus manner using a complex double deformation of the external momenta. In addition to the new soft theorems, the resulting master formula yields consistency conditions such as the conservation of electric charge, the Einstein equivalence principle, supergravity Ward identities, and the Weinberg-Witten theorem.

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arXiv2016

A Practical Approach to the Hamilton-Jacobi Formulation of Holographic Renormalization

We revisit the subject of holographic renormalization for asymptotically AdS spacetimes. For many applications of holography, one has to handle the divergences associated with the on-shell gravitational action. The brute force approach uses the Fefferman-Graham (FG) expansion near the AdS boundary to identify the divergences, but subsequent reversal of the expansion is needed to construct the infinite counterterms. While in principle straightforward, the method is cumbersome and application/reversal of FG is formally unsatisfactory. Various authors have proposed an alternative method based on the Hamilton-Jacobi equation. However, this approach may appear to be abstract, difficult to implement, and in some cases limited in applicability. In this paper, we clarify the Hamilton-Jacobi formulation of holographic renormalization and present a simple algorithm for its implementation to extract cleanly the infinite counterterms. While the derivation of the method relies on the Hamiltonian formulation of general relativity, the actual application of our algorithm does not. The work applies to any $D$-dimensional holographic dual with asymptotic AdS boundary, Euclidean or Lorentzian, and arbitrary slicing. We illustrate the method in several examples, including the FGPW model, a holographic model of 3d ABJM theory, and cases with marginal scalars such as a dilaton-axion system.

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