Publications from previous years
PUBLICATIONS 2017

qVirasoro modular triple
Authors: Fabrizio Nieri, Yiwen Pan, Maxim Zabzine
Preprint Number: UUITP38/17
Inspired by 5d supersymmetric YangMills theories placed on the compact space S5, we propose an intriguing algebraic construction for the qVirasoro algebra. We show that, when multiple qVirasoro “chiral” sectors have to be fused together, a natural SL(3, Z) structure arises. This construction, which we call the modular triple, is consistent with the observed triple factorization properties of supersymmetric partition functions derived from localization arguments. We also give a 2d CFTlike construction of the modular triple, and conjecture for the first time a (nonlocal) Lagrangian formulation for a qVirasoro model, resembling ordinary Liouville theory.

Gauged supergravities and spontaneous SUSY breaking from the double copy
Authors: Marco Chiodaroli, Murat Gunaydin, Henrik Johansson and Radu Roiban
Preprint Number: UUITP37/17
Supergravities with gauged Rsymmetry and Minkowski vacua allow for spontaneous supersymmetry breaking and, as such, provide a framework for building supergravity models of phenomenogical relevance. In this letter we initiate the study of doublecopy constructions for these supergravities. On general grounds we expect that their scattering amplitudes are described by a double copy of the type: (Higgsed gauge theory) ⊗ (gauge theory with broken SUSY). We present a simple realization in which the resulting supergravity has U(1)_R gauge symmetry, spontaneouslybroken N = 2 supersymmetry, and massive gravitini. This is the first instance of a doublecopy construction for a gauged supergravity and for a theory with spontaneouslybroken supersymmetry. The construction extends in a straightforward manner to a large family of gauged YangMillsEinstein supergravity theories with or without spontaneous gauge symmetry breaking.

Konishi OPE coefficient at the five loop order
Authors: Alessandro Georgoudis, Vasco Gonçalves and Raul Pereira
Preprint Number: UUITP35/17.
We study the OPE limit of a four point function in N = 4 SYM at the five loop
order and we extract the OPE coefficient at that order. 
Chiral Algebras, Localization and Surface Defects
Authors: Yiwen Pan and Wolfger Peelaers.
Preprint Number: UUITP34/17.
Abstract: Fourdimensional N = 2 superconformal quantum field theories contain a subsector carrying the structure of a chiral algebra. Using localization techniques, we show for the free hypermultiplet that this structure can be obtained directly from the path integral on the foursphere. We extend the localization computation to include supersymmetric surface defects described by a generic 4d/2d coupled system. The presence of a defect corresponds to considering a module of the chiral algebra: our results provide a calculational window into its structure constants.

Fivedimensional fermionic ChernSimons theory
Authors: Dongsu Bak and Andreas Gustavsson
Preprint Number: UUITP33/17
Abstract: We study 5d fermionic CS theory with a fermionic 2form gauge potential. This theory can be obtained from 5d MSYM theory by performing the maximal topological twist. We put the theory on a fivemanifold and compute the partition function. We find that it is a topological quantity, which involves the RaySinger torsion of the fivemanifold. For abelian gauge group we consider the uplift to the 6d theory and find a mismatch between the 5d partition function and the 6d index, due to the nontrivial dimensional reduction of a selfdual twoform gauge field on a circle. We also discuss an application of the 5d theory to generalized knots made of 2d sheets embedded in 5d. 
N = 2 supersymmetric AdS(4) solutions of type IIB supergravity
Authors: Achilleas Passias, Gautier Solard, Alessandro Tomasiello
Preprint number: UUITP32/17 
Restrictions of Heterotic G2 Structures and Instanton Connections
Authors: Xenia de la Ossa, Magdalena Larfors and Eirik E. Svanes
Preprint number: UUITP31/17
Abstract: This note revisits recent results regarding the geometry and moduli of solutions of the heterotic string on manifolds Y with a G2 structure. In particular, such heterotic G2 systems can be rephrased in terms of a differential Dˇ acting on a complex Ωˇ∗(Y,Q), where Q=T∗Y⊕End(TY)⊕End(V) and Dˇ is an appropriate projection of an exterior covariant derivative D which satisfies an instanton condition. The infinitesimal moduli are further parametrised by the first cohomology H1ˇ(Y,Q). We proceed to restrict this system to manifolds X with an SU(3) structure corresponding to supersymmetric compactifications to four dimensional Minkowski space, often referred to as StromingerHull solutions. In doing so, we derive a new result: the StromingerHull system is equivalent to a particular holomorphic YangMills covariant derivative on QX=T∗X⊕End(TX)⊕End(V).

On the Prospects for Detecting a Net Photon Circular Polarization Produced by Decaying Dark Matter
Authors: Andrey Elagin, Jason Kumar, Pearl Sandick, Fei Teng
Preprint Number: UUITP30/17
If dark matter interactions with Standard Model particles are CPviolating, then dark matter annihilation/decay can produce photons with a net circular polarization. We consider the prospects for experimentally detecting evidence for such a circular polarization. We identify optimal models for dark matter interactions with the Standard Model, from the point of view of detectability of the net polarization, for the case of either symmetric or asymmetric dark matter. We find that, for symmetric dark matter, evidence for net polarization could be found by a search of the Galactic Center by an instrument sensitive to circular polarization with an efficiencyweighted exposure of at least 50000 cm^2 yr, provided the systematic detector uncertainties are constrained at the 1% level. Much better sensitivity can be obtained in the case of asymmetric dark matter. We discuss the prospects for achieving the needed level of performance using possible detector technologies.

The FiveLoop FourPoint Integrand of N = 8 Supergravity as a Generalized Double Copy
Authors: Zvi Bern, John Joseph Carrasco, WeiMing Chen, Henrik Johansson, Radu Roiban, Mao Zeng
Preprint Number: UUITP29/17
We use the recently developed generalized doublecopy procedure to construct an integrand for the fiveloop fourpoint amplitude of N = 8 supergravity. [...] The fiveloop fourpoint integrand is a crucial ingredient towards future determinations of ultraviolet properties of N = 8 supergravity at five loops and beyond. We also present a nontrivial check of the consistency of the integrand, based on modern approaches for loop integration in the ultraviolet region.

A swamp of nonSUSY vacua
Authors: U. H. Danielsson, G. Dibitetto, and S. C. Vargas
Preprint Number: UUITP28/17
We consider known examples of nonsupersymmetric AdS7 and AdS4 solutions arising from compactifications of massive type IIA supergravity and study their stability, taking into account the coupling between closed and openstring sector excitations. Generically, open strings are found to develop modes with masses below the BreitenlohnerFreedman (BF) bound. We comment on the relation with the Weak Gravity Conjecture, and how this analysis may play an important role in examining the validity of nonsupersymmetric constructions in string theory.

6D Fractional Quantum Hall Effect
Authors: Jonathan J. Heckman and Luigi Tizzano
Preprint Number: UUITP27/17
Abstract:
We present a 6D generalization of the fractional quantum Hall effect involving membranes coupled to a threeform potential in the presence of a large background fourform flux. The low energy physics is governed by a bulk 7D topological field theory of abelian three form potentials with a single derivative ChernSimonslike action coupled to a 6D antichiral theory of Euclidean effective strings. We derive the fractional conductivity, and explain how continued fractions which figure prominently in the classification of 6D superconformal field theories correspond to a hierarchy of excited states. Using methods from conformal field theory we also compute the analog of the Laughlin wavefunction. Compactification of the 7D theory provides a uniform perspective on various lowerdimensional gapped systems coupled to boundary degrees of freedom. We also show that a supersymmetric version of the 7D theory embeds in Mtheory, and can be decoupled from gravity. Encouraged by this, we present a conjecture in which IIB string theory is an edge mode of a 10 + 2dimensional bulk topological theory, thus placing all twelve dimensions of Ftheory on a physical footing.

Connecting the ambitwistor and the sectorized heterotic strings
Authors: Thales Azevedo and Renann Lipinski Jusinskas
Preprint number UUITP26/17
The sectorized description of the (chiral) heterotic string using pure spinors has been misleadingly viewed as an infinite tension string. One evidence for this fact comes from the tree level 3point graviton amplitude, which we show to contain the usual Einstein term plus a higher curvature
contribution. After reintroducing a dimensionful parameter $\ell$ in the theory, we demonstrate that the heterotic model is in fact twofold, depending on the choice of the supersymmetric sector, and that the spectrum also contains one massive (open string like) multiplet. By taking the $\ell\to\infty$ limit, we finally show that the ambitwistor string is recovered, reproducing the unexpected heterotic state in Mason and Skinner's RNS description. 
Holographic microstate counting for AdS(4) black holes in massive IIA supergravity
Authors: Seyed Morteza Hosseini, Kiril Hristov, Achilleas Passias
Preprint number: UUITP25/17 
Ambitwistor formulations of R^2 gravity and (DF)^2 gauge theories
Authors: Thales Azevedo, Oluf Tang Engelund
Preprint number UUITP24/17
We consider Ddimensional amplitudes in R^2 gravities (conformal gravity in D=4) and in the recently introduced (DF)^2 gauge theory, from the perspective of the CHY formulae and ambitwistor string theory. These theories are related through the BCJ doublecopy construction, and the (DF)^2 gauge theory obeys colorkinematics duality. We work out the worldsheet details of these theories and show that they admit a formulation as integrals on the support of the scattering equations, or alternatively, as ambitwistor string theories. For gravity, this generalizes the work done by Berkovits and Witten on conformal gravity to D dimensions. The ambitwistor is also interpreted as a Ddimensional generalization of Witten's twistor string (SYM + conformal supergravity). As part of our ambitwistor investigation, we discover another (DF)^2 gauge theory containing a photon that couples to Einstein gravity. This theory can provide an alternative KLT description of Einstein gravity compared to the usual YangMills squared.

6d surface defects from massive type IIA
Authors: Giuseppe Dibitetto and Nicolò Petri
Preprint Number: UUITP23/17
We present a new BPS flow within minimal N=1 supergravity in seven dimensions describing a warped AdS_3 background supported by a ``dyonic'' profile of the threeform. Furthermore, we discuss the holographic interpretation of the above solution in terms of a defect CFT_2 inside the 6d (1,0) theory dual to the AdS in the asymptotic region. Finally we provide the brane picture of the aforementioned defect CFT as D2 and wrapped D4branes ending on a D6  NS5  D8 funnel in massive type IIA string theory.

BPS objects in D=7 supergravity and their Mtheory origin
Authors: Giuseppe Dibitetto and Nicolò Petri
Preprint Number: UUITP22/17
We study several different types of BPS flows within minimal N=1, D=7 supergravity with SU(2) gauge group and nonvanishing topological mass. After reviewing some known domain wall solutions involving only the metric and the R^+ scalar field, we move to considering more general flows involving a ``dyonic'' profile for the 3form gauge potential. In this context, we consider flows featuring a Mkw_3 as well as an AdS_3 slicing, write down the corresponding flow equations, and integrate them analytically to obtain many examples of asymptotically AdS_7 solutions in presence of a running 3form. Furthermore, we move to adding the possibility of nonvanishing vector fields, find the new corresponding flows and integrate them numerically. Finally, we discuss the elevendimensional interpretation of the aforementioned solutions as effective descriptions of M2  M5 bound states.

Conformal Gravity from Gauge Theory
Authors: Henrik Johansson and Josh Nohle
Preprint number UUITP21/17
We use the duality between color and kinematics to obtain scattering amplitudes in nonminimal conformal N = 0, 1, 2, 4 (super)gravity theories. Generic tree amplitudes can be constructed from a double copy between (super)YangMills theory and a new gauge theory built entirely out of dimensionsix operators. The latter theory is marginal in six dimensions and contains modes with a wrongsign propagator, echoing the behavior of conformal gravity. The dimensionsix Lagrangian is uniquely determined by demanding that its scattering amplitudes obey the colorkinematics duality. The conformal gravity amplitudes obtained from the double copy are compared with the BerkovitsWitten twistor string and shown to agree up to at least eight points in the MHV sector.

All (4,0): Sigma Models with (4,0) OffShell Supersymmetry
Authors: Chris Hull and Ulf Lindström
Preprint number UUITP20/17
Offshell $(4,0)$ supermultiplets in 2dimensions are constructed. These are used to construct sigma models whose target spaces are vector bundles over manifolds that are hyperk\"ahler with torsion. The offshell supersymmetry implies the complex structures are simultaneously integrable and allows us to construct actions using extended superspace and projective superspace, giving an explicit construction of the target space geometries.

Twoloop supersymmetric QCD and halfmaximal supergravity amplitudes
Author: Henrik Johansson, Gregor Kälin and Gustav Mogull
Preprint Number: UUITP19/17
Using the duality between color and kinematics, we construct twoloop fourpoint scattering amplitudes in N=2 superYangMills (SYM) theory coupled to N_f fundamental hypermultiplets. Our results are valid in D<=6 dimensions, where the upper bound corresponds to sixdimensional chiral N=(1,0) SYM theory. By exploiting a close connection with N=4 SYM theory  and, equivalently, sixdimensional N=(1,1) SYM theory  we find compact integrands with fourdimensional external vectors in both the maximallyhelicityviolating (MHV) and allchiralvector sectors. Via the doublecopy construction corresponding Ddimensional halfmaximal supergravity amplitudes with external graviton multiplets are obtained in the MHV and allchiral sectors. Appropriately tuning N_f enables us to consider both pure and mattercoupled supergravity, with arbitrary numbers of vector multiplets in D=4. As a bonus, we obtain the integrands of the genuinely sixdimensional supergravities with N=(1,1) and N=(2,0) supersymmetry. Finally, we extract the potential ultraviolet divergence of halfmaximal supergravity in D=52e and show that it nontrivially cancels out as expected.

Integrability in dipoledeformed N=4 super YangMills
Authors: M. Guica, F. LevkovichMaslyuk and K. Zarembo
Preprint number: UUITP18/17
We study the null dipole deformation of N=4 super YangMills theory, which is an example of a potentially solvable ``dipole CFT'': a theory that is nonlocal along a null direction, has nonrelativistic conformal invariance along the remaining ones, and is holographically dual
to a Schrödinger spacetime. We initiate the fieldtheoretical study of the spectrum in this model by
using integrability inherited from the parent theory.
The dipole deformation corresponds to a nondiagonal DrinfeldReshetikhin twist in the spin chain picture, which
renders the traditional Bethe ansatz inapplicable from the very beginning.
We use instead the Baxter equation supplemented
with nontrivial asymptotics,
which gives the full 1loop spectrum in the sl(2) sector. We show that
anomalous dimensions of long gauge theory operators perfectly
match the string theory prediction,
providing a quantitative test of Schrödinger holography. 
Machine Learning of CalabiYau Volumes
Authors: Daniel Krefl, RakKyeong Seong
Preprint Number: UUITP17/17
We employ machine learning techniques to investigate the volume minimum of SasakiEinstein base manifolds of noncompact toric CalabiYau 3folds. We find that the minimum volume can be approximated via a second order multiple linear regression on standard topological quantities obtained from the corresponding toric diagram. The approximation improves further after invoking a convolutional neural network with the full toric diagram of the CalabiYau 3folds as the input. We are thereby able to circumvent any minimization procedure that was previously necessary and find an explicit mapping between the minimum volume and the topological quantities of the toric diagram. Under the AdS/CFT correspondence, the minimum volumes of SasakiEinstein manifolds correspond to central charges of a class of 4d N=1 superconformal field theories. We therefore find empirical evidence for a function that gives values of central charges without the usual extremization procedure.

Anomalous Dimensions in the WF O(N) Model with a Monodromy Line Defect
Author: Alexander Söderberg
Preprint: UUITP16/17
Implications of inserting a monodromy line defect in three dimensional O(N) models are studied. We consider then the WF O(N) model, and study the twopoint Green's function for bulklocal fields found from both the bulkdefect expansion and Feynman diagrams, to find the anomalous dimensions for bulk and defectlocal primaries as well as one of the OPE coefficients as ϵexpansions to the first loop order. As a check on our results, we study the (ϕ^k)^2ϕ^j operator both using the bulkdefect expansion as well as the equations of motion.

Black holes as bubbles of AdS
Authors: Ulf Danielsson, Giuseppe Dibitetto, Suvendu Giri
Preprint number: UUITP15/17
In this paper we propose that bubbles of AdS within Minkowski spacetime, stablized at a finite radius by stiff matter and an electromagnetic gas, can be an alternative endpoint of gravitational collapse. The bubbles are horizonless with a size up to 12.5% larger than their Schwarzschild radius depending on their charge. We argue that they are stable against small perturbations, and have thermodynamical properties similar to those of real black holes. We provide a realization of the bubbles within string theory that relies on a specific brane intersection giving rise to a shell carrying dissolved charges from lower dimensional Dbranes as well as a gas of open strings. We also note that our construction proivdes a new way of understanding the entropy of ReissnerNordström black holes in the extremal limit.

Twopoint functions of SU(2)subsector and lengthtwo operators in dCFT
Authors: Erik Widen
Preprint number: UUITP14/17
We consider a particular set of twopoint functions in the setting of N = 4 SYM with a defect, dual to the fuzzyfunnel solution for the probe D5D3brane system. The twopoint functions in focus involve a single trace operator in the SU(2)subsector of arbitrary length and a lengthtwo operator built out of any scalars. By interpreting the contractions as a spinchain operator, simple expressions were found for the leading contribution to the twopoint functions, mapping them to earlier known formulas for the onepoint functions in this setting.

The infinitesimal moduli space of heterotic G_2 systems
Authors: Xenia de la Ossa, Magdalena Larfors, Eirik E. Svanes
Preprint number: UUITP13/17

AdS(5) compactifications with punctures in massive IIA supergravity
Authors: Ibrahima Bah, Achilleas Passias, Alessandro Tomasiello
Preprint number: UUITP12/17We find AdS(5) solutions holographically dual to compactifications of sixdimensional N=(1,0) supersymmetric field theories on Riemann surfaces with punctures. We simplify a previous analysis of supersymmetric AdS(5) IIA solutions, and with a suitable Ansatz we find explicit solutions organized in three classes, where an O8D8 stack, D6 and D4branes are simultaneously present, localized and partially localized. The D4branes are smeared over the Riemann surface and this is interpreted as the presence of a uniform distribution of punctures. For the first class we identify the corresponding sixdimensional theory as an Estring theory coupled to a quiver gauge theory. The second class of solutions lacks D6branes and its central charge scales as n^{5/2}, suggesting a fivedimensional origin for the dual field theory. The last class has elements of the previous two.

BPS Graphs: From Spectral Networks to BPS Quivers
Authors: Maxime Gabella, Pietro Longhi, Chan Y. Park and Masahito Yamazaki
Preprint number: UUITP11/17
We define “BPS graphs” on punctured Riemann surfaces associated with A_{N−1} theories of class S. BPS graphs provide a bridge between two powerful frameworks for studying the spectrum of BPS states: spectral networks and BPS quivers. They arise from degenerate spectral networks at maximal intersections of walls of marginal stability on the Coulomb branch. While the BPS spectrum is illdefined at such intersections, a BPS graph captures a useful basis of elementary BPS states. The topology of a BPS graph encodes a BPS quiver, even for higherrank theories and for theories with certain partial punctures. BPS graphs lead to a geometric realization of the combinatorics of FockGoncharov Ntriangulations and generalize them in several ways.

Elliptic modular double and 4d partition functions
Authors: Rebecca Lodin, Fabrizio Nieri, Maxim Zabzine
Preprint number: UUITP09/17
We consider 4d supersymmetric (special) unitary G quiver gauge theories on compact manifolds which are T2 fibrations over S2. We show that their partition functions are correlators of vertex operators and screening charges of the modular double version of elliptic W(G) algebras. We also consider a generating function of BPS surface defects supported on T2 and show that it can be identified with a particular coherent state in the Fock module over the elliptic Heisenberg algebra.

Oneloop tests of supersymmetric gauge theories on spheres
Authors: Joseph A. Minahan and Usman Naseer
Preprint number: UUITP08/17
We show that a recently conjectured form for perturbative supersymmetric partition functions on spheres of general dimension d is consistent with the flat space limit of 6dimensional N = 1 super YangMills. We also show that the partition functions for N = 1 8 and 9dimensional theories are consistent with their known flat space limits.

Explicit Formulae for YangMillsEinstein Amplitudes from the Double Copy
Authors: Marco Chiodaroli, Murat Gunaydin, Henrik Johansson and Radu Roiban
Preprint number: UUITP07/17
Using the doublecopy construction of YangMillsEinstein theories formulated
in our earlier work, we obtain compact presentations for singletrace
YangMillsEinstein tree amplitudes with up to five external gravitons and an
arbitrary number of gluons. These are written as linear combinations of
colororderd YangMills trees, where the coefficients are given by
color/kinematicssatisfying numerators in a YangMills+\phi^3 theory. 
Quantum String Test of Nonconformal Holography
Authors: Xinyi ChenLin, Daniel MedinaRincon and Konstantin Zarembo
Preprint number: UUITP06/17
We compute Luscher corrections to the effective string tension in the
PilchWarner background, holographically dual to N = 2* supersymmetric
YangMills theory. The same quantity can be calculated directly
from field theory by solving the localization matrix model at largeN.
We find complete agreement between the fieldtheory predictions and
explicit stringtheory calculation at strong coupling. 
Elliptic Genera of 2d (0,2) Gauge Theories from Brane Brick Models
Authors: Sebastian Franco, Dongwook Ghim, Sangmin Lee, RakKyeong Seong
Preprint Number: UUITP05/17
We compute the elliptic genus of abelian 2d (0,2) gauge theories corresponding to brane brick models. These theories are worldvolume theories on a single D1brane probing a toric CalabiYau 4fold singularity. We identify a match with the elliptic genus of the nonlinear sigma model on the same CalabiYau background, which is computed using a new localization formula. The matching implies that the quantum effects do not drastically alter the correspondence between the geometry and the 2d (0,2) gauge theory. In theories whose matter sector suffers from abelian gauge anomaly, we propose an ansatz for an anomaly cancelling term in the integral formula for the elliptic genus. We provide an example in which two brane brick models related to each other by GaddeGukovPutrov triality give the same elliptic genus.

Integrability in SigmaModels
Author: K. Zarembo
Preprint Number: UUITP04/17
Abstract: These lecture notes cover the following topics: (1) Homogeneous spaces, (2) Classical integrability of principal chiral field and semisymmetric cosets, (3) Topological terms in sigmamodels, (4) Backroundfield method and betafunction, (5) Smatrix bootstrap in the $O(N)$ model, (6) Supersymmetric cosets.

Connecting Fisher information to bulk entanglement in holography
Authors: Souvik Banerjee, Johanna Erdmenger, Debajyoti Sarkar
Preprint: UUITP03/17
Abstract: In the context of relating AdS/CFT to quantum information theory, we propose a holographic dual of Fisher information metric for mixed states in the boundary field theory. This amounts to a holographic measure for the distance between two mixed quantum states. For a spherical subregion in the boundary we show that this is related to a particularly regularized volume enclosed by the RyuTakayanagi surface. We further argue that the quantum correction to the proposed Fisher information metric is related to the quantum correction to the boundary entanglement entropy. We discuss consequences of this connection.

Semiholography illustrated with biholography
Authors : Souvik Banerjee, Nava Gaddam, Ayan Mukhopadhyay
Preprint number : UUITP02/17
Abstract : Semiholography has been proposed as an effective nonperturbative framework which can combine perturbative and nonperturbative effects consistently for theories like QCD. It is postulated that the strongly coupled nonperturbative sector has a holographic dual in the form of a classical gravity theory in the large N limit, and the perturbative fields determine the gravitational boundary conditions. In this work, we pursue a fundamental derivation of this framework particularly showing how perturbative physics by itself can determine the holographic dual of the infrared, and also the interactions between the perturbative and the holographic sectors. We firstly demonstrate that the interactions between the two sectors can be constrained through the existence of a conserved local energymomentum tensor for the full system up to hardsoft coupling constants. As an illustration, we set up a biholographic toy theory where both the UV and IR sectors are strongly coupled and holographic with distinct classical gravity duals. In this construction, the requirement that an appropriate gluing can cure the singularities (geodetic incompletenesses) of the respective geometries leads us to determine the parameters of the IR theory and the hardsoft couplings in terms of those of the UV theory. The high energy scale behaviour of the hardsoft couplings are stateindependent but their runnings turn out to be statedependent. We discuss how our approach can be adapted to the construction of the semiholographic framework for QCD.

Gravity Amplitudes as Generalized Double Copies
Authors: Zvi Bern, John Joseph Carrasco, WeiMing Chen, Henrik Johansson, Radu Roiban
Preprint Number: UUITP01/17
Whenever a gaugetheory integrand can be arranged into a form where the BCJ duality between color and kinematics is manifest, a corresponding gravity integrand can be obtained directly via the double copy procedure. However, finding such representations at loop level can be challenging. Here we show that we can instead start from generic gaugetheory integrands, where the duality is not manifest, and apply a modified doublecopy procedure that incorporates a set of contact terms generated by violations of dual Jacobi identities. We illustrate this with three, four and fiveloop examples in N = 8 supergravity.