arXiv subjects

Congkao Wen

Publications and source records attributed to Congkao Wen.

At least 73 records · Page 4Linked to original sources

arXiv2017

A note on NMHV form factors from the Graßmannian and the twistor string

In this note we investigate Graßmannian formulas for form factors of the chiral part of the stress-tensor multiplet in $\mathcal{N}=4$ superconformal Yang-Mills theory. We present an all-$n$ contour for the $G(3,n+2)$ Graßmannian integral of NMHV form factors derived from on-shell diagrams and the BCFW recursion relation. In addition, we study other $G(3,n+2)$ formulas obtained from the connected prescription introduced recently. We find a recursive expression for all $n$ and study its properties. For $n \geq 6$, our formula has the same recursive structure as its amplitude counterpart, making its soft behaviour manifest. Finally, we explore the connection between the two Graßmannian formulations, using the global residue theorem, and find that it is much more intricate compared to scattering amplitudes.

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arXiv2017

Two-point Correlators in N=2 Gauge Theories

We consider two-point correlators in SU(N) gauge theories on R4 with N=2 supersymmetry and Nf massless hypermultiplets in the fundamental representation. Using localization on S4, we compute the leading perturbative corrections to the two-point functions of chiral/anti-chiral operators made of scalar fields. The results are compared at two and three loops against direct field theory computations for some special operators whose correlators remain finite in perturbation theory at the specific loop order. In the conformal case, the match is shown up to two loops for a generic choice of operators and for arbitrary N.

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arXiv2017

The analytic structure of conformal blocks and the generalized Wilson-Fisher fixed points

We describe in detail the method used in our previous work arXiv:1611.10344 to study the Wilson-Fisher critical points nearby generalized free CFTs, exploiting the analytic structure of conformal blocks as functions of the conformal dimension of the exchanged operator. Our method is equivalent to the mechanism of conformal multiplet recombination set up by null states. We compute, to the first non-trivial order in the $ε$-expansion, the anomalous dimensions and the OPE coefficients of infinite classes of scalar local operators using just CFT data. We study single-scalar and $O(N)$-invariant theories, as well as theories with multiple deformations. When available we agree with older results, but we also produce a wealth of new ones. Unitarity and crossing symmetry are not used in our approach and we are able to apply our method to non-unitary theories as well. Some implications of our results for the study of the non-unitary theories containing partially conserved higher-spin currents are briefly mentioned.

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arXiv2017

Generalized Wilson-Fisher critical points from the conformal OPE

We study possible smooth deformations of Generalized Free Conformal Field Theories in arbitrary dimensions by exploiting the singularity structure of the conformal blocks dictated by the null states. We derive in this way, at the first non trivial order in the $ε$-expansion, the anomalous dimensions of an infinite class of scalar local operators, without using the equations of motion. In the cases where other computational methods apply, the results agree.

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arXiv2017

Einstein-Yang-Mills from pure Yang-Mills amplitudes

We present new relations for scattering amplitudes of color ordered gluons and gravitons in Einstein-Yang-Mills theory. Tree-level amplitudes of arbitrary multiplicities and polarizations involving up to three gravitons and up to two color traces are reduced to partial amplitudes of pure Yang-Mills theory. In fact, the double-trace identities apply to Einstein-Yang-Mills extended by a dilaton and a B-field. Our results generalize recent work of Stieberger and Taylor for the single graviton case with a single color trace. As the derivation is made in the dimension-agnostic Cachazo-He-Yuan formalism, our results are valid for external bosons in any number of spacetime dimensions. Moreover, they generalize to the superamplitudes in theories with 16 supercharges.

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arXiv2016

Exploring soft constraints on effective actions

We study effective actions for simultaneous breaking of space-time and internal symmetries. Novel features arise due to the mixing of Goldstone modes under the broken symmetries which, in contrast to the usual Adler's zero, leads to non-vanishing soft limits. Such scenarios are common for spontaneously broken SCFT's. We explicitly test these soft theorems for $\mathcal{N}=4$ sYM in the Coulomb branch both perturbatively and non-perturbatively. We explore the soft constraints systematically utilizing recursion relations. In the pure dilaton sector of a general CFT, we show that all amplitudes up to order $s^{n} \sim \partial^{2n}$ are completely determined in terms of the $k$-point amplitudes at order $s^k$ with $k \leq n$. Terms with at most one derivative acting on each dilaton insertion are completely fixed and coincide with those appearing in the conformal DBI, i.e. DBI in AdS. With maximal supersymmetry, the effective actions are further constrained, leading to new non-renormalization theorems. In particular, the effective action is fixed up to eight derivatives in terms of just one unknown four-point coefficient and one more coefficient for ten-derivative terms. Finally, we also study the interplay between scale and conformal invariance in this context.

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arXiv2016

The free $σ$CFTs

We introduce the conformal field theories that describe the shadows of the lowest dimension composites made out of massless free scalars and fermions in $d$ dimensions. We argue that these theories can be consistently defined as free CFTs for even $d\geq 4$. We use OPE techniques to study their spectrum and show that for $d\rightarrow\infty$ it matches that of free bosonic CFTs in $d=6$ and $d=4$ dimensions. For these $σ$CFTs we calculate $c_T$ in $d=6,8,10$ and $12$ dimensions using the OPE and also a direct construction of their higher-derivative energy momentum tensors. Our results agree with the general proposal of arXiv:1601.07198.

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arXiv2016

Non-Planar On-Shell Diagrams

We initiate a systematic study of non-planar on-shell diagrams in N=4 SYM and develop powerful technology for doing so. We introduce canonical variables generalizing face variables, which make the dlog form of the on-shell form explicit. We make significant progress towards a general classification of arbitrary on-shell diagrams by means of two classes of combinatorial objects: generalized matching and matroid polytopes. We propose a boundary measurement that connects general on-shell diagrams to the Grassmannian. Our proposal exhibits two important and non-trivial properties: positivity in the planar case and it matches the combinatorial description of the diagrams in terms of generalized matroid polytopes. Interestingly, non-planar diagrams exhibit novel phenomena, such as the emergence of constraints on Plucker coordinates beyond Plucker relations when deleting edges, which are neatly captured by the generalized matching and matroid polytopes. This behavior is tied to the existence of a new type of poles in the on-shell form at which combinations of Plucker coordinates vanish. Finally, we introduce a prescription, applicable beyond the MHV case, for writing the on-shell form as a function of minors directly from the graph.

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arXiv2016

Stratifying On-Shell Cluster Varieties: the Geometry of Non-Planar On-Shell Diagrams

The correspondence between on-shell diagrams in maximally supersymmetric Yang-Mills theory and cluster varieties in the Grassmannian remains largely unexplored beyond the planar limit. In this article, we describe a systematic program to survey such 'on-shell varieties', and use this to provide a complete classification in the case of $G(3,6)$. In particular, we find exactly 24 top-dimensional varieties and 10 co-dimension one varieties in $G(3,6)$---up to parity and relabeling of the external legs. We use this case to illustrate some of the novelties found for non-planar varieties relative to the case of positroids, and describe some of the features that we expect to hold more generally.

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arXiv2016

Instanton corrections to the effective action of N=4 SYM

We compute the one-instanton effective action of N=4 super Yang-Mills theory with gauge group Sp(2N). The result can be written in a very compact and manifestly supersymmetric form involving an integral over the superspace of an irrational function of the N=4 on-shell superfields. In the Coulomb branch, the instanton corrects both the MHV and next-to-next-MHV higher derivative terms D^4F^{2n+2} and F^{2n+4}. We confirm at the non-perturbative level the non-renormalization theorems for MHV F^{2n+2} terms that are expected to receive perturbative corrections only at n-loops. We compute also the one and two-loop corrections to the D^4F^4 term and show that its completion under SL(2,Z) duality is consistent with the one-instanton results of U(2) gauge group.

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arXiv2016

Recursion relations from soft theorems

We establish a set of new on-shell recursion relations for amplitudes satisfying soft theorems. The recursion relations can apply to those amplitudes whose additional physical inputs from soft theorems are enough to overcome the bad large-z behaviour. This work is a generalization of the recursion relations recently obtained by Cheung et al for amplitudes in scalar effective field theories with enhanced vanishing soft behaviours, which can be regarded as a special case of those with non-vanishing soft limits. We apply the recursion relations to tree-level amplitudes in various theories, including amplitudes in the Akulov-Volkov theory, amplitudes containing dilatons of spontaneously-broken conformal symmetry.

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arXiv2016

Universality in string interactions

In this letter, we provide evidence for universality in the low-energy expansion of tree-level string interactions. More precisely, in the alpha'-expansion of tree-level scattering amplitudes, we conjecture that the leading transcendental coefficient at each order in alpha' is universal for all perturbative string theories. We have checked this universality up to seven points and trace its origin to the ability to restructure the disk integrals of open bosonic string into those of the superstring. The accompanying kinematic functions have the same low-energy limit and do not introduce any transcendental numbers in their alpha'-corrections. Universality in the closed-string sector then follows from the KLT-relations.

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arXiv2016

Soft theorems from anomalous symmetries

We discuss constraints imposed by soft limits for effective field theories arising from symmetry breaking. In particular, we consider those associated with anomalous conformal symmetry as well as duality symmetries in supergravity. We verify these soft theorems for the dilaton effective action relevant for the a-theorem, as well as the one-loop effective action for N=4 supergravity. Using the universality of leading transcendental coefficients in the alpha' expansion of string theory amplitudes, we study the matrix elements of operator R^4 with half maximal supersymmetry. We construct the non-linear completion of R^4 that satisfies both single and double soft theorems up to seven points. This supports the existence of duality invariant completion of R^4.

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arXiv2015

Exact coefficients for higher dimensional operators with sixteen supersymmetries

We consider constraints on higher dimensional operators for supersymmetric effective field theories. In four dimensions with maximal supersymmetry and SU(4) R-symmetry, we demonstrate that the coefficients of abelian operators F^n with MHV helicity configurations must satisfy a recursion relation, and are completely determined by that of F^4. As the F^4 coefficient is known to be one-loop exact, this allows us to derive exact coefficients for all such operators. We also argue that the results are consistent with the SL(2,Z) duality symmetry. Breaking SU(4) to Sp(4), in anticipation for the Coulomb branch effective action, we again find an infinite class of operators whose coefficient that are determined exactly. We also consider three-dimensional N=8 as well as six-dimensional N=(2,0),(1,0) and (1,1) theories. In all cases, we demonstrate that the coefficient of dimension-six operator must be proportional to the square of that of dimension-four.

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arXiv2015

From U(1) to E8: soft theorems in supergravity amplitudes

It is known that for N=8 supergravity, the double-soft-scalar limit of a n-point amplitude is given by a sum of local SU(8) rotations acting on a (n-2)-point amplitude. For N<8 supergravity theories, complication arises due to the presence of a U(1) in the U(N) isotropy group, which introduces a soft-graviton singularity that obscures the action of the duality symmetry. In this paper, we introduce an anti-symmetrised extraction procedure that exposes the full duality group. We illustrate this procedure for tree-level amplitudes in 4<=N<8 supergravity in four dimensions, as well as N=16 supergravity in three dimensions. In three dimensions, as all bosonic degrees of freedom transform under the E8 duality group, supersymmetry ensures that the amplitude vanishes in the single-soft limit of all particle species, in contrast to its higher dimensional siblings. Using recursive formulas and generalized unitarity cuts in three dimensions, we demonstrate the action of the duality group for any tree-level and one-loop amplitudes. Finally we discuss the implications of the duality symmetry on possible counter terms for this theory. As a preliminary application, we show that the vanishing of single-soft limits of arbitrary component fields in three-dimensional supergravity rules out the direct dimensional reduction of D^8R^4 as a valid counter term.

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arXiv2015

Double Soft Theorems in Gauge and String Theories

We investigate the tree-level S-matrix in gauge theories and open superstring theory with several soft particles. We show that scattering amplitudes with two or three soft gluons of non-identical helicities behave universally in the limit, with multi-soft factors which are not the product of individual soft gluon factors. The results are obtained from the BCFW recursion relations in four dimensions, and further extended to arbitrary dimensions using the CHY formula. We also find new soft theorems for double soft limits of scalars and fermions in N=4 and pure N=2 SYM. Finally, we show that the double-soft-scalar theorems can be extended to open superstring theory without receiving any alpha' corrections.

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arXiv2015

New fermionic soft theorems

Soft limits of massless S-matrix are known to reflect symmetries of the theory. In particular for theories with Goldstone bosons, the double-soft limit of scalars reveals the coset structure of the vacuum manifold. In this letter, we propose that such universal double-soft behavior is not only true for scalars, but also for spin-1/2 particles in four dimensions and fermions in three dimensions. We first consider Akulov-Volkov theory, and demonstrate the double soft-limit of goldstinos yields the supersymmetry algebra. More surprisingly we also find amplitudes in 3<N<=8 supergravity theories in four dimensions as well as N=16 supergravity in three dimensions behave universally in the double-soft-fermion limit, analogue to the scalar ones. The validity of the new soft theorems at loop level is also studied. The results for supergravity are beyond what is implied by SUSY Ward identities, and may impose non-trivial constraints on the possible counter terms for supergravity theories.

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arXiv2014

Thresholds of Large N Factorization in CFT4 : Exploring bulk spacetime in AdS5

Large $N$ factorization ensures that, for low-dimension gauge-invariant operators in the half-BPS sector of ${\cal N}=4$ SYM, products of holomorphic traces have vanishing correlators with single anti-holomorphic traces. This vanishing is necessary to consistently map trace operators in the CFT$_4$ to a Fock space of graviton oscillations in the dual AdS$_5$. We investigate the regimes at which the CFT correlators do not vanish but become of order one in the large $N$ limit, which we call a factorization threshold. Quite generally, we find the threshold to be when the product of the two holomorphic operator dimensions is of order $N\log N$. Our analysis considers extremal and non-extremal correlators and correlators in states dual to LLM backgrounds, and we observe intriguing similarities between the the energy-dependent running coupling of non-abelian gauge theories and our threshold equations. Finally, we discuss some interpretations of the threshold within the bulk AdS spacetime.

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